Fix #714: [Model] KClique (#715)

* Add plan for #714: [Model] KClique

* Implement #714: [Model] KClique

* chore: remove plan file after implementation

* chore: add gh retry logic and enforce read-only agentic tests in review-pipeline

- pipeline_board.py: retry transient gh CLI failures (3 attempts with backoff)
- review-pipeline SKILL.md: explicitly instruct agentic-test subagent to skip fix mode

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

---------

Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
Co-authored-by: Xiwei Pan <xiwei.pan@connect.hkust-gz.edu.cn>

Author: 3 people

.claude/skills/review-pipeline/SKILL.md

@@ -186,7 +186,7 @@ Invoke `/review-quality` (file: `.claude/skills/review-quality/SKILL.md`) with t
    - Classify as: `confirmed` / `not reproducible in current worktree`
    - For confirmed issues, note severity and recommended fix
 
-**Do NOT fix any issues.** Only report them.
+**Do NOT fix any issues.** Only report them. When dispatching the agentic-test subagent, explicitly instruct it: "This is a read-only review run. Do NOT offer to fix issues, do NOT select option (a) 'Review together and fix', and do NOT modify any files. Report findings only and stop after generating the report."
 
 ### 2. Compose Combined Review Comment
 

docs/paper/reductions.typ

@@ -77,6 +77,7 @@
   "IsomorphicSpanningTree": [Isomorphic Spanning Tree],
   "KthBestSpanningTree": [Kth Best Spanning Tree],
   "KColoring": [$k$-Coloring],
+  "KClique": [$k$-Clique],
   "MinimumDominatingSet": [Minimum Dominating Set],
   "MaximumMatching": [Maximum Matching],
   "TravelingSalesman": [Traveling Salesman],
@@ -1431,6 +1432,32 @@ is feasible: each set induces a connected subgraph, the component weights are $2
     ]
   ]
 }
+#{
+  let x = load-model-example("KClique")
+  let nv = graph-num-vertices(x.instance)
+  let ne = graph-num-edges(x.instance)
+  let edges = x.instance.graph.edges
+  let k = x.instance.k
+  let sol = (config: x.optimal_config, metric: x.optimal_value)
+  let K = sol.config.enumerate().filter(((i, v)) => v == 1).map(((i, _)) => i)
+  let clique-edges = edges.filter(e => K.contains(e.at(0)) and K.contains(e.at(1)))
+  [
+    #problem-def("KClique")[
+      Given an undirected graph $G = (V, E)$ and an integer $k$, determine whether there exists a subset $K subset.eq V$ with $|K| >= k$ such that every pair of distinct vertices in $K$ is adjacent.
+    ][
+    $k$-Clique is the classical decision version of Clique, one of Karp's original NP-complete problems @karp1972 and listed as GT19 in Garey and Johnson @garey1979. Unlike Maximum Clique, the threshold $k$ is part of the input, so this formulation is the natural target for decision-to-decision reductions such as $3$SAT $arrow.r$ Clique. The best known exact algorithm matches Maximum Clique via the complement reduction to Maximum Independent Set and runs in $O^*(1.1996^n)$ @xiao2017.
+
+    *Example.* Consider the house graph $G$ with $n = #nv$ vertices, $|E| = #ne$ edges, and threshold $k = #k$. The set $K = {#K.map(i => $v_#i$).join(", ")}$ is a valid witness because all three pairs #clique-edges.map(((u, v)) => $(v_#u, v_#v)$).join(", ") are edges, so $|K| = 3 >= #k$ and this is a YES instance. This witness is unique, and no $4$-clique exists because every vertex outside $K$ misses at least one edge to the other selected vertices.
+
+    #figure({
+      let hg = house-graph()
+      draw-edge-highlight(hg.vertices, hg.edges, clique-edges, K)
+    },
+    caption: [The house graph with satisfying witness $K = {#K.map(i => $v_#i$).join(", ")}$ for $k = #k$. The selected vertices and their internal clique edges are highlighted in blue.],
+    ) <fig:house-kclique>
+    ]
+  ]
+}
 #{
   let x = load-model-example("MaximumClique")
   let nv = graph-num-vertices(x.instance)

problemreductions-cli/src/cli.rs

@@ -224,6 +224,7 @@ Flags by problem type:
   QUBO                            --matrix
   SpinGlass                       --graph, --couplings, --fields
   KColoring                       --graph, --k
+  KClique                         --graph, --k
   MinimumMultiwayCut              --graph, --terminals, --edge-weights
   PartitionIntoTriangles          --graph
   GraphPartitioning               --graph

