diff --git a/docs/paper/reductions.typ b/docs/paper/reductions.typ index 01372f7cb..7eb5af767 100644 --- a/docs/paper/reductions.typ +++ b/docs/paper/reductions.typ @@ -66,6 +66,7 @@ "MinimumVertexCover": [Minimum Vertex Cover], "MaxCut": [Max-Cut], "GraphPartitioning": [Graph Partitioning], + "BiconnectivityAugmentation": [Biconnectivity Augmentation], "HamiltonianPath": [Hamiltonian Path], "UndirectedTwoCommodityIntegralFlow": [Undirected Two-Commodity Integral Flow], "LengthBoundedDisjointPaths": [Length-Bounded Disjoint Paths], @@ -537,6 +538,52 @@ Graph Partitioning is a core NP-hard problem arising in VLSI design, parallel co caption: [Graph with $n = 6$ vertices partitioned into $A = {v_0, v_1, v_2}$ (blue) and $B = {v_3, v_4, v_5}$ (red). The 3 crossing edges $(v_1, v_3)$, $(v_2, v_3)$, $(v_2, v_4)$ are shown in bold red; internal edges are gray.], ) ] +#problem-def("BiconnectivityAugmentation")[ + Given an undirected graph $G = (V, E)$, a set $F$ of candidate edges on $V$ with $F inter E = emptyset$, weights $w: F -> RR$, and a budget $B in RR$, find $F' subset.eq F$ such that $sum_(e in F') w(e) <= B$ and the augmented graph $G' = (V, E union F')$ is biconnected, meaning $G'$ is connected and deleting any single vertex leaves it connected. +][ +Biconnectivity augmentation is a classical network-design problem: add backup links so the graph survives any single vertex failure. The weighted candidate-edge formulation modeled here captures communication, transportation, and infrastructure planning settings where only a prescribed set of new links is feasible and each carries a cost. In this library, the exact baseline is brute-force enumeration over the $m = |F|$ candidate edges, yielding $O^*(2^m)$ time and matching the exported complexity metadata for the model. + +*Example.* Consider the path graph $v_0 - v_1 - v_2 - v_3 - v_4 - v_5$ with candidate edges $(v_0, v_2)$, $(v_0, v_3)$, $(v_0, v_4)$, $(v_1, v_3)$, $(v_1, v_4)$, $(v_1, v_5)$, $(v_2, v_4)$, $(v_2, v_5)$, $(v_3, v_5)$ carrying weights $(1, 2, 3, 1, 2, 3, 1, 2, 1)$ and budget $B = 4$. Selecting $F' = {(v_0, v_2), (v_1, v_3), (v_2, v_4), (v_3, v_5)}$ uses total weight $1 + 1 + 1 + 1 = 4$ and eliminates every articulation point: after deleting any single vertex, the remaining graph is still connected. Reducing the budget to $B = 3$ makes the instance infeasible, because one of the path endpoints remains attached through a single articulation vertex. + +#figure( + canvas(length: 1cm, { + import draw: * + // 6 vertices in a horizontal line + let verts = range(6).map(k => (k * 1.5, 0)) + let path-edges = ((0,1),(1,2),(2,3),(3,4),(4,5)) + // Candidate edges: (u, v, weight, selected?) + let candidates = ( + (0, 2, 1, true), (0, 3, 2, false), (0, 4, 3, false), + (1, 3, 1, true), (1, 4, 2, false), (1, 5, 3, false), + (2, 4, 1, true), (2, 5, 2, false), (3, 5, 1, true), + ) + let blue = graph-colors.at(0) + let green = graph-colors.at(2) + let gray = luma(180) + // Draw path edges (existing graph) + for (u, v) in path-edges { + g-edge(verts.at(u), verts.at(v), stroke: 2pt + black) + } + // Draw candidate edges as arcs above the path + for (u, v, w, sel) in candidates { + let mid-x = (verts.at(u).at(0) + verts.at(v).at(0)) / 2 + let span = v - u + let height = span * 0.4 + let ctrl = (mid-x, height) + bezier(verts.at(u), verts.at(v), ctrl, + stroke: if sel { 2.5pt + green } else { (dash: "dashed", paint: gray, thickness: 0.8pt) }) + // Weight label + content((mid-x, height + 0.25), + text(7pt, fill: if sel { green.darken(30%) } else { gray })[#w]) + } + // Draw nodes + for (k, pos) in verts.enumerate() { + g-node(pos, name: "v" + str(k), label: [$v_#k$]) + } + }), + caption: [Biconnectivity Augmentation on a 6-vertex path with $B = 4$. Existing edges are black; green arcs show the selected augmentation $F'$ (total weight 4); dashed gray arcs are unselected candidates. The resulting graph $G' = (V, E union F')$ is biconnected.], +) +] #problem-def("BoundedComponentSpanningForest")[ Given an undirected graph $G = (V, E)$ with vertex weights $w: V -> ZZ_(gt.eq 0)$, a positive integer $K <= |V|$, and a positive bound $B$, determine whether there exists a partition of $V$ into $t$ non-empty sets $V_1, dots, V_t$ with $1 <= t <= K$ such that each induced subgraph $G[V_i]$ is connected and each part satisfies $sum_(v in V_i) w(v) <= B$. diff --git a/problemreductions-cli/src/cli.rs b/problemreductions-cli/src/cli.rs index e71a9e426..dd9df51d7 100644 --- a/problemreductions-cli/src/cli.rs +++ b/problemreductions-cli/src/cli.rs @@ -236,6 +236,7 @@ Flags by problem type: X3C (ExactCoverBy3Sets) --universe, --sets (3 elements each) SetBasis --universe, --sets, --k BicliqueCover --left, --right, --biedges, --k + BiconnectivityAugmentation --graph, --potential-edges, --budget [--num-vertices] BMF --matrix (0/1), --rank SteinerTree --graph, --edge-weights, --terminals CVP --basis, --target-vec [--bounds] @@ -271,6 +272,7 @@ Examples: pred create MIS/KingsSubgraph --positions \"0,0;1,0;1,1;0,1\" pred create MIS/UnitDiskGraph --positions \"0,0;1,0;0.5,0.8\" --radius 1.5 pred create MIS --random --num-vertices 10 --edge-prob 0.3 + pred create BiconnectivityAugmentation --graph 0-1,1-2,2-3 --potential-edges 0-2:3,0-3:4,1-3:2 --budget 5 pred create FVS --arcs \"0>1,1>2,2>0\" --weights 1,1,1 pred create UndirectedTwoCommodityIntegralFlow --graph 0-2,1-2,2-3 --capacities 1,1,2 --source-1 0 --sink-1 3 --source-2 1 --sink-2 3 --requirement-1 1 --requirement-2 1 pred create X3C --universe 9 --sets \"0,1,2;0,2,4;3,4,5;3,5,7;6,7,8;1,4,6;2,5,8\" @@ -438,6 +440,12 @@ pub struct CreateArgs { /// Directed arcs for directed graph problems (e.g., 0>1,1>2,2>0) #[arg(long)] pub arcs: Option, + /// Weighted potential augmentation edges (e.g., 0-2:3,1-3:5) + #[arg(long)] + pub potential_edges: Option, + /// Total budget for selected potential edges + #[arg(long)] + pub budget: Option, /// Deadlines for MinimumTardinessSequencing (comma-separated, e.g., "5,5,5,3,3") #[arg(long)] pub deadlines: Option, @@ -573,3 +581,46 @@ pub fn print_subcommand_help_hint(error_msg: &str) { } } } + +#[cfg(test)] +mod tests { + use super::*; + + #[test] + fn test_create_parses_biconnectivity_augmentation_flags() { + let cli = Cli::parse_from([ + "pred", + "create", + "BiconnectivityAugmentation", + "--graph", + "0-1,1-2", + "--potential-edges", + "0-2:3,1-3:5", + "--budget", + "7", + ]); + + let Commands::Create(args) = cli.command else { + panic!