{"total":19,"items":[{"citing_arxiv_id":"2605.22821","ref_index":35,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Tokenisation via Convex Relaxations","primary_cat":"cs.CL","submitted_at":"2026-05-21T17:59:56+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"ConvexTok uses convex relaxation of tokenization to a linear program, improving intrinsic metrics, bits-per-byte, and some downstream tasks while certifying near-optimality within 1% at typical vocabulary sizes.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.16001","ref_index":22,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"On the parameterized complexity of Broadcast Independence and Broadcast Packing","primary_cat":"cs.DS","submitted_at":"2026-05-15T14:31:51+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Broadcast Independence and Broadcast Packing are FPT parameterized by treewidth plus diameter via DP on nice tree decompositions, W[1]-hard for pathwidth, and admit a constant-factor approximation parameterized by treewidth.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.11288","ref_index":19,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"On $2$-factors of Hamiltonian graphs","primary_cat":"math.CO","submitted_at":"2026-05-11T22:16:43+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"Large Hamiltonian graphs with minimum degree n to the power 1 minus a small epsilon contain a 2-factor consisting of exactly k cycles.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"yield an analogous result when the host graph is not required to contain a Hamilton cycle, but only a 2-factor consisting of at most 𝑘 cycles; this answers a question of Bucić, Jahn, Pokrovskiy and Sudakov. 1.Introduction AHamilton cyclein a graph 𝐺 is a cycle that goes through every vertex of 𝐺, and a graph is Hamiltonianwhenever it contains a Hamilton cycle. The problem of determining whether a graph is Hamiltonian is famously NP-complete [19], and thus much effort has been devoted to finding simple sufficient conditions for Hamiltonicity. Perhaps the most famous of these is Dirac's condition: his classical theorem from 1952 [ 12] states that every graph 𝐺 on 𝑛≥ 3vertices with minimum degree 𝛿(𝐺) ≥𝑛/2contains a Hamilton cycle, and this minimum-degree condition is best possible, as can be seen by considering a slightly unbalanced complete bipartite graph."},{"citing_arxiv_id":"2605.10941","ref_index":37,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Average-Case Hardness of Binary-Encoded Clique in Proof and Communication Complexity","primary_cat":"cs.CC","submitted_at":"2026-05-11T17:59:43+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Exponential lower bounds for cutting planes and Res(⊕) on binary clique formulas for random dense graphs, with polynomial randomized communication complexity for falsified clause finding.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"threshold value is Θ(n −2/(k−1)). We also define thek-partiteversion of the same distribution: For a fixed partition of the nodes, G(n, p, k) is sampled from by first samplingG∼ G(nk, p) and then intersectingGwith a complete k-partite graph withnnodes in each part. 2.2 Proof Complexity We next recall some basic notions from proof complexity; see, e.g., [37, 11] for a more thorough exposition. A Boolean variablexor its negation xis called aliteral, and a disjunction of literals over pairwise disjoint variablesC=ℓ 1 ∨ · · · ∨ℓk is called aclause. ACNF formulais a conjunction of clausesF=C 1 ∧ · · · ∧C m. We sometimes call the clauses ofFaxioms, and denote the set of variables occurring inFas Vars(F). Cutting Planes."},{"citing_arxiv_id":"2605.09821","ref_index":20,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Online Steiner Forest with Recourse","primary_cat":"cs.DS","submitted_at":"2026-05-10T23:54:46+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"An algorithm for online Steiner forest achieves constant competitiveness with amortized O(log n) recourse.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.08498","ref_index":33,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"MathConstraint: Automated Generation of Verified Combinatorial Reasoning Instances for LLMs","primary_cat":"cs.LG","submitted_at":"2026-05-08T21:28:02+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"MathConstraint generates scalable, automatically verifiable combinatorial problems where LLMs achieve 18.5-66.9% accuracy without tools but roughly double that with solver access.