On Tradeoffs Between Width- and Fill-like Graph Parameters - Publication - MOST Wiedzy


On Tradeoffs Between Width- and Fill-like Graph Parameters


In this work we consider two two-criteria optimization problems: given an input graph, the goal is to find its interval (or chordal) supergraph that minimizes the number of edges and its clique number simultaneously. For the interval supergraph, the problem can be restated as simultaneous minimization of the path width pw(G) and the profile p(G) of the input graph G. We prove that for an arbitrary graph G and an integer t ∈ {1, … , pw(G) + 1}, there exists an interval supergraph G′ of G such that for its clique number it holds ω(G′)≤(1+2t)(pw(G)+ 1) and the number of its edges is bounded by |E(G′)| ≤ (t + 2)p(G). In other words, the pathwidth and the profile of a graph can be simultaneously minimized within the factors of 1+2t (plus a small constant) and t + 2, respectively. Note that for a fixed t, both upper bounds provide constant factor approximations. On the negative side, we show an example that proves that, for some graphs, there is no solution in which both parameters are optimal. In case of finding a chordal supergraph, the two corresponding graph parameters that reflect its clique size and number of edges are the treewidth and fill-in. We obtain that the treewidth and the fill-in problems are also ‘orthogonal’ in the sense that for some graphs, a solution that minimizes one of those parameters cannot minimize the other. As a motivating example, we recall graph searching games which illustrates a need of simultaneous minimization of these pairs of graph parameters.


  • 0


  • 0

    Web of Science

  • 0



artykuł w czasopiśmie wyróżnionym w JCR
Published in:
THEORY OF COMPUTING SYSTEMS no. 63, pages 450 - 465,
ISSN: 1432-4350
Publication year:
Bibliographic description:
Dereniowski D., Stański A.: On Tradeoffs Between Width- and Fill-like Graph Parameters// THEORY OF COMPUTING SYSTEMS. -Vol. 63, iss. 3 (2019), s.450-465
Digital Object Identifier (open in new tab) 10.1007/s00224-018-9882-1
Verified by:
Gdańsk University of Technology

seen 12 times

Recommended for you

Meta Tags