Solving Robust Variants of the Maximum Weighted Independent Set Problem on Trees

Ana Klobučar,Robert Manger

doi:10.3390/math8020285

Abstract

This paper deals with the maximum weighted independent set (MWIS) problem. We consider several robust variants of the MWIS problem on trees and prove that most of them are NP-hard. We propose a heuristic for solving the considered robust MWIS variants, which is customized for trees. We demonstrate by experiments that our algorithm produces high-quality solutions and runs much faster than a general-purpose optimization software.

Highlights

The maximum weighted independent set (MWIS) problem is posed in a graph in which vertices have nonnegative weights
With the above three theorems, we have proved that the absolute robust variant and the robust deviation variants of the MWIS problem on trees are NP-hard
We will present the results of experimental evaluation of our population algorithm from Section 4. It would be nice if we could test the algorithm on some well-known benchmark problem instances for robust variants of the MWIS problem

Summary

Introduction

The maximum weighted independent set (MWIS) problem is posed in a graph in which vertices have nonnegative weights. The problem consists of finding a subset of graph vertices that are not adjacent to each other and in which the sum of weights is as large as possible. The conventional MWIS problem is NP-hard in general [1], it still can be solved in polynomial time on some special classes of graphs, such as trees or interval graphs or apple-free graphs. The paper [2] specifies an algorithm for trees with linear complexity in terms of number of vertices. In Reference [3,4,5,6,7] we can find polynomial-time algorithms for interval or apple-free graphs

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Conclusion