("expected create command"); + }; + + assert_eq!(args.problem, "BiconnectivityAugmentation"); + assert_eq!(args.graph.as_deref(), Some("0-1,1-2")); + assert_eq!(args.potential_edges.as_deref(), Some("0-2:3,1-3:5")); + assert_eq!(args.budget.as_deref(), Some("7")); + } + + #[test] + fn test_create_help_mentions_biconnectivity_augmentation_flags() { + let cmd = Cli::command(); + let create = cmd.find_subcommand("create").expect("create subcommand"); + let help = create + .get_after_help() + .expect("create after_help") + .to_string(); + + assert!(help.contains("BiconnectivityAugmentation")); + assert!(help.contains("--potential-edges")); + assert!(help.contains("--budget")); + } +} diff --git a/problemreductions-cli/src/commands/create.rs b/problemreductions-cli/src/commands/create.rs index 03220f4f6..ad872b5b5 100644 --- a/problemreductions-cli/src/commands/create.rs +++ b/problemreductions-cli/src/commands/create.rs @@ -16,6 +16,7 @@ use problemreductions::models::misc::{ BinPacking, FlowShopScheduling, LongestCommonSubsequence, MinimumTardinessSequencing, PaintShop, SequencingWithinIntervals, ShortestCommonSupersequence, SubsetSum, }; +use problemreductions::models::BiconnectivityAugmentation; use problemreductions::prelude::*; use problemreductions::registry::collect_schemas; use problemreductions::topology::{ @@ -77,19 +78,13 @@ fn all_data_flags_empty(args: &CreateArgs) -> bool { && args.pattern.is_none() && args.strings.is_none() && args.arcs.is_none() - && args.deadlines.is_none() + && args.potential_edges.is_none() + && args.budget.is_none() && args.precedence_pairs.is_none() && args.task_lengths.is_none() && args.deadline.is_none() && args.num_processors.is_none() && args.alphabet_size.is_none() - && args.capacities.is_none() - && args.source_1.is_none() - && args.sink_1.is_none() - && args.source_2.is_none() - && args.sink_2.is_none() - && args.requirement_1.is_none() - && args.requirement_2.is_none() } fn emit_problem_output(output: &ProblemJsonOutput, out: &OutputConfig) -> Result<()> { @@ -228,10 +223,13 @@ fn type_format_hint(type_name: &str, graph_type: Option<&str>) -> &'static str { }, "Vec" => "comma-separated integers: 1,1,2", "Vec" => "comma-separated: 1,2,3", + "Vec<(usize, usize, W)>" | "Vec<(usize,usize,W)>" => { + "comma-separated weighted edges: 0-2:3,1-3:5" + } "Vec" => "semicolon-separated clauses: \"1,2;-1,3\"", "Vec>" => "semicolon-separated rows: \"1,0.5;0.5,2\"", "Vec>" => "semicolon-separated groups: \"0,1;2,3\"", - "usize" => "integer", + "usize" | "W::Sum" => "integer", "u64" => "integer", "Vec" => "comma-separated integers: 0,0,5", "i64" => "integer", @@ -269,6 +267,9 @@ fn example_for(canonical: &str, graph_type: Option<&str>) -> &'static str { "MaxCut" | "MaximumMatching" | "TravelingSalesman" => { "--graph 0-1,1-2,2-3 --edge-weights 1,1,1" } + "BiconnectivityAugmentation" => { + "--graph 0-1,1-2,2-3 --potential-edges 0-2:3,0-3:4,1-3:2 --budget 5" + } "Satisfiability" => "--num-vars 3 --clauses \"1,2;-1,3\"", "KSatisfiability" => "--num-vars 3 --clauses \"1,2,3;-1,2,-3\" --k 3", "QUBO" => "--matrix \"1,0.5;0.5,2\"", @@ -315,6 +316,7 @@ fn help_flag_name(canonical: &str, field_name: &str) -> String { "right_size" => "right".to_string(), "edges" => "biedges".to_string(), "vertex_weights" => "weights".to_string(), + "potential_weights" => "potential-edges".to_string(), "edge_lengths" => "edge-weights".to_string(), "num_tasks" => "n".to_string(), "precedences" => "precedence-pairs".to_string(), @@ -561,6 +563,26 @@ pub fn create(args: &CreateArgs, out: &OutputConfig) -> Result<()> { ) } + // Biconnectivity augmentation + "BiconnectivityAugmentation" => { + let (graph, _) = parse_graph(args).map_err(|e| { + anyhow::anyhow!( + "{e}\n\nUsage: pred create BiconnectivityAugmentation --graph 0-1,1-2,2-3 --potential-edges 0-2:3,0-3:4,1-3:2 --budget 5" + ) + })?; + let potential_edges = parse_potential_edges(args)?; + validate_potential_edges(&graph, &potential_edges)?; + let budget = parse_budget(args)?; + ( + ser(BiconnectivityAugmentation::new( + graph, + potential_edges, + budget, + ))?, + resolved_variant.clone(), + ) + } + // Bounded Component Spanning Forest "BoundedComponentSpanningForest" => { let usage = "Usage: pred create BoundedComponentSpanningForest --graph 0-1,1-2,2-3,3-4,4-5,5-6,6-7,0-7,1-5,2-6 --weights 2,3,1,2,3,1,2,1 --k 3 --bound 6"; @@ -1673,7 +1695,8 @@ fn variant_map(pairs: &[(&str, &str)]) -> BTreeMap { util::variant_map(pairs) } -/// Parse `--graph` into a SimpleGraph, inferring num_vertices from max index. +/// Parse `--graph` into a SimpleGraph, optionally preserving isolated vertices +/// via `--num-vertices`. fn parse_graph(args: &CreateArgs) -> Result<(SimpleGraph, usize)> { let edges_str = args .graph @@ -1681,10 +1704,12 @@ fn parse_graph(args: &CreateArgs) -> Result<(SimpleGraph, usize)> { .ok_or_else(|| anyhow::anyhow!("This problem requires --graph (e.g., 0-1,1-2,2-3)"))?; if edges_str.trim().is_empty() { - bail!( - "Empty graph string. To create a graph with isolated vertices, use:\n \ - pred create --random --num-vertices N --edge-prob 0.0" - ); + let num_vertices = args.num_vertices.ok_or_else(|| { + anyhow::anyhow!( + "Empty graph string. To create a graph with isolated vertices, pass --num-vertices N as well." + ) + })?; + return Ok((SimpleGraph::empty(num_vertices), num_vertices)); } let edges: Vec<(usize, usize)> = edges_str @@ -1707,12 +1732,23 @@ fn parse_graph(args: &CreateArgs) -> Result<(SimpleGraph, usize)> { }) .collect::>>()?; - let num_vertices = edges + let inferred_num_vertices = edges .iter() .flat_map(|(u, v)| [*u, *v]) .max() .map(|m| m + 1) .unwrap_or(0); + let num_vertices = match args.num_vertices { + Some(explicit) if explicit < inferred_num_vertices => { + bail!