TY - JOUR
T1 - Graph orientation algorithms to minimize the maximum outdegree
AU - Asahiro, Yuichi
AU - Miyano, Eiji
AU - Ono, Hirotaka
AU - Zenmyo, Kouhei
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 -