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 wmin , (2−ε)}-approximation algorithm for the general case, where w max and w min are the maximum and the minimum weights of edges, respectively, and ε is some small positive real number that depends on the input.
They build on the work of Venkateswaran and give a combinatorial { wmax w min , (2− )}-approximation algorithm where w max and w min are the maximum and minimum weights of edges respectively, and is a constant which depends on the input REF .
Graph Orientation Algorithms to Minimize the Maximum Outdegree
CATS
Mathematics Computer Science