( + "--num-vertices {} is too small for the provided graph; need at least {}", + explicit, + inferred_num_vertices + ); + } + Some(explicit) => explicit, + None => inferred_num_vertices, + }; Ok((SimpleGraph::new(num_vertices, edges), num_vertices)) } @@ -2093,6 +2129,73 @@ fn parse_matrix(args: &CreateArgs) -> Result>> { .collect() } +fn parse_potential_edges(args: &CreateArgs) -> Result> { + let edges_str = args.potential_edges.as_deref().ok_or_else(|| { + anyhow::anyhow!("BiconnectivityAugmentation requires --potential-edges (e.g., 0-2:3,1-3:5)") + })?; + + edges_str + .split(',') + .map(|entry| { + let entry = entry.trim(); + let (edge_part, weight_part) = entry.split_once(':').ok_or_else(|| { + anyhow::anyhow!("Invalid potential edge '{entry}': expected u-v:w") + })?; + let (u_str, v_str) = edge_part.split_once('-').ok_or_else(|| { + anyhow::anyhow!("Invalid potential edge '{entry}': expected u-v:w") + })?; + let u = u_str.trim().parse::()?; + let v = v_str.trim().parse::()?; + if u == v { + bail!("Self-loop detected in potential edge {u}-{v}"); + } + let weight = weight_part.trim().parse::()?; + Ok((u, v, weight)) + }) + .collect() +} + +fn validate_potential_edges( + graph: &SimpleGraph, + potential_edges: &[(usize, usize, i32)], +) -> Result<()> { + let num_vertices = graph.num_vertices(); + let mut seen_potential_edges = BTreeSet::new(); + for &(u, v, _) in potential_edges { + if u >= num_vertices || v >= num_vertices { + bail!( + "Potential edge {u}-{v} references a vertex outside the graph (num_vertices = {num_vertices})" + ); + } + let edge = if u <= v { (u, v) } else { (v, u) }; + if graph.has_edge(edge.0, edge.1) { + bail!( + "Potential edge {}-{} already exists in the graph", + edge.0, + edge.1 + ); + } + if !seen_potential_edges.insert(edge) { + bail!( + "Duplicate potential edge {}-{} is not allowed", + edge.0, + edge.1 + ); + } + } + Ok(()) +} + +fn parse_budget(args: &CreateArgs) -> Result { + let budget = args + .budget + .as_deref() + .ok_or_else(|| anyhow::anyhow!("BiconnectivityAugmentation requires --budget (e.g., 5)"))?; + budget + .parse::() + .map_err(|e| anyhow::anyhow!("Invalid budget '{budget}': {e}")) +} + /// Parse `--arcs` as directed arc pairs and build a `DirectedGraph`. /// /// Returns `(graph, num_arcs)`. Infers vertex count from arc endpoints @@ -2435,3 +2538,181 @@ mod tests { ); } } + +#[cfg(test)] +mod tests { + use super::*; + + fn empty_args() -> CreateArgs { + CreateArgs { + problem: "BiconnectivityAugmentation".to_string(), + graph: None, + weights: None, + edge_weights: None, + couplings: None, + fields: None, + clauses: None, + num_vars: None, + matrix: None, + k: None, + random: false, + num_vertices: None, + edge_prob: None, + seed: None, + target: None, + m: None, + n: None, + positions: None, + radius: None, + sizes: None, + capacity: None, + sequence: None, + sets: None, + universe: None, + biedges: None, + left: None, + right: None, + rank: None, + basis: None, + target_vec: None, + bounds: None, + strings: None, + arcs: None, + potential_edges: None, + budget: None, + } + } + + #[test] + fn test_all_data_flags_empty_treats_potential_edges_as_input() { + let mut args = empty_args(); + args.potential_edges = Some("0-2:3,1-3:5".to_string()); + assert!(!all_data_flags_empty(&args)); + } + + #[test] + fn test_all_data_flags_empty_treats_budget_as_input() { + let mut args = empty_args(); + args.budget = Some("7".to_string()); + assert!(!all_data_flags_empty(&args)); + } + + #[test] + fn test_parse_potential_edges() { + let mut args = empty_args(); + args.potential_edges = Some("0-2:3,1-3:5".to_string()); + + let potential_edges = parse_potential_edges(&args).unwrap(); + + assert_eq!(potential_edges, vec![(0, 2, 3), (1, 3, 5)]); + } + + #[test] + fn test_parse_potential_edges_rejects_missing_weight() { + let mut args = empty_args(); + args.potential_edges = Some("0-2,1-3:5".to_string()); + + let err = parse_potential_edges(&args).unwrap_err().to_string(); + + assert!(err.contains("u-v:w")); + } + + #[test] + fn test_parse_budget() { + let mut args = empty_args(); + args.budget = Some("7".to_string()); + + assert_eq!(parse_budget(&args).unwrap(), 7); + } + + #[test] + fn test_parse_graph_respects_explicit_num_vertices() { + let mut args = empty_args(); + args.graph = Some("0-1".to_string()); + args.num_vertices = Some(3); + + let (graph, num_vertices) = parse_graph(&args).unwrap(); + + assert_eq!(num_vertices, 3); + assert_eq!(graph.num_vertices(), 3); + assert_eq!(graph.edges(), vec![(0, 1)]); + } + + #[test] + fn test_validate_potential_edges_rejects_existing_graph_edge() { + let err = validate_potential_edges(&SimpleGraph::path(3), &[(0, 1, 5)]) + .unwrap_err() + .to_string(); + + assert!(err.contains("already exists in the graph")); + } + + #[test] + fn test_validate_potential_edges_rejects_duplicate_edges() { + let err = validate_potential_edges(&SimpleGraph::path(4), &[(0, 3, 1), (3, 0, 2)]) + .unwrap_err() + .to_string(); + + assert!(err.contains("Duplicate potential edge")); + } + + #[test] + fn test_create_biconnectivity_augmentation_json() { + let mut args = empty_args(); + args.graph = Some("0-1,1-2,2-3".to_string()); + args.potential_edges = Some("0-2:3,0-3:4,1-3:2".to_string()); + args.budget = Some("5".to_string()); + + let output_path = std::env::temp_dir().join("pred_test_create_biconnectivity.json"); + let out = OutputConfig { + output: Some(output_path.clone()), + quiet: true, + json: false, + auto_json: false, + }; + + create(&args, &out).unwrap(); + + let content = std::fs::read_to_string(&output_path).unwrap(); + let json: serde_json::Value = serde_json::from_str(&content).unwrap(); + assert_eq!(json["type"], "BiconnectivityAugmentation"); + assert_eq!(json["data"]["budget"], 5); + assert_eq!( + json["data"]["potential_weights"][0], + serde_json::json!