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"[31] Xia Jiang, Jing Chen, Cong Zhang, Jie Gao, Chengpeng Hu, Chenhao Zhang, Yaoxin Wu, and Yingqian Zhang. Reasoning in a combinatorial and constrained world: Benchmarking llms on natural-language combinatorial optimization.arXiv preprint arXiv:2602.02188, 2026. [32] Haocheng Ju and Bin Dong. Ai for mathematics: Progress, challenges, and prospects.arXiv preprint arXiv:2601.13209, 2026. [33] Richard M. Karp.Reducibility among Combinatorial Problems, pages 85-103. Springer US, Boston, MA, 1972. ISBN 978-1-4684-2001-2. doi: 10.1007/978-1-4684-2001-2_9. URL https://doi.org/10.1007/978-1-4684-2001-2_9. [34] Markus Kirchweger and Stefan Szeider. Sat modulo symmetries for graph generation. In27th International Conference on Principles and Practice of Constraint Programming (CP 2021),"},{"citing_arxiv_id":"2605.06123","ref_index":37,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Back to the Beginning of Heuristic Design: Bridging Code and Knowledge with LLMs","primary_cat":"cs.AI","submitted_at":"2026-05-07T12:30:58+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A knowledge-first approach to LLM-driven automatic heuristic design in combinatorial optimization yields better discovery efficiency, transfer, and generalization than code-centric baselines by formalizing a distortion-compression trade-off.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2605.06037","ref_index":22,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"A virtually connected probabilistic computer as a solver for higher-order, densely connected, or reconfigurable combinatorial optimisation problems","primary_cat":"cs.AR","submitted_at":"2026-05-07T11:26:07+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"Simulations predict that a virtually connected photonic probabilistic computer solves Erdos-Renyi graph spin-glass ground states orders of magnitude faster than digital annealing units by avoiding embedding and sparsification.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"For the higher-order set cover problem, we show that this leads to a clear deterioration in solution quality for a fixed number of iterations. Regarding the spin-glass problem, we solve the NP-complete weighted Max-Cut problem on Erd˝os-Rényi graphs with edge weights randomly chosen from {−1,1} , making the results directly relevant to a broad class of computational tasks, that can be expressed through NP-complete reductions [22]. We compare our estimated VCPC performance to findings reported in Ref. [6], arguing that the predicted TTS on the hardware introduced in Ref. [14] would achieve orders of magnitude improvements over those reported for digital annealing. The remainder of this paper is structured as follows. We provide an overview of probabilistic computing in Sec."},{"citing_arxiv_id":"2605.01410","ref_index":17,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Facial diagrams and cycle double cover","primary_cat":"math.CO","submitted_at":"2026-05-02T12:13:31+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"Studying twists of edges in embeddings of cubic graphs yields bounds on the number of singular edges.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.24237","ref_index":5,"ref_count":2,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Computational Complexity of the Interval Ordering Problem","primary_cat":"cs.DS","submitted_at":"2026-04-27T09:46:02+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"Dynamic programming solves interval ordering in O(2^n poly(n)) time via oracle access to f, in polynomial time when f-f(0) is subadditive or superadditive, with a 2^{n-1} lower bound and NP-hardness for some simple f.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.20589","ref_index":41,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"The Mihail-Vazirani conjecture and strong edge-expansion in random $0/1$ polytopes","primary_cat":"math.CO","submitted_at":"2026-04-22T14:08:16+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"Random 0/1 polytopes have edge-expansion Θ(d) whp for p ≤ 1-ε and Ω(d^k) for any k when p ≤ 1/2-ε, verifying the Mihail-Vazirani conjecture in strong form with a phase transition at p=1/2.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2604.10828","ref_index":20,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Maximum Independent Sets in Disk Graphs with Disks in Convex Position","primary_cat":"cs.CG","submitted_at":"2026-04-12T21:49:26+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"O(n^3 log n) algorithm computes maximum (weighted) independent sets for disk graphs with all disks on the convex hull, plus O(n^3 log^2 n) for k-dispersion on the same inputs.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"Anindependent setin a graph is a subset of vertices with no edges between any two of them. The maximum independent set problemasks for an independent set of maximum cardinality. In weighted graphs, where each vertex is assigned a weight, themaximum-weight independent set problemseeks an independent set of maximum total weight. In general graphs, these problems are computationally intractable [20]. This hardness has moti- vated research along two complementary directions. One direction focuses on designing approximation algorithms, which trade exactness for efficiency. The other aims to identify restricted settings, such as specific graph classes or additional structural constraints, under which exact polynomial-time algo- rithms become possible."