problemreductions-cli/src/commands/create.rs

@@ -385,6 +385,7 @@ fn example_for(canonical: &str, graph_type: Option<&str>) -> &'static str {
             Some("UnitDiskGraph") => "--positions \"0,0;1,0;0.5,0.8\" --radius 1.5",
             _ => "--graph 0-1,1-2,2-3 --weights 1,1,1,1",
         },
+        "KClique" => "--graph 0-1,0-2,1-3,2-3,2-4,3-4 --k 3",
         "GraphPartitioning" => "--graph 0-1,1-2,2-3,0-2,1-3,0-3",
         "GeneralizedHex" => "--graph 0-1,0-2,0-3,1-4,2-4,3-4,4-5 --source 0 --sink 5",
         "MinimumCutIntoBoundedSets" => {
@@ -1376,6 +1377,13 @@ pub fn create(args: &CreateArgs, out: &OutputConfig) -> Result<()> {
             util::ser_kcoloring(graph, k)?
         }
 
+        "KClique" => {
+            let usage = "Usage: pred create KClique --graph 0-1,0-2,1-3,2-3,2-4,3-4 --k 3";
+            let (graph, _) = parse_graph(args).map_err(|e| anyhow::anyhow!("{e}\n\n{usage}"))?;
+            let k = parse_kclique_threshold(args.k, graph.num_vertices(), usage)?;
+            (ser(KClique::new(graph, k))?, resolved_variant.clone())
+        }
+
         // SAT
         "Satisfiability" => {
             let num_vars = args.num_vars.ok_or_else(|| {
@@ -3403,6 +3411,21 @@ fn ser<T: Serialize>(problem: T) -> Result<serde_json::Value> {
     util::ser(problem)
 }
 
+fn parse_kclique_threshold(
+    k_flag: Option<usize>,
+    num_vertices: usize,
+    usage: &str,
+) -> Result<usize> {
+    let k = k_flag.ok_or_else(|| anyhow::anyhow!("KClique requires --k\n\n{usage}"))?;
+    if k == 0 {
+        bail!("KClique: --k must be positive");
+    }
+    if k > num_vertices {
+        bail!("KClique: k must be <= graph num_vertices");
+    }
+    Ok(k)
+}
+
 fn variant_map(pairs: &[(&str, &str)]) -> BTreeMap<String, String> {
     util::variant_map(pairs)
 }
@@ -4450,6 +4473,21 @@ fn create_random(
             }
         }
 
+        "KClique" => {
+            let edge_prob = args.edge_prob.unwrap_or(0.5);
+            if !(0.0..=1.0).contains(&edge_prob) {
+                bail!("--edge-prob must be between 0.0 and 1.0");
+            }
+            let graph = util::create_random_graph(num_vertices, edge_prob, args.seed);
+            let usage =
+                "Usage: pred create KClique --random --num-vertices 5 [--edge-prob 0.5] [--seed 42] --k 3";
+            let k = parse_kclique_threshold(args.k, graph.num_vertices(), usage)?;
+            (
+                ser(KClique::new(graph, k))?,
+                variant_map(&[("graph", "SimpleGraph")]),
+            )
+        }
+
         // MinimumCutIntoBoundedSets (graph + edge weights + s/t/B/K)
         "MinimumCutIntoBoundedSets" => {
             let edge_prob = args.edge_prob.unwrap_or(0.5);
@@ -4702,7 +4740,7 @@ fn create_random(
         _ => bail!(
             "Random generation is not supported for {canonical}. \
              Supported: graph-based problems (MIS, MVC, MaxCut, MaxClique, \
-             MaximumMatching, MinimumDominatingSet, SpinGlass, KColoring, TravelingSalesman, \
+             MaximumMatching, MinimumDominatingSet, SpinGlass, KColoring, KClique, TravelingSalesman, \
              SteinerTreeInGraphs, HamiltonianCircuit, SteinerTree, OptimalLinearArrangement, HamiltonianPath, GeneralizedHex)"
         ),
     };
@@ -5349,4 +5387,69 @@ mod tests {
         let err = create(&args, &out).unwrap_err().to_string();
         assert!(err.contains("out of bounds for left partition size 4"));
     }
+
+    #[test]
+    fn test_create_kclique() {
+        use crate::dispatch::ProblemJsonOutput;
+        use problemreductions::models::graph::KClique;
+
+        let mut args = empty_args();
+        args.problem = Some("KClique".to_string());
+        args.graph = Some("0-1,0-2,1-3,2-3,2-4,3-4".to_string());
+        args.k = Some(3);
+
+        let output_path =
+            std::env::temp_dir().join(format!("kclique-create-{}.json", std::process::id()));
+        let out = OutputConfig {
+            output: Some(output_path.clone()),
+            quiet: true,
+            json: false,
+            auto_json: false,
+        };
+
+        create(&args, &out).unwrap();
+
+        let json = std::fs::read_to_string(&output_path).unwrap();
+        let created: ProblemJsonOutput = serde_json::from_str(&json).unwrap();
+        assert_eq!(created.problem_type, "KClique");
+        assert_eq!(
+            created.variant.get("graph").map(String::as_str),
+            Some("SimpleGraph")
+        );
+
+        let problem: KClique<SimpleGraph> = serde_json::from_value(created.data).unwrap();
+        assert_eq!(problem.k(), 3);
+        assert_eq!(problem.num_vertices(), 5);
+        assert!(problem.evaluate(&[0, 0, 1, 1, 1]));
+
+        let _ = std::fs::remove_file(output_path);
+    }
+
+    #[test]
+    fn test_create_kclique_requires_valid_k() {
+        let mut args = empty_args();
+        args.problem = Some("KClique".to_string());
+        args.graph = Some("0-1,0-2,1-3,2-3,2-4,3-4".to_string());
+        args.k = None;
+
+        let out = OutputConfig {
+            output: None,
+            quiet: true,
+            json: false,
+            auto_json: false,
+        };
+
+        let err = create(&args, &out).unwrap_err();
+        assert!(
+            err.to_string().contains("KClique requires --k"),
+            "unexpected error: {err}"
+        );
+
+        args.k = Some(6);
+        let err = create(&args, &out).unwrap_err();
+        assert!(
+            err.to_string().contains("k must be <= graph num_vertices"),
+            "unexpected error: {err}"
+        );
+    }
 }

