Finding the ℓ-core of a tree

Authors:
Ronald I. Becker;Yen I. Chang;Isabella Lari;Andrea Scozzari;Giovanni Storchi
Affiliations:
Department of Mathematics, University of Cape Town, Rondebosh 7700, South Africa and Technion, Haifa, Haifa, Israel;Department of Mathematics, University of Cape Town, Rondebosh 7700, South Africa;Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma "La Sapienza" P.le A. Moro 5, 00185 Roma, Italy;Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma "La Sapienza" P.le A. Moro 5, 00185 Roma, Italy;Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma "La Sapienza" P.le A. Moro 5, 00185 Roma, Italy
Venue:
Discrete Applied Mathematics - Special issue: Third ALIO-EURO meeting on applied combinatorial optimization
Year:
2002

Citing 2
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Abstract

An l-core of a tree T = (V,E) with |V|= n, is a path P with length at most ℓ that is central with respect to the property of minimizing the sum of the distances from the vertices in P to all the vertices of T not in P. The distance between two vertices is the length of the shortest path joining them. In this paper we present efficient algorithms for finding the ℓ-core of a tree. For unweighted trees we present an O(nℓ) time algorithm, while for weighted trees we give a procedure with time complexity of O(nlog2n). The algorithms use two different types of recursive principle in their operation.