Graph Orientation Algorithms to Minimize the Maximum Outdegree

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 NP-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 wmin , (2-)}-approximation algorithm for the general case, where wmax and wmin are the maximum and the minimum weights of edges, respectively, and is some small positive real number that depends on the input.

• Type: Conference
• Year: 2006
• Where: CATS
• Authors: Yuichi Asahiro, Eiji Miyano, Hirotaka Ono, Kouhei Zenmyo
• Keywords: CATS 2006, CATS 2007, Maximum Weighted Outdegree, Optimal Orientation Algorithms, Weighted Graph