([0, 2, 3]) + ); + + std::fs::remove_file(output_path).ok(); + } + + #[test] + fn test_create_biconnectivity_augmentation_json_with_isolated_vertices() { + let mut args = empty_args(); + args.graph = Some("0-1".to_string()); + args.num_vertices = Some(3); + args.potential_edges = Some("1-2:1".to_string()); + args.budget = Some("1".to_string()); + + let output_path = + std::env::temp_dir().join("pred_test_create_biconnectivity_isolated.json"); + let out = OutputConfig { + output: Some(output_path.clone()), + quiet: true, + json: false, + auto_json: false, + }; + + create(&args, &out).unwrap(); + + let content = std::fs::read_to_string(&output_path).unwrap(); + let json: serde_json::Value = serde_json::from_str(&content).unwrap(); + let problem: BiconnectivityAugmentation = + serde_json::from_value(json["data"].clone()).unwrap(); + + assert_eq!(problem.num_vertices(), 3); + assert_eq!(problem.potential_weights(), &[(1, 2, 1)]); + assert_eq!(problem.budget(), &1); + + std::fs::remove_file(output_path).ok(); + } +} diff --git a/problemreductions-cli/src/problem_name.rs b/problemreductions-cli/src/problem_name.rs index 12404ab7a..cea49403b 100644 --- a/problemreductions-cli/src/problem_name.rs +++ b/problemreductions-cli/src/problem_name.rs @@ -279,6 +279,10 @@ mod tests { assert_eq!(resolve_alias("3SAT"), "3SAT"); // pass-through assert_eq!(resolve_alias("QUBO"), "QUBO"); assert_eq!(resolve_alias("MaxCut"), "MaxCut"); + assert_eq!( + resolve_alias("biconnectivityaugmentation"), + "BiconnectivityAugmentation" + ); // Pass-through for full names assert_eq!( resolve_alias("MaximumIndependentSet"), diff --git a/src/example_db/fixtures/examples.json b/src/example_db/fixtures/examples.json index 6e52883b2..48c677752 100644 --- a/src/example_db/fixtures/examples.json +++ b/src/example_db/fixtures/examples.json @@ -2,6 +2,7 @@ "models": [ {"problem":"BMF","variant":{},"instance":{"k":2,"m":3,"matrix":[[true,true,false],[true,true,true],[false,true,true]],"n":3},"samples":[{"config":[1,0,1,1,0,1,1,1,0,0,1,1],"metric":{"Valid":0}}],"optimal":[{"config":[0,1,1,1,1,0,0,1,1,1,1,0],"metric":{"Valid":0}},{"config":[1,0,1,1,0,1,1,1,0,0,1,1],"metric":{"Valid":0}}]}, {"problem":"BicliqueCover","variant":{},"instance":{"graph":{"edges":[[0,0],[0,1],[1,1],[1,2]],"left_size":2,"right_size":3},"k":2},"samples":[{"config":[1,0,0,1,1,0,1,1,0,1],"metric":{"Valid":6}}],"optimal":[{"config":[0,1,0,1,0,1,0,1,0,1],"metric":{"Valid":5}},{"config":[1,0,1,0,1,0,1,0,1,0],"metric":{"Valid":5}}]}, + {"problem":"BiconnectivityAugmentation","variant":{"graph":"SimpleGraph","weight":"i32"},"instance":{"budget":4,"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[1,2,null],[2,3,null],[3,4,null],[4,5,null]],"node_holes":[],"nodes":[null,null,null,null,null,null]}},"potential_weights":[[0,2,1],[0,3,2],[0,4,3],[1,3,1],[1,4,2],[1,5,3],[2,4,1],[2,5,2],[3,5,1]]},"samples":[{"config":[1,0,0,1,0,0,1,0,1],"metric":true}],"optimal":[{"config":[0,0,1,0,0,0,0,0,1],"metric":true},{"config":[0,1,0,0,0,0,0,1,0],"metric":true},{"config":[0,1,0,0,0,0,1,0,1],"metric":true},{"config":[1,0,0,0,0,1,0,0,0],"metric":true},{"config":[1,0,0,0,1,0,0,0,1],"metric":true},{"config":[1,0,0,1,0,0,0,1,0],"metric":true},{"config":[1,0,0,1,0,0,1,0,1],"metric":true}]}, 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{"source":{"problem":"TravelingSalesman","variant":{"graph":"SimpleGraph","weight":"i32"},"instance":{"edge_weights":[10,15,20,35,25,30],"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,2,null],[0,3,null],[1,2,null],[1,3,null],[2,3,null]],"node_holes":[],"nodes":[null,null,null,null]}}}},"target":{"problem":"ILP","variant":{"variable":"bool"},"instance":{"constraints":[{"cmp":"Eq","rhs":1.0,"terms":[[0,1.0],[1,1.0],[2,1.0],[3,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[4,1.0],[5,1.0],[6,1.0],[7,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[8,1.0],[9,1.0],[10,1.0],[11,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[12,1.0],[13,1.0],[14,1.0],[15,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[0,1.0],[4,1.0],[8,1.0],[12,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[1,1.0],[5,1.0],[9,1.0],[13,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[2,1.0],[6,1.0],[10,1.0],[14,1.0]]},{"cmp":"Eq","rhs":1.0,"terms":[[3,1.0],[7,1.0],[11,1.0],[15,1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[16,1.0],[0,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[16,1.0],[5,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[16,1.0],[0,-1.0],[5,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[17,1.0],[4,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[17,1.0],[1,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[17,1.0],[4,-1.0],[1,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[18,1.0],[1,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[18,1.0],[6,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[18,1.0],[1,-1.0],[6,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[19,1.0],[5,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[19,1.0],[2,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[19,1.0],[5,-1.0],[2,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[20,1.0],[2,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[20,1.0],[7,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[20,1.0],[2,-1.0],[7,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[21,1.0],[6,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[21,1.0],[3,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[21,1.0],[6,-1.0],[3,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[22,1.0],[3,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[22,1.0],[4,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[22,1.0],[3,-1.0],[4,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[23,1.0],[7,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[23,1.0],[0,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[23,1.0],[7,-1.0],[0,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[24,1.0],[0