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Fix #399: Add MinSumMulticenter model (#635)
* Add plan for #399: MinSumMulticenter model * Implement MinSumMulticenter (p-median) model (#399) Add the MinSumMulticenter problem — a facility location optimization problem that minimizes total weighted distance from vertices to K selected centers. Includes graph + vertex weights + edge lengths input, Bellman-Ford shortest path computation, CLI support, and comprehensive unit tests (19 tests including solver, serialization, edge cases). Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * chore: remove plan file after implementation * Address Copilot review comments for MinSumMulticenter - Fix docstring: "multi-source Dijkstra" → "multi-source Bellman-Ford" - Add iteration cap (n-1) to prevent non-termination with negative edges - Fix potential borrow issue: clone du instead of dereferencing - Add MCP tools support (create_problem_inner + create_random_inner) - Regenerate problem_schemas.json to include MinSumMulticenter Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * Rename MinSumMulticenter to MinimumSumMulticenter Per issue #399 and human review comment, the naming convention requires the full "Minimum" prefix (matching MinimumVertexCover, MinimumDominatingSet, etc.). Rename struct, files, module paths, CLI aliases, and regenerate schemas. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * Add MinimumSumMulticenter paper section Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com> * Fix trait consistency, switch to Dijkstra for MinimumSumMulticenter 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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@@ -58,6 +58,7 @@
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"SubsetSum": [Subset Sum],
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"MinimumFeedbackArcSet": [Minimum Feedback Arc Set],
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"MinimumFeedbackVertexSet": [Minimum Feedback Vertex Set],
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"MinimumSumMulticenter": [Minimum Sum Multicenter],
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"SubgraphIsomorphism": [Subgraph Isomorphism],
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"SubsetSum": [Subset Sum],
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)
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) <fig:fvs-example>
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]
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#problem-def("MinimumSumMulticenter")[
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Given a graph $G = (V, E)$ with vertex weights $w: V -> ZZ_(>= 0)$, edge lengths $l: E -> ZZ_(>= 0)$, and a positive integer $K <= |V|$, find a set $P subset.eq V$ of $K$ vertices (centers) that minimizes the total weighted distance $sum_(v in V) w(v) dot d(v, P)$, where $d(v, P) = min_(p in P) d(v, p)$ is the shortest-path distance from $v$ to the nearest center in $P$.
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][
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Also known as the _p-median problem_. This is a classical NP-complete facility location problem from Garey & Johnson (A2 ND51). The goal is to optimally place $K$ service centers (e.g., warehouses, hospitals) to minimize total service cost. NP-completeness was established by Kariv and Hakimi (1979) via transformation from Dominating Set. The problem remains NP-complete even with unit weights and unit edge lengths, but is solvable in polynomial time for fixed $K$ or when $G$ is a tree.
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The best known exact algorithm runs in $O^*(2^n)$ time by brute-force enumeration of all $binom(n, K)$ vertex subsets. Constant-factor approximation algorithms exist: Charikar et al. (1999) gave the first constant-factor result, and the best known ratio is $(2 + epsilon)$ by Cohen-Addad et al. (STOC 2022).
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Variables: $n = |V|$ binary variables, one per vertex. $x_v = 1$ if vertex $v$ is selected as a center. A configuration is valid when exactly $K$ centers are selected and all vertices are reachable from at least one center.
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]
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== Set Problems
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#problem-def("MaximumSetPacking")[

‎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": "MinimumSumMulticenter",
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"description": "Find K centers minimizing total weighted distance (p-median problem)",
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"fields": [
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{
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"name": "graph",
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"type_name": "G",
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"description": "The underlying graph G=(V,E)"
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},
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{
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"name": "vertex_weights",
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"type_name": "Vec<W>",
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"description": "Vertex weights w: V -> R"
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},
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{
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"name": "edge_lengths",
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"type_name": "Vec<W>",
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"description": "Edge lengths l: E -> R"
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},
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{
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"name": "k",
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"type_name": "usize",
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"description": "Number of centers to place"
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}
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]
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},
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{
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"name": "MinimumVertexCover",
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"description": "Find minimum weight vertex cover in a graph",
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}
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]
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},
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{
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"name": "PartitionIntoTriangles",
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"description": "Partition vertices into triangles (K3 subgraphs)",
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"fields": [
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{
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"name": "graph",
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"type_name": "G",
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"description": "The underlying graph G=(V,E) with |V| divisible by 3"
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}
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]
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},
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{
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"name": "QUBO",
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"description": "Minimize quadratic unconstrained binary objective",

