Minimum Eccentricity Shortest Path Problem: An Approximation Algorithm and Relation with the k-Laminarity ProblemReport as inadecuate




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1 MAP5 - MAP5 - Mathématiques Appliquées à Paris 5 2 GANG - Networks, Graphs and Algorithms IRIF - Institut de Recherche en Informatique Fondamentale, Inria de Paris 3 IRIF - Institut de Recherche en Informatique Fondamentale

Abstract : The Minimum Eccentricity Shortest Path MESP Problem consists in determining a shortest path a path whose length is the distance between its extremities of minimum eccentricity in a graph. It was introduced by Dragan and Leitert 9 who described a linear-time algorithm which is an 8-approximation of the problem. In this paper, we study deeper the double-BFS procedure used in that algorithm and extend it to obtain a linear-time 3-approximation algorithm. We moreover study the link between the MESP problem and the notion of laminarity, introduced by Völkel et al 12, corresponding to its restriction to a diameter i.e. a shortest path of maximum length, and show tight bounds between MESP and laminarity parameters.

Keywords : BFS Eccentricity Diameter Graph theory Graph search Approximation Algorithms k-Laminar Graph





Author: Étienne Birmelé - Fabien De Montgolfier - Léo Planche -

Source: https://hal.archives-ouvertes.fr/



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