Local search with dynamic-threshold configuration checking and incremental neighborhood updating for maximum k-plex problem

Abstract

The Maximum k-plex Problem is an important combinatorial optimization problem with increasingly wide applications. In this paper, we propose a novel strategy, named Dynamicthreshold Configuration Checking (DCC), to reduce the cycling problem of local search. Due to the complicated neighborhood relations, all the previous local search algorithms for this problem spend a large amount of time in identifying feasible neighbors in each step. To further improve the performance on dense and challenging instances, we propose Double-attributes Incremental Neighborhood Updating (DINU) scheme which reduces the worst-case time complexity per iteration from O(|V | · ΔG) to O(k · ΔG). Based on DCC strategy and DINU scheme, we develop a local search algorithm named DCCplex. According to the experiment result, DCCplex shows promising result on DIMACS and BHOSLIB benchmark as well as real-world massive graphs. Especially, DCCplex updates the lower bound of the maximum k-plex for most dense and challenging instances.