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Block decomposition approach to compute a minimum geodetic set∗∗∗

Published online by Cambridge University Press:  10 June 2014

Tınaz Ekim  and
Aysel Erey
Tınaz Ekim
Affiliation:
Boğaziçi University, Department of Industrial Engineering, 34342 Bebek, Istanbul, Turkey.. tinaz.ekim@boun.edu.tr
Aysel Erey
Affiliation:
Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia B3H 3J5, Canada.; eaysel@mathstat.dal.ca
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Abstract

In this paper, we develop a divide-and-conquer approach, called block decomposition, to solve the minimum geodetic set problem. This provides us with a unified approach for all graphs admitting blocks for which the problem of finding a minimum geodetic set containing a given set of vertices (g-extension problem) can be efficiently solved. Our method allows us to derive linear time algorithms for the minimum geodetic set problem in (a proper superclass of) block-cacti and monopolar chordal graphs. Also, we show that hull sets and geodetic sets of block-cacti are the same, and the minimum geodetic set problem is NP-hard in cobipartite graphs. We conclude by pointing out several interesting research directions.

Keywords

Convexitygeodetic sethull setgraph classes
Type
Research Article
Information
RAIRO - Operations Research , Volume 48 , Issue 4 , October 2014 , pp. 497 - 507
Copyright
© EDP Sciences, ROADEF, SMAI 2014

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