Fix #228: Add MinimumCutIntoBoundedSets model#637
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## main #637 +/- ##
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+ Coverage 96.77% 96.79% +0.01%
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Lines 29919 30136 +217
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Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
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Pull request overview
Adds the MinimumCutIntoBoundedSets satisfaction/decision model (Garey & Johnson ND17) to the library, with accompanying unit tests, CLI support for create/load/serialize, and paper documentation updates.
Changes:
- Introduces
MinimumCutIntoBoundedSets<G, W>model with schema registration, variants, and evaluation logic. - Adds comprehensive unit tests covering evaluation, serialization, and BruteForce solver behavior.
- Extends CLI to resolve the new problem name/alias, create instances (including random generation), and load/serialize JSON for the new type; updates paper docs to include the new problem.
Reviewed changes
Copilot reviewed 10 out of 10 changed files in this pull request and generated 8 comments.
Show a summary per file
| File | Description |
|---|---|
| src/models/graph/minimum_cut_into_bounded_sets.rs | New model implementation + schema entry + variant declaration + tests module hookup |
| src/unit_tests/models/graph/minimum_cut_into_bounded_sets.rs | New unit tests for the model (evaluation/serialization/solver/variant) |
| src/models/graph/mod.rs | Registers the new graph model module and re-export |
| src/models/mod.rs | Re-exports the new model at the models root |
| src/lib.rs | Adds the model to the public prelude |
| problemreductions-cli/src/problem_name.rs | Adds alias resolution for minimumcutintoboundedsets |
| problemreductions-cli/src/dispatch.rs | Adds JSON load + Any serialization support for the new model |
| problemreductions-cli/src/commands/create.rs | Adds pred create support (explicit and random) for the new model |
| problemreductions-cli/src/cli.rs | Adds new CLI flags for source/sink/size_bound/cut_bound and updates help text |
| docs/paper/reductions.typ | Adds paper definition section + label mapping for the new problem |
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| let source = args | ||
| .source | ||
| .context("--source is required for MinimumCutIntoBoundedSets")?; | ||
| let sink = args | ||
| .sink | ||
| .context("--sink is required for MinimumCutIntoBoundedSets")?; | ||
| let size_bound = args | ||
| .size_bound | ||
| .context("--size-bound is required for MinimumCutIntoBoundedSets")?; | ||
| let cut_bound = args | ||
| .cut_bound | ||
| .context("--cut-bound is required for MinimumCutIntoBoundedSets")?; | ||
| ( | ||
| ser(MinimumCutIntoBoundedSets::new( | ||
| graph, | ||
| edge_weights, | ||
| source, | ||
| sink, | ||
| size_bound, | ||
| cut_bound, | ||
| ))?, |
| "MinimumCutIntoBoundedSets" => { | ||
| let (graph, _) = parse_graph(args).map_err(|e| { | ||
| anyhow::anyhow!( | ||
| "{e}\n\nUsage: pred create MinimumCutIntoBoundedSets --graph 0-1,1-2,2-3 --edge-weights 1,1,1 --source 0 --sink 2 --size-bound 2 --cut-bound 1" |
| Given an undirected graph $G = (V, E)$ with edge weights $w: E -> ZZ^+$, designated vertices $s, t in V$, a positive integer $B <= |V|$, and a positive integer $K$, determine whether there exists a partition of $V$ into disjoint sets $V_1$ and $V_2$ such that $s in V_1$, $t in V_2$, $|V_1| <= B$, $|V_2| <= B$, and | ||
| $ sum_({u,v} in E: u in V_1, v in V_2) w({u,v}) <= K. $ | ||
| ][ | ||
| Minimum Cut Into Bounded Sets (Garey & Johnson ND17) combines the classical minimum $s$-$t$ cut problem with a balance constraint on partition sizes. Without the balance constraint ($B = |V|$), the problem reduces to standard minimum $s$-$t$ cut, solvable in polynomial time via network flow. Adding the requirement $|V_1| <= B$ and $|V_2| <= B$ makes the problem NP-complete; it remains NP-complete even for $B = |V| slash 2$ and unit edge weights (the minimum bisection problem) @garey1976. Applications include VLSI layout, load balancing, and graph bisection. |
| ][ | ||
