2021/11/09 by Amitabh Basu, Basu, Amitabh, Tongtong Chen +5
Computer Science · Engineering · #68Q17 #68Q25 #90C11 #90C26 #90C57 #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #F.2.0 #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2111.05225
openalex publication_date 2021/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Inspired by branch-and-bound and cutting plane proofs in mixed-integer optimization and proof complexity, we develop a general approach via Hoffman's Helly systems. This helps to distill the main ideas behind optimality and infeasibility certificates in optimization. The first part of the paper formalizes the notion of a certificate and its size in this general setting. The second part of the paper establishes lower and upper bounds on the sizes of these certificates in various different settings. We show that some important techniques existing in the literature are purely combinatorial in nature and do not depend on any underlying geometric notions.