‎problemreductions-cli/src/commands/create.rs‎

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@@ -93,6 +93,7 @@ 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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"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\"",
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)
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}
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// MinimumSumMulticenter (p-median)
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"MinimumSumMulticenter" => {
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let (graph, n) = parse_graph(args).map_err(|e| {
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anyhow::anyhow!(
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"{e}\n\nUsage: pred create MinimumSumMulticenter --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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})?;
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let vertex_weights = parse_vertex_weights(args, n)?;
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let edge_lengths = parse_edge_weights(args, graph.num_edges())?;
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let k = args.k.ok_or_else(|| {
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anyhow::anyhow!(
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"MinimumSumMulticenter requires --k (number of centers)\n\n\
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Usage: pred create MinimumSumMulticenter --graph 0-1,1-2,2-3 --k 2"
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)
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})?;
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(
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ser(MinimumSumMulticenter::new(
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graph,
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vertex_weights,
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edge_lengths,
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k,
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))?,
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resolved_variant.clone(),
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)
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}
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// SubgraphIsomorphism
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"SubgraphIsomorphism" => {
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let (host_graph, _) = parse_graph(args).map_err(|e| {

‎problemreductions-cli/src/dispatch.rs‎

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@@ -210,6 +210,7 @@ pub fn load_problem(
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"MaximumClique" => deser_opt::<MaximumClique<SimpleGraph, i32>>(data),
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"MaximumMatching" => deser_opt::<MaximumMatching<SimpleGraph, i32>>(data),
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"MinimumDominatingSet" => deser_opt::<MinimumDominatingSet<SimpleGraph, i32>>(data),
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"MinimumSumMulticenter" => deser_opt::<MinimumSumMulticenter<SimpleGraph, i32>>(data),
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"GraphPartitioning" => deser_opt::<GraphPartitioning<SimpleGraph>>(data),
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"MaxCut" => deser_opt::<MaxCut<SimpleGraph, i32>>(data),
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"MaximalIS" => deser_opt::<MaximalIS<SimpleGraph, i32>>(data),
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"MaximumClique" => try_ser::<MaximumClique<SimpleGraph, i32>>(any),
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"MaximumMatching" => try_ser::<MaximumMatching<SimpleGraph, i32>>(any),
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"MinimumDominatingSet" => try_ser::<MinimumDominatingSet<SimpleGraph, i32>>(any),
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"MinimumSumMulticenter" => try_ser::<MinimumSumMulticenter<SimpleGraph, i32>>(any),
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"GraphPartitioning" => try_ser::<GraphPartitioning<SimpleGraph>>(any),
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"MaxCut" => try_ser::<MaxCut<SimpleGraph, i32>>(any),
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"MaximalIS" => try_ser::<MaximalIS<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;
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use problemreductions::models::formula::{CNFClause, Satisfiability};
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use problemreductions::models::graph::{
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MaxCut, MaximumClique, MaximumIndependentSet, MaximumMatching, MinimumDominatingSet,
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MinimumVertexCover, SpinGlass, TravelingSalesman,
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MaxCut, MaximumClique, MaximumIndependentSet, MaximumMatching, MinimumSumMulticenter,
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MinimumDominatingSet, MinimumVertexCover, SpinGlass, TravelingSalesman,
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};
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use problemreductions::models::misc::Factoring;
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use problemreductions::registry::collect_schemas;
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(ser(Factoring::new(bits_m, bits_n, target))?, variant)
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}
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// MinimumSumMulticenter (p-median)
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"MinimumSumMulticenter" => {
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let (graph, n) = parse_graph_from_params(params)?;
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let vertex_weights = parse_vertex_weights_from_params(params, n)?;
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let edge_lengths = parse_edge_lengths_from_params(params, graph.num_edges())?;
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let k = params
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.get("k")
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.and_then(|v| v.as_u64())
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.map(|v| v as usize)
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.ok_or_else(|| {
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anyhow::anyhow!("MinimumSumMulticenter requires 'k' (number of centers)")
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})?;
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let variant = variant_map(&[("graph", "SimpleGraph"), ("weight", "i32")]);
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(
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ser(MinimumSumMulticenter::new(graph, vertex_weights, edge_lengths, k))?,
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variant,
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)
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}
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_ => anyhow::bail!("{}", unknown_problem_error(&canonical)),
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};
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util::validate_k_param(resolved_variant, k_flag, Some(3), "KColoring")?;
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util::ser_kcoloring(graph, k)?
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}
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"MinimumSumMulticenter" => {
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let edge_prob = params
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.get("edge_prob")
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.and_then(|v| v.as_f64())
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.unwrap_or(0.5);
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if !(0.0..=1.0).contains(&edge_prob) {
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anyhow::bail!("edge_prob must be between 0.0 and 1.0");
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}
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let graph = util::create_random_graph(num_vertices, edge_prob, seed);
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let num_edges = graph.num_edges();
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let vertex_weights = vec![1i32; num_vertices];
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let edge_lengths = vec![1i32; num_edges];
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let k = params
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.get("k")
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.and_then(|v| v.as_u64())
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.map(|v| v as usize)
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.unwrap_or(1.max(num_vertices / 3));
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let variant = variant_map(&[("graph", "SimpleGraph"), ("weight", "i32")]);
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(
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ser(MinimumSumMulticenter::new(graph, vertex_weights, edge_lengths, k))?,
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variant,
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)
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}
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_ => anyhow::bail!(
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"Random generation is not supported for {}. \
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Supported: graph-based problems (MIS, MVC, MaxCut, MaxClique, \
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MaximumMatching, MinimumDominatingSet, SpinGlass, KColoring, TravelingSalesman)",
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MaximumMatching, MinimumDominatingSet, SpinGlass, KColoring, \
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TravelingSalesman, MinimumSumMulticenter)",
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canonical
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),
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};
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}
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}
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/// Parse `edge_lengths` field from JSON params as edge lengths (i32), defaulting to all 1s.
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fn parse_edge_lengths_from_params(
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params: &serde_json::Value,
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num_edges: usize,
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) -> anyhow::Result<Vec<i32>> {
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match params.get("edge_lengths").and_then(|v| v.as_str()) {
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Some(w) => {
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let lengths: Vec<i32> = w
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.split(',')
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.map(|s| s.trim().parse::<i32>())
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.collect::<std::result::Result<Vec<_>, _>>()?;
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if lengths.len() != num_edges {
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anyhow::bail!(
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"Expected {} edge lengths but got {}",
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num_edges,
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lengths.len()
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);
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}
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Ok(lengths)
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}
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None => Ok(vec![1i32; num_edges]),
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}
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}
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/// Parse `clauses` field from JSON params as semicolon-separated clauses.
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fn parse_clauses_from_params(params: &serde_json::Value) -> anyhow::Result<Vec<CNFClause>> {
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let clauses_str = params

