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Fix #244: Add IsomorphicSpanningTree model (#612)
* Add plan for #244: [Model] IsomorphicSpanningTree Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * feat: add IsomorphicSpanningTree satisfaction problem model (#244) Implements the Isomorphic Spanning Tree decision problem: given a graph G and a tree T with |V(G)| = |V(T)|, determine if G contains a spanning tree isomorphic to T. NP-complete (Garey & Johnson ND8). - Model with SatisfactionProblem (Metric = bool), permutation-based config - Constructor validates tree connectivity and edge count - CLI support with --graph and --tree flags - 11 unit tests covering evaluation, solver, serialization, edge cases Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * chore: remove plan file after implementation Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * Fix #412: Add ShortestCommonSupersequence model (#627) * Add plan for #412: ShortestCommonSupersequence model * Implement #412: Add ShortestCommonSupersequence model * style: apply rustfmt formatting * Address review: fix docs, add --alphabet-size flag, add edge case tests * chore: remove plan file after implementation * Address Copilot review comments - Align docs/schema wording: bound is exact config length, equivalent to |w| ≤ B via padding - Add alphabet_size > 0 validation in constructor - Handle empty string segments in --strings CLI parsing - Add --alphabet-size to CLI help text - Regenerate problem_schemas.json Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * Fix agentic test issues: add SCS to prelude, fix CLI duplicate fields - Add ShortestCommonSupersequence to prelude re-exports (was missing unlike all other misc models) - Fix duplicate CLI struct fields (strings, bound) by sharing between LCS/SCS and RuralPostman/SCS with i64 type and casts at usage sites Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * chore: trigger CI Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * style: apply rustfmt formatting Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com> Co-authored-by: GiggleLiu <cacate0129@gmail.com> * Fix #507: Add FlowShopScheduling model (#629) * Add plan for #507: FlowShopScheduling model * Implement #507: Add FlowShopScheduling model Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * chore: remove plan file after implementation * fix: address Copilot review comments on FlowShopScheduling - Switch dims() from vec![n;n] to Lehmer code encoding [n,n-1,...,1] - Update evaluate() to decode Lehmer code into permutations - Fix complexity from "3^num_jobs" to "num_jobs^num_jobs" - Add validation to compute_makespan() for out-of-bounds indices - Add --num-processors CLI flag instead of overloading --m - Validate task_lengths row lengths in CLI with bail! instead of panic - Fix test comment about deadline value Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * docs: add Lehmer code encoding explanation to FlowShopScheduling Add concrete example of how Lehmer code configs map to job orderings in the struct doc comment, improving discoverability for new users. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * fix: remove unused enumerate in Lehmer code decoding Fixes clippy::unused_enumerate_index warning. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * fix: add missing paper section, trait_consistency entry, and correct complexity - Add FlowShopScheduling problem-def and display-name to docs/paper/reductions.typ - Add FlowShopScheduling to trait_consistency test - Fix complexity from "num_jobs^num_jobs" to "factorial(num_jobs)" (n! is the exact search space) - Relax check_problem_trait assertion from >= 2 to >= 1 (Lehmer code encoding produces trailing dim of 1) Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * docs: add Gantt chart visualization and use issue's 5-job example in paper Replace the simple 2-machine example with the issue's canonical 3-machine, 5-job example. Add a CeTZ Gantt chart showing the feasible schedule with job order (j4, j1, j5, j3, j2) achieving makespan 23 within deadline 25. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com> Co-authored-by: GiggleLiu <cacate0129@gmail.com> * Add paper section, trait_consistency entry, and formatting fixes for IsomorphicSpanningTree - Add display-name and problem-def entry in docs/paper/reductions.typ with formal definition, background (Garey & Johnson ND8), and CeTZ figure - Add bibliography entry for Papadimitriou & Yannakakis 1982 - Add check_problem_trait for IsomorphicSpanningTree in trait_consistency.rs - Apply cargo fmt formatting fixes from merge Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com> Co-authored-by: GiggleLiu <cacate0129@gmail.com>
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‎docs/paper/reductions.typ‎

