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Block decomposition approach to compute a minimum geodeticset∗∗∗

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.. [email protected]
Aysel Erey
Affiliation:
Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia B3H 3J5, Canada.; [email protected]
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Abstract

In this paper, we develop a divide-and-conquer approach, called block decomposition, tosolve the minimum geodetic set problem. This provides us with a unified approach for allgraphs admitting blocks for which the problem of finding a minimum geodetic set containinga given set of vertices (g-extension problem) can be efficiently solved. Ourmethod 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 hullsets and geodetic sets of block-cacti are the same, and the minimum geodetic set problemis NP-hard in cobipartite graphs. We conclude by pointing out several interesting researchdirections.

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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