| Minimum Cut Into Bounded Sets (Garey & Johnson ND17) combines the classical minimum $s$-$t$ cut problem with a balance constraint on partition sizes. Without the balance constraint ($B = |V|$), the problem reduces to standard minimum $s$-$t$ cut, solvable in polynomial time via network flow. Adding the requirement $|V_1| <= B$ and $|V_2| <= B$ makes the problem NP-complete; it remains NP-complete even for $B = |V| slash 2$ and unit edge weights (the minimum bisection problem) @garey1976. Applications include VLSI layout, load balancing, and graph bisection. | ||
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| The best known exact algorithm is brute-force enumeration of all $2^n$ vertex partitions in $O(2^n)$ time. For the special case of minimum bisection, Cygan et al. @cygan2014 showed fixed-parameter tractability with respect to the cut size. No polynomial-time finite approximation factor exists for balanced graph partition unless $P = N P$ (Andreev and Racke, 2006). Arora, Rao, and Vazirani @arora2009 gave an $O(sqrt(log n))$-approximation for balanced separator. |
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| fn evaluate(&self, config: &[usize]) -> bool { | ||
| let n = self.graph.num_vertices(); | ||
| if config.len() != n { | ||
| return false; | ||
| } | ||
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| // Check source is in V1 (config=0) and sink is in V2 (config=1) | ||
| if config[self.source] != 0 { | ||
| return false; | ||
| } | ||
| if config[self.sink] != 1 { | ||
| return false; | ||
| } |
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| // Check size bounds | ||
| let count_v1 = config.iter().filter(|&&x| x == 0).count(); | ||
| let count_v2 = config.iter().filter(|&&x| x == 1).count(); | ||
| if count_v1 > self.size_bound || count_v2 > self.size_bound { | ||
| return false; | ||
| } |
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| inventory::submit! { | ||
| ProblemSchemaEntry { | ||
| name: "MinimumCutIntoBoundedSets", | ||
| module_path: module_path!(), | ||
| description: "Partition vertices into two bounded-size sets with cut weight at most K", | ||
| fields: &[ | ||
| FieldInfo { name: "graph", type_name: "G", description: "The undirected graph G = (V, E)" }, | ||
| FieldInfo { name: "edge_weights", type_name: "Vec<W>", description: "Edge weights w: E -> Z+" }, | ||
| FieldInfo { name: "source", type_name: "usize", description: "Source vertex s (must be in V1)" }, | ||
| FieldInfo { name: "sink", type_name: "usize", description: "Sink vertex t (must be in V2)" }, | ||
| FieldInfo { name: "size_bound", type_name: "usize", description: "Maximum size B for each partition set" }, | ||
| FieldInfo { name: "cut_bound", type_name: "W::Sum", description: "Maximum total cut weight K" }, | ||
| ], | ||
| } | ||
| } |
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| let graph = util::create_random_graph(num_vertices, edge_prob, args.seed); | ||
| let num_edges = graph.num_edges(); | ||
| let edge_weights = vec![1i32; num_edges]; | ||
| let source = 0; | ||
| let sink = if num_vertices > 1 { | ||
| num_vertices - 1 | ||
| } else { | ||
| 0 | ||
| }; |
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
- Add missing ProblemSchemaEntry fields (display_name, aliases, dimensions) - Add 'default sat' prefix to declare_variants! macro - Remove duplicate source/sink CLI fields (already defined by main) Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
- Add canonical_model_example_specs() for MinimumCutIntoBoundedSets using the 8-vertex issue #228 instance, register in graph/mod.rs - Add brute-force test verifying K=5 has no solution on the issue instance Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
GiggleLiu
approved these changes
Mar 19, 2026
3 tasks
…-into-bounded-sets # Conflicts: # docs/paper/reductions.typ # problemreductions-cli/src/cli.rs # problemreductions-cli/src/commands/create.rs # src/models/mod.rs
Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
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Summary
Add the MinimumCutIntoBoundedSets satisfaction problem (Garey & Johnson ND17). This is a graph partitioning problem that combines minimum s-t cut with balance constraints on partition sizes.
Fixes #228