NuMVC: An Efficient Local Search Algorithm for Minimum Vertex Cover

02/04/2014
by   Shaowei Cai, et al.
0

The Minimum Vertex Cover (MVC) problem is a prominent NP-hard combinatorial optimization problem of great importance in both theory and application. Local search has proved successful for this problem. However, there are two main drawbacks in state-of-the-art MVC local search algorithms. First, they select a pair of vertices to exchange simultaneously, which is time-consuming. Secondly, although using edge weighting techniques to diversify the search, these algorithms lack mechanisms for decreasing the weights. To address these issues, we propose two new strategies: two-stage exchange and edge weighting with forgetting. The two-stage exchange strategy selects two vertices to exchange separately and performs the exchange in two stages. The strategy of edge weighting with forgetting not only increases weights of uncovered edges, but also decreases some weights for each edge periodically. These two strategies are used in designing a new MVC local search algorithm, which is referred to as NuMVC. We conduct extensive experimental studies on the standard benchmarks, namely DIMACS and BHOSLIB. The experiment comparing NuMVC with state-of-the-art heuristic algorithms show that NuMVC is at least competitive with the nearest competitor namely PLS on the DIMACS benchmark, and clearly dominates all competitors on the BHOSLIB benchmark. Also, experimental results indicate that NuMVC finds an optimal solution much faster than the current best exact algorithm for Maximum Clique on random instances as well as some structured ones. Moreover, we study the effectiveness of the two strategies and the run-time behaviour through experimental analysis.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/19/2015

Exploiting Reduction Rules and Data Structures: Local Search for Minimum Vertex Cover in Massive Graphs

The Minimum Vertex Cover (MinVC) problem is a well-known NP-hard problem...
research
07/25/2023

A Dual-mode Local Search Algorithm for Solving the Minimum Dominating Set Problem

Given a graph, the minimum dominating set (MinDS) problem is to identify...
research
10/29/2020

A Local Search Framework for Experimental Design

We present a local search framework to design and analyze both combinato...
research
09/26/2011

Dynamic Local Search for the Maximum Clique Problem

In this paper, we introduce DLS-MC, a new stochastic local search algori...
research
08/16/2022

An Adaptive Repeated-Intersection-Reduction Local Search for the Maximum Independent Set Problem

The maximum independent set (MIS) problem, a classical NP-hard problem w...
research
02/27/2020

Improving the Performance of Stochastic Local Search for Maximum Vertex Weight Clique Problem Using Programming by Optimization

The maximum vertex weight clique problem (MVWCP) is an important general...
research
01/24/2022

An Effective Iterated Two-stage Heuristic Algorithm for the Multiple Traveling Salesmen Problem

The multiple Traveling Salesmen Problem mTSP is a general extension of t...

Please sign up or login with your details

Forgot password? Click here to reset