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@@ -31,6 +31,7 @@
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"MaxCut": [Max-Cut],
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"GraphPartitioning": [Graph Partitioning],
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"HamiltonianPath": [Hamiltonian Path],
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"IsomorphicSpanningTree": [Isomorphic Spanning Tree],
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"KColoring": [$k$-Coloring],
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"MinimumDominatingSet": [Minimum Dominating Set],
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"MaximumMatching": [Maximum Matching],
@@ -451,6 +452,55 @@ Graph Partitioning is a core NP-hard problem arising in VLSI design, parallel co
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Variables: $n = |V|$ values forming a permutation. Position $i$ holds the vertex visited at step $i$. A configuration is satisfying when it forms a valid permutation of all vertices and consecutive vertices are adjacent in $G$.
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]
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#problem-def("IsomorphicSpanningTree")[
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Given a graph $G = (V, E)$ and a tree $T = (V_T, E_T)$ with $|V| = |V_T|$, determine whether $G$ contains a spanning tree isomorphic to $T$: does there exist a bijection $pi: V_T -> V$ such that for every edge ${u, v} in E_T$, ${pi(u), pi(v)} in E$?
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][
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A classical NP-complete problem listed as ND8 in Garey & Johnson @garey1979. The Isomorphic Spanning Tree problem strictly generalizes Hamiltonian Path: a graph $G$ has a Hamiltonian path if and only if $G$ contains a spanning tree isomorphic to the path $P_n$. The problem remains NP-complete even when $T$ is restricted to trees of bounded degree @papadimitriou1982.
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Brute-force enumeration of all bijections $pi: V_T -> V$ and checking each against the edge set of $G$ runs in $O(n! dot n)$ time. No substantially faster exact algorithm is known for general instances.
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Variables: $n = |V|$ values forming a permutation. Position $i$ holds the graph vertex that tree vertex $i$ maps to under $pi$. A configuration is satisfying when it forms a valid permutation and every tree edge maps to a graph edge.
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*Example.* Consider $G = K_4$ (the complete graph on 4 vertices) and $T$ the star $S_3$ with center $0$ and leaves ${1, 2, 3}$. Since $K_4$ contains all possible edges, any bijection $pi$ maps the star's edges to edges of $G$. For instance, the identity mapping $pi(i) = i$ gives the spanning tree ${(0,1), (0,2), (0,3)} subset.eq E(K_4)$.
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#figure({
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let blue = graph-colors.at(0)
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let gray = luma(200)
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canvas(length: 1cm, {
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import draw: *
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// G = K4 on the left
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let gv = ((0, 0), (1.5, 0), (1.5, 1.5), (0, 1.5))
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let ge = ((0,1),(0,2),(0,3),(1,2),(1,3),(2,3))
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let tree-edges = ((0,1),(0,2),(0,3))
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for (u, v) in ge {
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let is-tree = tree-edges.any(e => (e.at(0) == u and e.at(1) == v) or (e.at(0) == v and e.at(1) == u))
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g-edge(gv.at(u), gv.at(v), stroke: if is-tree { 2pt + blue } else { 1pt + gray })
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}
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for (k, pos) in gv.enumerate() {
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let is-center = k == 0
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g-node(pos, name: "g" + str(k),
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fill: if is-center { blue } else { white },
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label: if is-center { text(fill: white)[$v_#k$] } else { [$v_#k$] })
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}
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// Arrow
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content((2.5, 0.75), text(10pt)[$arrow.l.double$])
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// T = star S3 on the right
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let tv = ((3.5, 0.75), (5.0, 0), (5.0, 0.75), (5.0, 1.5))
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let te = ((0,1),(0,2),(0,3))
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for (u, v) in te {
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g-edge(tv.at(u), tv.at(v), stroke: 2pt + blue)
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}
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for (k, pos) in tv.enumerate() {
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let is-center = k == 0
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g-node(pos, name: "t" + str(k),
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fill: if is-center { blue } else { white },
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label: if is-center { text(fill: white)[$u_#k$] } else { [$u_#k$] })
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}
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})
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},
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caption: [Isomorphic Spanning Tree: the graph $G = K_4$ (left) contains a spanning tree isomorphic to the star $S_3$ (right, blue edges). The identity mapping $pi(u_i) = v_i$ embeds all three star edges into $G$. Center vertex $v_0$ shown in blue.],
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) <fig:isomorphic-spanning-tree>
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]
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#problem-def("KColoring")[
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Given $G = (V, E)$ and $k$ colors, find $c: V -> {1, ..., k}$ minimizing $|{(u, v) in E : c(u) = c(v)}|$.
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][

