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The Maximum Happy Induced Subgraph Problem: Bounds and Algorithms
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posted on 2021-01-01, 00:00 authored by R Lewis, Dhananjay ThiruvadyDhananjay Thiruvady, Kerri MorganIn 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.
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Journal
Computers and Operations ResearchVolume
126Article number
105114Pagination
1 - 15Publisher
ElsevierLocation
Amsterdam, The NetherlandsPublisher DOI
ISSN
0305-0548Language
engPublication classification
C1 Refereed article in a scholarly journalUsage metrics
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