problemreductions-cli/src/mcp/tools.rs

@@ -2,7 +2,7 @@ use crate::util;
 use problemreductions::models::algebraic::QUBO;
 use problemreductions::models::formula::{CNFClause, Satisfiability};
 use problemreductions::models::graph::{
-    MaxCut, MaximumClique, MaximumIndependentSet, MaximumMatching, MinimumDominatingSet,
+    KClique, MaxCut, MaximumClique, MaximumIndependentSet, MaximumMatching, MinimumDominatingSet,
     MinimumSumMulticenter, MinimumVertexCover, SpinGlass, TravelingSalesman,
 };
 use problemreductions::models::misc::Factoring;
@@ -68,7 +68,7 @@ pub struct CreateProblemParams {
     )]
     pub problem_type: String,
     #[schemars(
-        description = "Problem parameters as JSON object. Graph problems: {\"edges\": \"0-1,1-2\", \"weights\": \"1,2,3\"}. SAT: {\"num_vars\": 3, \"clauses\": \"1,2;-1,3\"}. QUBO: {\"matrix\": \"1,0.5;0.5,2\"}. KColoring: {\"edges\": \"0-1,1-2\", \"k\": 3}. Factoring: {\"target\": 15, \"bits_m\": 4, \"bits_n\": 4}. Random graph: {\"random\": true, \"num_vertices\": 10, \"edge_prob\": 0.3}. Geometry graphs (use with MIS/KingsSubgraph etc.): {\"positions\": \"0,0;1,0;1,1\"}. UnitDiskGraph: {\"positions\": \"0.0,0.0;1.0,0.0\", \"radius\": 1.5}"
+        description = "Problem parameters as JSON object. Graph problems: {\"edges\": \"0-1,1-2\", \"weights\": \"1,2,3\"}. SAT: {\"num_vars\": 3, \"clauses\": \"1,2;-1,3\"}. QUBO: {\"matrix\": \"1,0.5;0.5,2\"}. KColoring: {\"edges\": \"0-1,1-2\", \"k\": 3}. KClique: {\"edges\": \"0-1,0-2,1-3,2-3,2-4,3-4\", \"k\": 3}. Factoring: {\"target\": 15, \"bits_m\": 4, \"bits_n\": 4}. Random graph: {\"random\": true, \"num_vertices\": 10, \"edge_prob\": 0.3}. Geometry graphs (use with MIS/KingsSubgraph etc.): {\"positions\": \"0,0;1,0;1,1\"}. UnitDiskGraph: {\"positions\": \"0.0,0.0;1.0,0.0\", \"radius\": 1.5}"
     )]
     pub params: serde_json::Value,
 }
@@ -406,6 +406,16 @@ impl McpServer {
                 util::ser_kcoloring(graph, k)?
             }
 
