arXiv:2608. 16861v1 Announce Type: cross Abstract: We initiate a polyhedral study of the graph multi-separator problem proposed by Irmai et al.
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arXiv:2607. 29555v1 Announce Type: new Abstract: Lacoste-Julien and Jaggi conjectured in 2015 that the pyramidal width of a polytope cannot increase when a vertex is added, provided that every old point remains a vertex.
arXiv:2606. 29477v1 Announce Type: cross Abstract: The specification number $\sigma_n(f)$ of a Boolean threshold function $f$ on $n$ variables is the least number of points whose $f$-values determine $f$ uniquely among all threshold functions.
arXiv:2608. 14396v1 Announce Type: cross Abstract: The alternating direction method of multipliers (ADMM), as a landmark algorithm, has attracted tremendous research attention and extensive practical applications over the past two decades.
The paper introduces a path‑closed framework for realizing independence systems via zero‑cost choices of primary terminals in directed acyclic flow instances, extending the triangle mechanism to all finite loopless independence systems. It shows that such systems, including all finite simple graphs and hypergraph independence systems without singleton forbidden hyperedges, admit polynomial‑size realizations measured by the incidence size of minimal forbidden sets. The authors further specialize to odd cycles, deriving a rational family that yields a fractional cheap‑selection vector violating the odd‑cycle inequality and establishing an exact additive‑congestion threshold that approaches 1/2 for large cycles.
arXiv:2410. 04907v2 Announce Type: replace-cross Abstract: In this paper we contribute to the frequently studied question of how to decompose a continuous piecewise linear (CPWL) function into a difference of two convex CPWL functions.
The paper investigates the maximum strong independent set problem in finite hypergraphs, where the goal is to find the largest vertex set that intersects each hyperedge in at most one vertex. It introduces an incidence-structural toolkit, proving exact reductions for dominance, incidence twins, and weight‑1 blocks, and derives closed‑form and low‑weight upper bounds. The authors also present puncturing and covering certificates that refine these bounds and analyze a layered greedy clustering algorithm driven by block weights and residual incidence, providing feasibility, maximality, conditional optimality, and incidence‑local complexity guarantees.