,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[24,1.0],[9,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[24,1.0],[0,-1.0],[9,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[25,1.0],[8,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[25,1.0],[1,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[25,1.0],[8,-1.0],[1,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[26,1.0],[1,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[26,1.0],[10,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[26,1.0],[1,-1.0],[10,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[27,1.0],[9,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[27,1.0],[2,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[27,1.0],[9,-1.0],[2,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[28,1.0],[2,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[28,1.0],[11,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[28,1.0],[2,-1.0],[11,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[29,1.0],[10,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[29,1.0],[3,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[29,1.0],[10,-1.0],[3,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[30,1.0],[3,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[30,1.0],[8,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[30,1.0],[3,-1.0],[8,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[31,1.0],[11,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[31,1.0],[0,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[31,1.0],[11,-1.0],[0,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[32,1.0],[0,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[32,1.0],[13,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[32,1.0],[0,-1.0],[13,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[33,1.0],[12,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[33,1.0],[1,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[33,1.0],[12,-1.0],[1,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[34,1.0],[1,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[34,1.0],[14,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[34,1.0],[1,-1.0],[14,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[35,1.0],[13,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[35,1.0],[2,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[35,1.0],[13,-1.0],[2,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[36,1.0],[2,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[36,1.0],[15,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[36,1.0],[2,-1.0],[15,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[37,1.0],[14,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[37,1.0],[3,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[37,1.0],[14,-1.0],[3,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[38,1.0],[3,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[38,1.0],[12,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[38,1.0],[3,-1.0],[12,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[39,1.0],[15,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[39,1.0],[0,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[39,1.0],[15,-1.0],[0,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[40,1.0],[4,-1.0]]},{"cmp":"Le","rhs":0.0,"terms":[[40,1.0],[9,-1.0]]},{"cmp":"Ge","rhs":-1.0,"terms":[[40,1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+ {"source":{"problem":"TravelingSalesman","variant":{"graph":"SimpleGraph","weight":"i32"},"instance":{"edge_weights":[1,2,3],"graph":{"inner":{"edge_property":"undirected","edges":[[0,1,null],[0,2,null],[1,2,null]],"node_holes":[],"nodes":[null,null,null]}}}},"target":{"problem":"QUBO","variant":{"weight":"f64"},"instance":{"matrix":[[-14.0,14.0,14.0,14.0,1.0,1.0,14.0,2.0,2.0],[0.0,-14.0,14.0,1.0,14.0,1.0,2.0,14.0,2.0],[0.0,0.0,-14.0,1.0,1.0,14.0,2.0,2.0,14.0],[0.0,0.0,0.0,-14.0,14.0,14.0,14.0,3.0,3.0],[0.0,0.0,0.0,0.0,-14.0,14.0,3.0,14.0,3.0],[0.0,0.0,0.0,0.0,0.0,-14.0,3.0,3.0,14.0],[0.0,0.0,0.0,0.0,0.0,0.0,-14.0,14.0,14.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,-14.0,14.0],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,-14.0]],"num_vars":9}},"solutions":[{"source_config":[1,1,1],"target_config":[0,0,1,0,1,0,1,0,0]}]} ] } diff --git a/src/lib.rs b/src/lib.rs index 42bc6c927..3b8dc3bae 100644 --- a/src/lib.rs +++ b/src/lib.rs @@ -45,9 +45,10 @@ pub mod prelude { pub use crate::models::algebraic::{BMF, QUBO}; pub use crate::models::formula::{CNFClause, CircuitSAT, KSatisfiability, Satisfiability}; pub use crate::models::graph::{ - BicliqueCover, BoundedComponentSpanningForest, DirectedTwoCommodityIntegralFlow, - GraphPartitioning, HamiltonianPath, IsomorphicSpanningTree, LengthBoundedDisjointPaths, - SpinGlass, SteinerTree, SubgraphIsomorphism, + BicliqueCover, BiconnectivityAugmentation, BoundedComponentSpanningForest, + DirectedTwoCommodityIntegralFlow, GraphPartitioning, HamiltonianPath, + IsomorphicSpanningTree, LengthBoundedDisjointPaths, SpinGlass, SteinerTree, + SubgraphIsomorphism, }; pub use crate::models::graph::{ KColoring, MaxCut, MaximalIS, MaximumClique, MaximumIndependentSet, MaximumMatching, diff --git a/src/models/graph/biconnectivity_augmentation.rs b/src/models/graph/biconnectivity_augmentation.rs new file mode 100644 index 000000000..e6ebedc02 --- /dev/null +++ b/src/models/graph/biconnectivity_augmentation.rs @@ -0,0 +1,315 @@ +//! Biconnectivity augmentation problem implementation. +//! +//! Given a graph, weighted potential edges, and a budget, determine whether +//! adding some subset of the potential edges can make the graph biconnected +//! without exceeding the budget. + +use crate::registry::{FieldInfo, ProblemSchemaEntry, VariantDimension}; +use crate::topology::{Graph, SimpleGraph}; +use crate::traits::{Problem, SatisfactionProblem}; +use crate::types::WeightElement; +use num_traits::Zero; +use serde::{Deserialize, Serialize}; +use std::collections::BTreeSet; + +inventory::submit! { + ProblemSchemaEntry { + name: "BiconnectivityAugmentation", + display_name: "Biconnectivity Augmentation", + aliases: &[], + dimensions: &[ + VariantDimension::new("graph", "SimpleGraph", &["SimpleGraph"]), + VariantDimension::new("weight", "i32", &["i32"]), + ], + module_path: module_path!