+            "KClique" => {
+                let (graph, _) = parse_graph_from_params(params)?;
+                let k_flag = params.get("k").and_then(|v| v.as_u64()).map(|v| v as usize);
+                let k = parse_kclique_threshold(k_flag, graph.num_vertices())?;
+                (
+                    ser(KClique::new(graph, k))?,
+                    variant_map(&[("graph", "SimpleGraph")]),
+                )
+            }
+
             // SAT
             "Satisfiability" => {
                 let num_vars = params
@@ -613,6 +623,22 @@ impl McpServer {
                     util::validate_k_param(resolved_variant, k_flag, Some(3), "KColoring")?;
                 util::ser_kcoloring(graph, k)?
             }
+            "KClique" => {
+                let edge_prob = params
+                    .get("edge_prob")
+                    .and_then(|v| v.as_f64())
+                    .unwrap_or(0.5);
+                if !(0.0..=1.0).contains(&edge_prob) {
+                    anyhow::bail!("edge_prob must be between 0.0 and 1.0");
+                }
+                let graph = util::create_random_graph(num_vertices, edge_prob, seed);
+                let k_flag = params.get("k").and_then(|v| v.as_u64()).map(|v| v as usize);
+                let k = parse_kclique_threshold(k_flag, graph.num_vertices())?;
+                (
+                    ser(KClique::new(graph, k))?,
+                    variant_map(&[("graph", "SimpleGraph")]),
+                )
+            }
             "MinimumSumMulticenter" => {
                 let edge_prob = params
                     .get("edge_prob")
@@ -644,7 +670,7 @@ impl McpServer {
             _ => anyhow::bail!(
                 "Random generation is not supported for {}. \
                  Supported: graph-based problems (MIS, MVC, MaxCut, MaxClique, \
-                 MaximumMatching, MinimumDominatingSet, SpinGlass, KColoring, \
+                 MaximumMatching, MinimumDominatingSet, SpinGlass, KColoring, KClique, \
                  TravelingSalesman, MinimumSumMulticenter)",
                 canonical
             ),
@@ -1231,6 +1257,17 @@ fn parse_graph_from_params(params: &serde_json::Value) -> anyhow::Result<(Simple
     Ok((SimpleGraph::new(num_vertices, edges), num_vertices))
 }
 
+fn parse_kclique_threshold(k_flag: Option<usize>, num_vertices: usize) -> anyhow::Result<usize> {
+    let k = k_flag.ok_or_else(|| anyhow::anyhow!("KClique requires 'k'"))?;
+    if k == 0 {
+        anyhow::bail!("KClique: 'k' must be positive");
+    }
+    if k > num_vertices {
+        anyhow::bail!("KClique: k must be <= graph num_vertices");
+    }
+    Ok(k)
+}
+
 /// Parse `weights` field from JSON params as vertex weights (i32), defaulting to all 1s.
 fn parse_vertex_weights_from_params(
     params: &serde_json::Value,

scripts/pipeline_board.py

@@ -61,8 +61,38 @@
 FAILURE_LABELS = {"PoorWritten", "Wrong", "Trivial", "Useless"}
 
 
-def run_gh(*args: str) -> str:
-    return subprocess.check_output(["gh", *args], text=True)
+def run_gh(*args: str, retries: int = 3, retry_delay: float = 5.0) -> str:
+    """Run a ``gh`` CLI command, retrying on transient failures.
+
+    The ``gh project`` subcommands occasionally fail with cryptic errors
+    like "unknown owner type" due to transient API issues or token
+    refresh races (see cli/cli#7985, cli/cli#8885).  Retrying after a
+    short delay resolves these reliably.
+    """
+    last_exc: subprocess.CalledProcessError | None = None
+    for attempt in range(retries):
+        try:
+            return subprocess.check_output(
+                ["gh", *args], text=True, stderr=subprocess.PIPE,
+            )
+        except subprocess.CalledProcessError as exc:
+            last_exc = exc
+            stderr = (exc.stderr or "").strip()
+            if attempt < retries - 1:
+                print(
+                    f"[run_gh] attempt {attempt + 1}/{retries} failed "
+                    f"(rc={exc.returncode}, stderr={stderr!r}), "
+                    f"retrying in {retry_delay}s…",
+                    file=sys.stderr,
+                )
+                time.sleep(retry_delay)
+            else:
+                print(
+                    f"[run_gh] all {retries} attempts failed "
+                    f"(stderr={stderr!r})",
+                    file=sys.stderr,
+                )
+    raise last_exc  # type: ignore[misc]
 
 
 def _graphql_board_query(project_id: str, page_size: int, cursor: str | None) -> str:

src/lib.rs

@@ -50,7 +50,7 @@ pub mod prelude {
     pub use crate::models::graph::{
         BalancedCompleteBipartiteSubgraph, BicliqueCover, BiconnectivityAugmentation,
         BoundedComponentSpanningForest, DirectedTwoCommodityIntegralFlow, GeneralizedHex,
-        GraphPartitioning, HamiltonianCircuit, HamiltonianPath, IsomorphicSpanningTree,
+        GraphPartitioning, HamiltonianCircuit, HamiltonianPath, IsomorphicSpanningTree, KClique,
         KthBestSpanningTree, LengthBoundedDisjointPaths, SpinGlass, SteinerTree,
         StrongConnectivityAugmentation, SubgraphIsomorphism,
     };