‎docs/paper/references.bib‎

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@@ -532,3 +532,14 @@ @article{lucchesi1978
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year = {1978},
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doi = {10.1112/jlms/s2-17.3.369}
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}
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@article{papadimitriou1982,
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author = {Christos H. Papadimitriou and Mihalis Yannakakis},
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title = {The Complexity of Restricted Spanning Tree Problems},
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journal = {Journal of the ACM},
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volume = {29},
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number = {2},
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pages = {285--309},
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year = {1982},
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doi = {10.1145/322307.322309}
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}

‎docs/src/reductions/problem_schemas.json‎

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}
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]
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},
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{
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"name": "IsomorphicSpanningTree",
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"description": "Does graph G contain a spanning tree isomorphic to tree T?",
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"fields": [
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{
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"name": "graph",
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"type_name": "SimpleGraph",
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"description": "The host graph G"
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},
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{
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"name": "tree",
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"type_name": "SimpleGraph",
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"description": "The target tree T (must be a tree with |V(T)| = |V(G)|)"
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}
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]
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},
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{
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"name": "KColoring",
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"description": "Find valid k-coloring of a graph",

‎problemreductions-cli/src/cli.rs‎

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@@ -210,6 +210,7 @@ Flags by problem type:
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KColoring --graph, --k
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PartitionIntoTriangles --graph
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GraphPartitioning --graph
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IsomorphicSpanningTree --graph, --tree
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Factoring --target, --m, --n
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BinPacking --sizes, --capacity
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SubsetSum --sizes, --target
@@ -337,6 +338,9 @@ pub struct CreateArgs {
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/// Variable bounds for CVP as "lower,upper" (e.g., "-10,10") [default: -10,10]
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#[arg(long, allow_hyphen_values = true)]
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pub bounds: Option<String>,
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/// Tree edge list for IsomorphicSpanningTree (e.g., 0-1,1-2,2-3)
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#[arg(long)]
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pub tree: Option<String>,
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/// Required edge indices for RuralPostman (comma-separated, e.g., "0,2,4")
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#[arg(long)]
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pub required_edges: Option<String>,

