2015/03/28 by Konstanty Junosza-Szaniawski, Junosza-Szaniawski, Konstanty, Michał Tuczyński +1
Computer Science · Mathematics · #05C15 #Advanced Graph Theory Research #Combinatorics (math.CO) #Complexity and Algorithms in Graphs #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #G.1.2 #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1503.08323
openalex publication_date 2015/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we give an algorithm for counting the number of all independent sets in a given graph which works in time O^*(1.1394n) for subcubic graphs and in time O^*(1.2369n) for general graphs, where n is the number of vertices in the instance graph, and polynomial space. The result comes from combining two well known methods "Divide and Conquer" and "Measure and Conquer". We introduce this new concept of Divide, Measure and Conquer method and expect it will find applications in other problems. The algorithm of Björklund, Husfeldt and Koivisto for graph colouring with our algorithm used as a subroutine has complexity O^*(2.2369n) and is currently the fastest graph colouring algorithm in polynomial space.