(), + description: "Add weighted potential edges to make a graph biconnected within budget", + fields: &[ + FieldInfo { name: "graph", type_name: "G", description: "The underlying graph G=(V,E)" }, + FieldInfo { name: "potential_weights", type_name: "Vec<(usize, usize, W)>", description: "Potential edges with augmentation weights" }, + FieldInfo { name: "budget", type_name: "W::Sum", description: "Maximum total augmentation weight B" }, + ], + } +} + +/// The Biconnectivity Augmentation problem. +/// +/// Given a graph `G = (V, E)`, weighted potential edges, and a budget `B`, +/// determine whether there exists a subset of potential edges `E'` such that: +/// - `sum_{e in E'} w(e) <= B` +/// - `(V, E union E')` is biconnected +#[derive(Debug, Clone, Serialize, Deserialize)] +#[serde(bound( + serialize = "G: serde::Serialize, W: serde::Serialize, W::Sum: serde::Serialize", + deserialize = "G: serde::Deserialize<'de>, W: serde::Deserialize<'de>, W::Sum: serde::Deserialize<'de>" +))] +pub struct BiconnectivityAugmentation +where + W: WeightElement, +{ + /// The underlying graph. + graph: G, + /// Potential augmentation edges with their weights. + potential_weights: Vec<(usize, usize, W)>, + /// Maximum total weight of selected potential edges. + budget: W::Sum, +} + +impl BiconnectivityAugmentation { + /// Create a new biconnectivity augmentation instance. + /// + /// # Panics + /// Panics if any potential edge references a vertex index outside the graph, + /// is a self-loop, duplicates another candidate edge, or already exists in + /// the input graph. + pub fn new(graph: G, potential_weights: Vec<(usize, usize, W)>, budget: W::Sum) -> Self { + let num_vertices = graph.num_vertices(); + let mut seen_potential_edges = BTreeSet::new(); + for &(u, v, _) in &potential_weights { + assert!( + u < num_vertices && v < num_vertices, + "potential edge ({}, {}) references vertex >= num_vertices ({})", + u, + v, + num_vertices + ); + assert!(u != v, "potential edge ({}, {}) is a self-loop", u, v); + let edge = normalize_edge(u, v); + assert!( + !graph.has_edge(edge.0, edge.1), + "potential edge ({}, {}) already exists in the graph", + edge.0, + edge.1 + ); + assert!( + seen_potential_edges.insert(edge), + "potential edge ({}, {}) is duplicated", + edge.0, + edge.1 + ); + } + + Self { + graph, + potential_weights, + budget, + } + } + + /// Get a reference to the underlying graph. + pub fn graph(&self) -> &G { + &self.graph + } + + /// Get the weighted potential edges. + pub fn potential_weights(&self) -> &[(usize, usize, W)] { + &self.potential_weights + } + + /// Get the budget. + pub fn budget(&self) -> &W::Sum { + &self.budget + } + + /// Get the number of vertices in the underlying graph. + pub fn num_vertices(&self) -> usize { + self.graph.num_vertices() + } + + /// Get the number of edges in the underlying graph. + pub fn num_edges(&self) -> usize { + self.graph.num_edges() + } + + /// Get the number of potential augmentation edges. + pub fn num_potential_edges(&self) -> usize { + self.potential_weights.len() + } + + /// Check if the problem uses a non-unit weight type. + pub fn is_weighted(&self) -> bool { + !W::IS_UNIT + } + + fn augmented_graph(&self, config: &[usize]) -> Option { + if config.len() != self.num_potential_edges() || config.iter().any(|&value| value >= 2) { + return None; + } + + let mut total = W::Sum::zero(); + let mut edges = BTreeSet::new(); + + for (u, v) in self.graph.edges() { + edges.insert(normalize_edge(u, v)); + } + + for (selected, &(u, v, ref weight)) in config.iter().zip(&self.potential_weights) { + if *selected == 1 { + total += weight.to_sum(); + if total > self.budget.clone() { + return None; + } + edges.insert(normalize_edge(u, v)); + } + } + + Some(SimpleGraph::new( + self.num_vertices(), + edges.into_iter().collect(), + )) + } +} + +impl Problem for BiconnectivityAugmentation +where + G: Graph + crate::variant::VariantParam, + W: WeightElement + crate::variant::VariantParam, +{ + const NAME: &'static str = "BiconnectivityAugmentation"; + type Metric = bool; + + fn variant() -> Vec<(&'static str, &'static str)> { + crate::variant_params![G, W] + } + + fn dims(&self) -> Vec { + vec![2; self.num_potential_edges()] + } + + fn evaluate(&self, config: &[usize]) -> bool { + self.augmented_graph(config) + .is_some_and(|graph| is_biconnected(&graph)) + } +} + +impl SatisfactionProblem for BiconnectivityAugmentation +where + G: Graph + crate::variant::VariantParam, + W: WeightElement + crate::variant::VariantParam, +{ +} + +fn normalize_edge(u: usize, v: usize) -> (usize, usize) { + if u <= v { + (u, v) + } else { + (v, u) + } +} + +struct DfsState { + visited: Vec, + discovery_time: Vec, + low: Vec, + parent: Vec>, + time: usize, + has_articulation_point: bool, +} + +fn dfs_articulation_points(graph: &G, vertex: usize, state: &mut DfsState) { + if state.has_articulation_point { + return; + } + + state.visited[vertex] = true; + state.time += 1; + state.discovery_time[vertex] = state.time; + state.low[vertex] = state.time; + + let mut child_count = 0; + for neighbor in graph.neighbors(vertex) { + if !state.visited[neighbor] { + child_count += 1; + state.parent[neighbor] = Some(vertex); + dfs_articulation_points(graph, neighbor, state); + state.low[vertex] = state.low[vertex].min(state.low[neighbor]); + + if state.parent[vertex].is_none() && child_count > 1 { + state.has_articulation_point = true; + return; + } + + if state.parent[vertex].is_some() && state.low[neighbor] >= state.discovery_time[vertex] + { + state.has_articulation_point = true; + return; + } + } else if state.parent[vertex] != Some(neighbor) { + state.low[vertex] = state.low[vertex].min(state.discovery_time[neighbor]); + } + } +} + +fn