‎problemreductions-cli/src/problem_name.rs‎

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("MaxMatching", "MaximumMatching"),
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("FVS", "MinimumFeedbackVertexSet"),
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("FAS", "MinimumFeedbackArcSet"),
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("pmedian", "MinimumSumMulticenter"),
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];
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/// Resolve a short alias to the canonical problem name.
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"lcs" | "longestcommonsubsequence" => "LongestCommonSubsequence".to_string(),
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"fvs" | "minimumfeedbackvertexset" => "MinimumFeedbackVertexSet".to_string(),
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"fas" | "minimumfeedbackarcset" => "MinimumFeedbackArcSet".to_string(),
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"minimumsummulticenter" | "pmedian" => "MinimumSumMulticenter".to_string(),
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"subsetsum" => "SubsetSum".to_string(),
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_ => input.to_string(), // pass-through for exact names
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}

‎src/lib.rs‎

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};
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pub use crate::models::graph::{
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KColoring, MaxCut, MaximalIS, MaximumClique, MaximumIndependentSet, MaximumMatching,
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MinimumDominatingSet, MinimumFeedbackArcSet, MinimumFeedbackVertexSet, MinimumVertexCover,
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MinimumDominatingSet, MinimumFeedbackArcSet, MinimumFeedbackVertexSet,
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MinimumSumMulticenter, MinimumVertexCover,
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PartitionIntoTriangles, RuralPostman, TravelingSalesman,
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};
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pub use crate::models::misc::{

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