TY - JOUR

T1 - Graph orientation algorithms to minimize the maximum outdegree

AU - Asahiro, Yuichi

AU - Miyano, Eiji

AU - Ono, Hirotaka

AU - Zenmyo, Kouhei

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2007/4

Y1 - 2007/4

N2 - This paper studies the problem of orienting all edges of a weighted graph such that the maximum weighted outdegree of vertices is minimized. This problem, which has applications in the guard arrangement for example, can be shown to be AP-hard generally. In this paper we first give optimal orientation algorithms which run in polynomial time for the following special cases: (i) the input is an unweighted graph, and (ii) the input graph is a tree. Then, by using those algorithms as sub-procedures, we provide a simple, combinatorial, min{w max/wmin, (2 - ε)}-approximation algorithm for the general case, where wmax and wmin are the maximum and the minimum weights of edges, respectively, and ε is some small positive real number that depends on the input.

AB - This paper studies the problem of orienting all edges of a weighted graph such that the maximum weighted outdegree of vertices is minimized. This problem, which has applications in the guard arrangement for example, can be shown to be AP-hard generally. In this paper we first give optimal orientation algorithms which run in polynomial time for the following special cases: (i) the input is an unweighted graph, and (ii) the input graph is a tree. Then, by using those algorithms as sub-procedures, we provide a simple, combinatorial, min{w max/wmin, (2 - ε)}-approximation algorithm for the general case, where wmax and wmin are the maximum and the minimum weights of edges, respectively, and ε is some small positive real number that depends on the input.

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U2 - 10.1142/S0129054107004644

DO - 10.1142/S0129054107004644

M3 - Article

AN - SCOPUS:34247237820

VL - 18

SP - 197

EP - 215

JO - International Journal of Foundations of Computer Science

JF - International Journal of Foundations of Computer Science

SN - 0129-0541

IS - 2

ER -