is_biconnected(graph: &G) -> bool { + let num_vertices = graph.num_vertices(); + if num_vertices <= 1 { + return true; + } + + let mut state = DfsState { + visited: vec![false; num_vertices], + discovery_time: vec![0; num_vertices], + low: vec![0; num_vertices], + parent: vec![None; num_vertices], + time: 0, + has_articulation_point: false, + }; + + dfs_articulation_points(graph, 0, &mut state); + + !state.has_articulation_point && state.visited.into_iter().all(|seen| seen) +} + +crate::declare_variants! { + default sat BiconnectivityAugmentation => "2^num_potential_edges", +} + +#[cfg(feature = "example-db")] +pub(crate) fn canonical_model_example_specs() -> Vec { + vec![crate::example_db::specs::ModelExampleSpec { + id: "biconnectivity_augmentation", + build: || { + let problem = BiconnectivityAugmentation::new( + SimpleGraph::path(6), + vec![ + (0, 2, 1), + (0, 3, 2), + (0, 4, 3), + (1, 3, 1), + (1, 4, 2), + (1, 5, 3), + (2, 4, 1), + (2, 5, 2), + (3, 5, 1), + ], + 4, + ); + crate::example_db::specs::satisfaction_example( + problem, + vec![vec![1, 0, 0, 1, 0, 0, 1, 0, 1]], + ) + }, + }] +} + +#[cfg(test)] +pub(crate) fn example_instance() -> BiconnectivityAugmentation { + BiconnectivityAugmentation::new( + SimpleGraph::path(6), + vec![ + (0, 2, 1), + (0, 3, 2), + (0, 4, 3), + (1, 3, 1), + (1, 4, 2), + (1, 5, 3), + (2, 4, 1), + (2, 5, 2), + (3, 5, 1), + ], + 4, + ) +} + +#[cfg(test)] +#[path = "../../unit_tests/models/graph/biconnectivity_augmentation.rs"] +mod tests; diff --git a/src/models/graph/mod.rs b/src/models/graph/mod.rs index 2152db586..2e68a846d 100644 --- a/src/models/graph/mod.rs +++ b/src/models/graph/mod.rs @@ -17,6 +17,7 @@ //! - [`SpinGlass`]: Ising model Hamiltonian //! - [`HamiltonianPath`]: Hamiltonian path (simple path visiting every vertex) //! - [`BicliqueCover`]: Biclique cover on bipartite graphs +//! - [`BiconnectivityAugmentation`]: Biconnectivity augmentation with weighted potential edges //! - [`BoundedComponentSpanningForest`]: Partition vertices into bounded-weight connected components //! - [`OptimalLinearArrangement`]: Optimal linear arrangement (total edge length at most K) //! - [`MinimumFeedbackArcSet`]: Minimum feedback arc set on directed graphs @@ -30,6 +31,7 @@ //! - [`UndirectedTwoCommodityIntegralFlow`]: Two-commodity integral flow on undirected graphs pub(crate) mod biclique_cover; +pub(crate) mod biconnectivity_augmentation; pub(crate) mod bounded_component_spanning_forest; pub(crate) mod directed_two_commodity_integral_flow; pub(crate) mod graph_partitioning; @@ -58,6 +60,7 @@ pub(crate) mod traveling_salesman; pub(crate) mod undirected_two_commodity_integral_flow; pub use biclique_cover::BicliqueCover; +pub use biconnectivity_augmentation::BiconnectivityAugmentation; pub use bounded_component_spanning_forest::BoundedComponentSpanningForest; pub use directed_two_commodity_integral_flow::DirectedTwoCommodityIntegralFlow; pub use graph_partitioning::GraphPartitioning; @@ -105,6 +108,7 @@ pub(crate) fn canonical_model_example_specs() -> Vec as Problem>::NAME, + "BiconnectivityAugmentation" + ); + assert_eq!( + as Problem>::variant(), + vec![("graph", "SimpleGraph"), ("weight", "i32")] + ); + + let unit_problem = + BiconnectivityAugmentation::<_, One>::new(SimpleGraph::path(3), vec![(0, 2, One)], 1); + assert!(!unit_problem.is_weighted()); +} + +#[test] +#[should_panic(expected = "references vertex >= num_vertices")] +fn test_biconnectivity_augmentation_creation_rejects_invalid_potential_edge() { + BiconnectivityAugmentation::new(SimpleGraph::path(4), vec![(0, 4, 1)], 1); +} + +#[test] +#[should_panic(expected = "already exists in the graph")] +fn test_biconnectivity_augmentation_creation_rejects_existing_edge_candidate() { + BiconnectivityAugmentation::new(SimpleGraph::path(4), vec![(1, 2, 1)], 1); +} + +#[test] +#[should_panic(expected = "is duplicated")] +fn test_biconnectivity_augmentation_creation_rejects_duplicate_candidate() { + BiconnectivityAugmentation::new(SimpleGraph::path(4), vec![(0, 3, 1), (3, 0, 2)], 2); +} + +#[test] +fn test_biconnectivity_augmentation_evaluation() { + let problem = BiconnectivityAugmentation::new( + SimpleGraph::path(4), + vec![(0, 2, 5), (1, 3, 1), (0, 3, 2)], + 2, + ); + + assert!(!problem.evaluate(&[0, 0, 0])); + assert!(!problem.evaluate(&[0, 1, 0])); + assert!(problem.evaluate(&[0, 0, 1])); + assert!(!problem.evaluate(&[0, 1, 1])); + assert!(!problem.evaluate(&[2, 0, 0])); + assert!(!problem.evaluate(&[1, 0])); +} + +#[test] +fn test_biconnectivity_augmentation_serialization() { + let problem = + BiconnectivityAugmentation::new(SimpleGraph::path(4), vec![(0, 3, 2), (1, 3, 1)], 2); + + let json = serde_json::to_value(&problem).unwrap(); + let restored: BiconnectivityAugmentation = + serde_json::from_value(json).unwrap(); + + assert_eq!(restored.graph(), problem.graph()); + assert_eq!(restored.potential_weights(), problem.potential_weights()); + assert_eq!(restored.budget(), problem.budget()); +} + +#[test] +fn test_biconnectivity_augmentation_solver() { + let problem = BiconnectivityAugmentation::new( + SimpleGraph::path(4), + vec![(0, 2, 5), (1, 3, 1), (0, 3, 2)], + 2, + ); + let solver = BruteForce::new(); + + let solution = solver + .find_satisfying(&problem) + .expect("expected a satisfying augmentation"); + assert_eq!(solution, vec![0, 0, 1]); + + let all_solutions = solver.find_all_satisfying(&problem); + assert_eq!(all_solutions, vec![vec![0, 0, 1]]); +} + +#[test] +fn test_biconnectivity_augmentation_no_solution() { + let problem = BiconnectivityAugmentation::new(SimpleGraph::path(4), vec![(0, 2, 1)], 1); + let solver = BruteForce::new(); + + assert!(solver.find_satisfying(&problem).is_none()); + assert!(solver.find_all_satisfying(&problem).is_empty()); +} + +#[test] +fn test_biconnectivity_augmentation_paper_example() { + let problem = example_instance(); + let solver = BruteForce::new(); + let satisfying_config = vec![1, 0, 0, 1, 0, 0, 1, 0, 1]; + let satisfying_solutions = solver.find_all_satisfying(&problem); + + assert!