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The Maximum Happy Induced Subgraph Problem: Bounds and Algorithms

journal contribution
posted on 2021-01-01, 00:00 authored by R Lewis, Dhananjay ThiruvadyDhananjay Thiruvady, Kerri Morgan
In this paper we consider a combinatorial optimisation problem that takes as input a graph in which some of the vertices have been preassigned to colours. The aim is to then identify the largest induced subgraph in which all remaining vertices are able to assume the same colour as all of their neighbours. This problem shares similarities with the graph colouring problem, vertex cut problems, and the maximum happy vertices problem. It is NP-hard in general. In this paper we derive a number of upper and lower bounds and also show how certain problem instances can be broken up into smaller subproblems. We also propose one exact and two heuristic algorithms for this problem and use these to investigate the factors that make some problem instances more difficult to solve than others.

History

Journal

Computers and Operations Research

Volume

126

Article number

105114

Pagination

1 - 15

Publisher

Elsevier

Location

Amsterdam, The Netherlands

ISSN

0305-0548

Language

eng

Publication classification

C1 Refereed article in a scholarly journal