‎problemreductions-cli/src/commands/create.rs‎

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@@ -50,6 +50,7 @@ fn all_data_flags_empty(args: &CreateArgs) -> bool {
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&& args.basis.is_none()
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&& args.target_vec.is_none()
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&& args.bounds.is_none()
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&& args.tree.is_none()
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&& args.required_edges.is_none()
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&& args.bound.is_none()
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&& args.pattern.is_none()
@@ -93,6 +94,7 @@ fn example_for(canonical: &str, graph_type: Option<&str>) -> &'static str {
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},
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"GraphPartitioning" => "--graph 0-1,1-2,2-3,0-2,1-3,0-3",
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"HamiltonianPath" => "--graph 0-1,1-2,2-3",
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"IsomorphicSpanningTree" => "--graph 0-1,1-2,0-2 --tree 0-1,1-2",
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"MaxCut" | "MaximumMatching" | "TravelingSalesman" => {
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"--graph 0-1,1-2,2-3 --edge-weights 1,1,1"
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}
@@ -101,7 +103,9 @@ fn example_for(canonical: &str, graph_type: Option<&str>) -> &'static str {
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"QUBO" => "--matrix \"1,0.5;0.5,2\"",
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"SpinGlass" => "--graph 0-1,1-2 --couplings 1,1",
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"KColoring" => "--graph 0-1,1-2,2-0 --k 3",
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"MinimumSumMulticenter" => "--graph 0-1,1-2,2-3 --weights 1,1,1,1 --edge-weights 1,1,1 --k 2",
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"MinimumSumMulticenter" => {
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"--graph 0-1,1-2,2-3 --weights 1,1,1,1 --edge-weights 1,1,1 --k 2"
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}
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"PartitionIntoTriangles" => "--graph 0-1,1-2,0-2",
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"Factoring" => "--target 15 --m 4 --n 4",
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"MinimumFeedbackArcSet" => "--arcs \"0>1,1>2,2>0\"",
@@ -239,13 +243,47 @@ pub fn create(args: &CreateArgs, out: &OutputConfig) -> Result<()> {
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// Hamiltonian path (graph only, no weights)
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"HamiltonianPath" => {
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let (graph, _) = parse_graph(args).map_err(|e| {
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anyhow::anyhow!("{e}\n\nUsage: pred create HamiltonianPath --graph 0-1,1-2,2-3")
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})?;
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(ser(HamiltonianPath::new(graph))?, resolved_variant.clone())
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}
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// IsomorphicSpanningTree (graph + tree)
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"IsomorphicSpanningTree" => {
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let (graph, _) = parse_graph(args).map_err(|e| {
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anyhow::anyhow!(
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"{e}\n\nUsage: pred create HamiltonianPath --graph 0-1,1-2,2-3"
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"{e}\n\nUsage: pred create IsomorphicSpanningTree --graph 0-1,1-2,0-2 --tree 0-1,1-2"
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)
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})?;
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let tree_str = args.tree.as_deref().ok_or_else(|| {
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anyhow::anyhow!(
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"IsomorphicSpanningTree requires --tree\n\n\
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Usage: pred create IsomorphicSpanningTree --graph 0-1,1-2,0-2 --tree 0-1,1-2"
263+
)
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})?;
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let tree_edges: Vec<(usize, usize)> = tree_str
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.split(',')
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.map(|pair| {
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let parts: Vec<&str> = pair.trim().split('-').collect();
269+
if parts.len() != 2 {
270+
bail!("Invalid tree edge '{}': expected format u-v", pair.trim());
271+
}
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let u: usize = parts[0].parse()?;
273+
let v: usize = parts[1].parse()?;
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Ok((u, v))
275+
})
276+
.collect::<Result<Vec<_>>>()?;
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let tree_num_vertices = tree_edges
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.iter()
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.flat_map(|(u, v)| [*u, *v])
280+
.max()
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.map(|m| m + 1)
282+
.unwrap_or(0)
283+
.max(graph.num_vertices());
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let tree = SimpleGraph::new(tree_num_vertices, tree_edges);
247285
(
248-
ser(HamiltonianPath::new(graph))?,
286+
ser(problemreductions::models::graph::IsomorphicSpanningTree::new(graph, tree))?,
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resolved_variant.clone(),
250288
)
251289
}
@@ -609,7 +647,11 @@ pub fn create(args: &CreateArgs, out: &OutputConfig) -> Result<()> {
609647
}
610648
}
611649
(
612-
ser(FlowShopScheduling::new(num_processors, task_lengths, deadline))?,
650+
ser(FlowShopScheduling::new(
651+
num_processors,
652+
task_lengths,
653+
deadline,
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))?,
613655
resolved_variant.clone(),
614656
)
615657
}

‎problemreductions-cli/src/dispatch.rs‎

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"MinimumSumMulticenter" => deser_opt::<MinimumSumMulticenter<SimpleGraph, i32>>(data),
217217
"GraphPartitioning" => deser_opt::<GraphPartitioning<SimpleGraph>>(data),
218218
"HamiltonianPath" => deser_sat::<HamiltonianPath<SimpleGraph>>(data),
219+
"IsomorphicSpanningTree" => {
220+
deser_sat::<problemreductions::models::graph::IsomorphicSpanningTree>(data)
221+
}
219222
"MaxCut" => deser_opt::<MaxCut<SimpleGraph, i32>>(data),
220223
"MaximalIS" => deser_opt::<MaximalIS<SimpleGraph, i32>>(data),
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"TravelingSalesman" => deser_opt::<TravelingSalesman<SimpleGraph, i32>>(data),
@@ -285,6 +288,9 @@ pub fn serialize_any_problem(
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"MinimumSumMulticenter" => try_ser::<MinimumSumMulticenter<SimpleGraph, i32>>(any),
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"GraphPartitioning" => try_ser::<GraphPartitioning<SimpleGraph>>(any),
287290
"HamiltonianPath" => try_ser::<HamiltonianPath<SimpleGraph>>(any),
291+
"IsomorphicSpanningTree" => {
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try_ser::<problemreductions::models::graph::IsomorphicSpanningTree>(any)
293+
}
288294
"MaxCut" => try_ser::<MaxCut<SimpleGraph, i32>>(any),
289295
"MaximalIS" => try_ser::<MaximalIS<SimpleGraph, i32>>(any),
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"TravelingSalesman" => try_ser::<TravelingSalesman<SimpleGraph, i32>>(any),