(problem.evaluate(&satisfying_config)); + assert!(satisfying_solutions.contains(&satisfying_config)); + + let over_budget_problem = BiconnectivityAugmentation::new( + SimpleGraph::path(6), + vec![ + (0, 2, 1), + (0, 3, 2), + (0, 4, 3), + (1, 3, 1), + (1, 4, 2), + (1, 5, 3), + (2, 4, 1), + (2, 5, 2), + (3, 5, 1), + ], + 3, + ); + assert!(!over_budget_problem.evaluate(&satisfying_config)); + assert!(solver.find_satisfying(&over_budget_problem).is_none()); +} + +#[test] +fn test_is_biconnected() { + assert!(is_biconnected(&SimpleGraph::cycle(4))); + assert!(is_biconnected(&SimpleGraph::complete(3))); + assert!(!is_biconnected(&SimpleGraph::path(4))); + assert!(!is_biconnected(&SimpleGraph::new(4, vec![(0, 1), (2, 3)]))); +} diff --git a/src/unit_tests/trait_consistency.rs b/src/unit_tests/trait_consistency.rs new file mode 100644 index 000000000..af7aff505 --- /dev/null +++ b/src/unit_tests/trait_consistency.rs @@ -0,0 +1,157 @@ +use crate::models::algebraic::*; +use crate::models::formula::*; +use crate::models::graph::*; +use crate::models::misc::*; +use crate::models::set::*; +use crate::topology::{BipartiteGraph, SimpleGraph}; +use crate::traits::Problem; +use crate::variant::K3; + +fn check_problem_trait(problem: &P, name: &str) { + let dims = problem.dims(); + assert!( + !dims.is_empty() || name.contains("empty"), + "{} should have dimensions", + name + ); + for d in &dims { + assert!( + *d >= 2, + "{} should have at least 2 choices per dimension", + name + ); + } +} + +#[test] +fn test_all_problems_implement_trait_correctly() { + check_problem_trait( + &MaximumIndependentSet::new(SimpleGraph::new(3, vec![(0, 1)]), vec![1i32; 3]), + "MaximumIndependentSet", + ); + check_problem_trait( + &MinimumVertexCover::new(SimpleGraph::new(3, vec![(0, 1)]), vec![1i32; 3]), + "MinimumVertexCover", + ); + check_problem_trait( + &MaxCut::new(SimpleGraph::new(3, vec![(0, 1)]), vec![1i32]), + "MaxCut", + ); + check_problem_trait( + &KColoring::::new(SimpleGraph::new(3, vec![(0, 1)])), + "KColoring", + ); + check_problem_trait( + &MinimumDominatingSet::new(SimpleGraph::new(3, vec![(0, 1)]), vec![1i32; 3]), + "MinimumDominatingSet", + ); + check_problem_trait( + &MaximalIS::new(SimpleGraph::new(3, vec![(0, 1)]), vec![1i32; 3]), + "MaximalIS", + ); + check_problem_trait( + &MaximumMatching::new(SimpleGraph::new(3, vec![(0, 1)]), vec![1i32]), + "MaximumMatching", + ); + check_problem_trait( + &BiconnectivityAugmentation::new(SimpleGraph::path(4), vec![(0, 3, 2)], 2), + "BiconnectivityAugmentation", + ); + check_problem_trait( + &Satisfiability::new(3, vec![CNFClause::new(vec![1])]), + "SAT", + ); + check_problem_trait( + &SpinGlass::new(3, vec![((0, 1), 1.0)], vec![0.0; 3]), + "SpinGlass", + ); + check_problem_trait(&QUBO::from_matrix(vec![vec![1.0; 3]; 3]), "QUBO"); + check_problem_trait( + &MinimumSetCovering::::new(3, vec![vec![0, 1]]), + "MinimumSetCovering", + ); + check_problem_trait( + &MaximumSetPacking::::new(vec![vec![0, 1]]), + "MaximumSetPacking", + ); + check_problem_trait(&PaintShop::new(vec!["a", "a"]), "PaintShop"); + check_problem_trait(&BMF::new(vec![vec![true]], 1), "BMF"); + check_problem_trait( + &BicliqueCover::new(BipartiteGraph::new(2, 2, vec![(0, 0)]), 1), + "BicliqueCover", + ); + check_problem_trait(&Factoring::new(6, 2, 2), "Factoring"); + + let circuit = Circuit::new(vec![Assignment::new( + vec!["x".to_string()], + BooleanExpr::constant(true), + )]); + check_problem_trait(&CircuitSAT::new(circuit), "CircuitSAT"); +} + +#[test] +fn test_direction() { + use crate::traits::OptimizationProblem; + use crate::types::Direction; + + // Minimization problems + assert_eq!( + MinimumVertexCover::new(SimpleGraph::new(2, vec![(0, 1)]), vec![1i32; 2]).direction(), + Direction::Minimize + ); + assert_eq!( + MinimumDominatingSet::new(SimpleGraph::new(2, vec![(0, 1)]), vec![1i32; 2]).direction(), + Direction::Minimize + ); + assert_eq!( + MinimumSetCovering::::new(2, vec![vec![0, 1]]).direction(), + Direction::Minimize + ); + assert_eq!( + PaintShop::new(vec!["a", "a"]).direction(), + Direction::Minimize + ); + assert_eq!( + QUBO::from_matrix(vec![vec![1.0]]).direction(), + Direction::Minimize + ); + assert_eq!( + SpinGlass::new(1, vec![], vec![0.0]).direction(), + Direction::Minimize + ); + assert_eq!( + BMF::new(vec![vec![true]], 1).direction(), + Direction::Minimize + ); + assert_eq!(Factoring::new(6, 2, 2).direction(), Direction::Minimize); + assert_eq!( + BicliqueCover::new(BipartiteGraph::new(2, 2, vec![(0, 0)]), 1).direction(), + Direction::Minimize + ); + + // Maximization problems + assert_eq!( + MaximumIndependentSet::new(SimpleGraph::new(2, vec![(0, 1)]), vec![1i32; 2]).direction(), + Direction::Maximize + ); + assert_eq!( + MaximalIS::new(SimpleGraph::new(2, vec![(0, 1)]), vec![1i32; 2]).direction(), + Direction::Maximize + ); + assert_eq!( + MaxCut::new(SimpleGraph::new(2, vec![(0, 1)]), vec![1i32]).direction(), + Direction::Maximize + ); + assert_eq!( + MaximumMatching::new(SimpleGraph::new(2, vec![(0, 1)]), vec![1i32]).direction(), + Direction::Maximize + ); + assert_eq!( + MaximumSetPacking::::new(vec![vec![0]]).direction(), + Direction::Maximize + ); + assert_eq!( + MaximumClique::new(SimpleGraph::new(2, vec![(0, 1)]), vec![1i32; 2]).direction(), + Direction::Maximize + ); +} diff --git a/tests/suites/integration.rs b/tests/suites/integration.rs index 49e43f6fa..d7a256a4a 100644 --- a/tests/suites/integration.rs +++ b/tests/suites/integration.rs @@ -109,6 +109,19 @@ mod all_problems_solvable { } } + #[test] + fn test_biconnectivity_augmentation_solvable() { + let problem = BiconnectivityAugmentation::new( + SimpleGraph::path(4), + vec![(0, 2, 5), (1, 3, 1), (0, 3, 2)], + 2, + ); + let solver = BruteForce::new(); + let satisfying = solver.find_all_satisfying(&problem); + assert_eq!(satisfying, vec![vec![0, 0, 1]]); + assert!(satisfying.iter().all(|config| problem.evaluate(config))); + } + #[test] fn test_satisfiability_solvable() { let problem = Satisfiability::new(