by Yuichi Asahiro, Eiji Miyano, Hirotaka Ono, Kouhei Zenmyo
http://crpit.com/confpapers/CRPITV51Asahiro.pdf
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Abstract:
We study the problem of orienting the 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 N P-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, or more generally, a graph with identically weighted edges, and (ii) the input graph is a tree. Then, by using those algorithms as sub-procedures, we provide a simple, combinatorial, min { wmax, (2−ε)}-approximation wmin 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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