},{"citing_arxiv_id":"2604.04896","ref_index":19,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Measuring Depth of Matroids","primary_cat":"math.CO","submitted_at":"2026-04-06T17:44:04+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":7.0,"formal_verification":"none","one_line_summary":"A unified framework yields eight depth measures on matroids with six shown functionally inequivalent, two matching branch-depth and tree-depth, and all coinciding on matroids versus matrices over any field.","context_count":1,"top_context_role":"background","top_context_polarity":"background","context_text":"between matroid depth parameters and integer programming, in particular, integer programs of bounded primal tree-depth. ByInteger programming (IP), we mean the following problem: min{f(x)|Ax=v,l≤x≤u,x∈Zn}. Here, A is a Zm×nmatrix (theconstraint matrix), f : Rn→Ra separable convex function (theobjective function), b∈Zm the right-hand side vector, andl,u∈(Z∪{±∞})n the lower and upper bounds. Integer programming is known to beNP-hard [19] in general. However, when the constraint matrix has a certain restricted structure, the problem often becomes tractable. One notable class of integer programs for which tractability has been established is the class of programs whose constraint matrices have bounded tree-depth [21]. Unfortunately, tree-depth as a matrix parameter has the disadvantage that it is not"},{"citing_arxiv_id":"2603.09483","ref_index":13,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"An Integer Linear Programming Model for the Evolomino Puzzle","primary_cat":"math.OC","submitted_at":"2026-03-10T10:37:42+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":5.0,"formal_verification":"none","one_line_summary":"An ILP formulation for Evolomino encodes puzzle rules as linear constraints and supports generation of unique instances, with solver tests up to 18x18 grids.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2507.21883","ref_index":34,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Sampling (noisy) quantum circuits through randomized rounding","primary_cat":"quant-ph","submitted_at":"2025-07-29T14:56:17+00:00","verdict":"CONDITIONAL","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"Gaussian randomized rounding on two-qubit marginals of depth-D circuits with local depolarizing noise p yields samples whose expected Max-Cut cost matches the noisy quantum device up to an approximation ratio of 1-O[(1-p)^D].","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2507.05045","ref_index":5,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"GPU accelerated variant of Schroeppel-Shamir's algorithm for solving the market split problem","primary_cat":"math.OC","submitted_at":"2025-07-07T14:28:43+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":4.0,"formal_verification":"none","one_line_summary":"A hybrid CPU-GPU algorithm derived from Schroeppel-Shamir's subset sum method solves market split feasibility instances with up to 10 constraints and 90 variables, with reported runtimes under 15 minutes for (9,80) and up to one day for (10,90).","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2504.07204","ref_index":4,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"Rounding the Lov\\'asz Theta Function with a Value Function Approximation","primary_cat":"math.OC","submitted_at":"2025-04-09T18:30:14+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":8.0,"formal_verification":"none","one_line_summary":"A new single-SDP rounding method for Lovász theta that provably recovers maximum weighted stable sets in generalized split graphs and other perfect graph subclasses via value function approximation and dynamic programming.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2503.09983","ref_index":22,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"On tropical knapsack-type problems","primary_cat":"math.CO","submitted_at":"2025-03-13T02:48:42+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"NP-completeness of knapsack and subset sum proven for max-plus and max-times matrix semigroups, with pseudo-polynomial and polynomial algorithms demonstrated.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null},{"citing_arxiv_id":"2402.14493","ref_index":35,"ref_count":1,"confidence":0.88,"is_internal_anchor":false,"paper_title":"An Improved Pseudopolynomial Time Algorithm for Subset Sum","primary_cat":"cs.DS","submitted_at":"2024-02-22T12:38:42+00:00","verdict":"UNVERDICTED","verdict_confidence":"LOW","novelty_score":6.0,"formal_verification":"none","one_line_summary":"The authors give an Õ(n + √(wt))-time algorithm for Subset Sum.","context_count":0,"top_context_role":null,"top_context_polarity":null,"context_text":null}],"limit":50,"offset":0}