A General Label Search to investigate classical graph search algorithms

Authors:
R. Krueger;G. Simonet;A. Berry
Affiliations:
Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 3G4;LIRMM, Univ. Montpellier 2, CNRS, 161, Rue Ada, F-34392 Montpellier, France;LIMOS, Ensemble scientifique des Cézeaux, F-63177 Aubière, France
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

Many graph search algorithms use a labeling of the vertices to compute an ordering of the vertices. We generalize this idea by devising a general vertex labeling algorithmic process called General Label Search (GLS), which uses a labeling structure which, when specified, defines specific algorithms. We characterize the vertex orderings computable by the basic types of searches in terms of properties of their associated labeling structures. We then consider performing graph searches in the complement without computing it, and provide characterizations for some searches, but show that for some searches such as the basic Depth-First Search, no algorithm of the GLS family can exactly find all the orderings of the complement. Finally, we present some implementations and complexity results of GLS on a graph and on its complement.