Happy Set Problem on Subclasses of Co-comparability Graphs

Research output: Contribution to journalArticlepeer-review


In this paper, we investigate the complexity of the Maximum Happy Set problem on subclasses of co-comparability graphs. For a graph G and its vertex subset S, a vertex v∈ S is happy if all v’s neighbors in G are contained in S. Given a graph G and a non-negative integer k, Maximum Happy Set is the problem of finding a vertex subset S of G such that | S| = k and the number of happy vertices in S is maximized. In this paper, we first show that Maximum Happy Set is NP-hard even for co-bipartite graphs. We then give an algorithm for n-vertex interval graphs whose running time is O(n2+ k3n) ; this improves the best known running time O(kn8) for interval graphs. We also design algorithms for n-vertex permutation graphs and d-trapezoid graphs which run in O(n2+ k3n) and O(n2+ d2(k+ 1) 3dn) time, respectively. These algorithmic results provide a nice contrast to the fact that Maximum Happy Set remains NP-hard for chordal graphs, comparability graphs, and co-comparability graphs.

Original languageEnglish
Publication statusAccepted/In press - 2022


  • Co-comparability graphs
  • Graph algorithm
  • Happy set problem
  • Interval graphs
  • Permutation graphs
  • d-trapezoid graphs

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics


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