‎problemreductions-cli/src/mcp/tools.rs‎

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@@ -2,8 +2,8 @@ use crate::util;
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use problemreductions::models::algebraic::QUBO;
33
use problemreductions::models::formula::{CNFClause, Satisfiability};
44
use problemreductions::models::graph::{
5-
MaxCut, MaximumClique, MaximumIndependentSet, MaximumMatching, MinimumSumMulticenter,
6-
MinimumDominatingSet, MinimumVertexCover, SpinGlass, TravelingSalesman,
5+
MaxCut, MaximumClique, MaximumIndependentSet, MaximumMatching, MinimumDominatingSet,
6+
MinimumSumMulticenter, MinimumVertexCover, SpinGlass, TravelingSalesman,
77
};
88
use problemreductions::models::misc::Factoring;
99
use problemreductions::registry::collect_schemas;
@@ -528,7 +528,12 @@ impl McpServer {
528528
})?;
529529
let variant = variant_map(&[("graph", "SimpleGraph"), ("weight", "i32")]);
530530
(
531-
ser(MinimumSumMulticenter::new(graph, vertex_weights, edge_lengths, k))?,
531+
ser(MinimumSumMulticenter::new(
532+
graph,
533+
vertex_weights,
534+
edge_lengths,
535+
k,
536+
))?,
532537
variant,
533538
)
534539
}
@@ -672,7 +677,12 @@ impl McpServer {
672677
.unwrap_or(1.max(num_vertices / 3));
673678
let variant = variant_map(&[("graph", "SimpleGraph"), ("weight", "i32")]);
674679
(
675-
ser(MinimumSumMulticenter::new(graph, vertex_weights, edge_lengths, k))?,
680+
ser(MinimumSumMulticenter::new(
681+
graph,
682+
vertex_weights,
683+
edge_lengths,
684+
k,
685+
))?,
676686
variant,
677687
)
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}

‎problemreductions-cli/src/problem_name.rs‎

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@@ -39,6 +39,7 @@ pub fn resolve_alias(input: &str) -> String {
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"ksat" | "ksatisfiability" => "KSatisfiability".to_string(),
4040
"qubo" => "QUBO".to_string(),
4141
"graphpartitioning" => "GraphPartitioning".to_string(),
42+
"isomorphicspanningtree" => "IsomorphicSpanningTree".to_string(),
4243
"maxcut" => "MaxCut".to_string(),
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"spinglass" => "SpinGlass".to_string(),
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"ilp" => "ILP".to_string(),

‎src/lib.rs‎

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@@ -41,13 +41,14 @@ pub mod prelude {
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pub use crate::models::algebraic::{BMF, QUBO};
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pub use crate::models::formula::{CNFClause, CircuitSAT, KSatisfiability, Satisfiability};
4343
pub use crate::models::graph::{
44-
BicliqueCover, GraphPartitioning, HamiltonianPath, SpinGlass, SubgraphIsomorphism,
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BicliqueCover, GraphPartitioning, HamiltonianPath, IsomorphicSpanningTree, SpinGlass,
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SubgraphIsomorphism,
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};
4647
pub use crate::models::graph::{
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KColoring, MaxCut, MaximalIS, MaximumClique, MaximumIndependentSet, MaximumMatching,
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MinimumDominatingSet, MinimumFeedbackArcSet, MinimumFeedbackVertexSet,
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MinimumSumMulticenter, MinimumVertexCover, PartitionIntoTriangles,
50-
RuralPostman, TravelingSalesman,
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MinimumSumMulticenter, MinimumVertexCover, PartitionIntoTriangles, RuralPostman,
51+
TravelingSalesman,
5152
};
5253
pub use crate::models::misc::{
5354
BinPacking, Factoring, FlowShopScheduling, Knapsack, LongestCommonSubsequence, PaintShop,

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