2024/05/02 by Yasuko Matsui, Matsui, Yasuko, Takeshi Naitoh +3
Engineering · #Advanced Numerical Analysis Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #G.2.1 #Optimization and Packing Problems #Scheduling and Optimization Algorithms
paper · pdf · doi:10.48550/arxiv.2405.01039
openalex publication_date 2024/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Efficiently enumerating all the extreme points of a polytope identified by a system of linear inequalities is a well-known challenge issue.We consider a special case and present an algorithm that enumerates all the extreme points of a bisubmodular polyhedron in O(n4|V|) time and O(n2) space complexity, where n is the dimension of underlying space and V is the set of outputs. We use the reverse search and signed poset linked to extreme points to avoid the redundant search. Our algorithm is a generalization of enumerating all the extreme points of a base polyhedron which comprises some combinatorial enumeration problems.