Journal of Graph Algorithms and Applications
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Graph Orientations Optimizing the Number of Light or Heavy Vertices
Vol. 19, no. 1, pp. 441-465, 2015. Regular paper.
Abstract This paper introduces four graph orientation problems named MAXIMIZE W-LIGHT, MINIMIZE W-LIGHT, MAXIMIZE W-HEAVY, and MINIMIZE W-HEAVY, where W can be any fixed non-negative integer. In each problem, the input is an undirected, unweighted graph G and the objective is to assign a direction to every edge in G so that the number of vertices with outdegree at most W or at least W in the resulting directed graph is maximized or minimized. A number of results on the computational complexity and polynomial-time approximability of these problems for different values of W and various special classes of graphs are derived. In particular, it is shown that MAXIMIZE 0-LIGHT and MINIMIZE 1-HEAVY are identical to MAXIMUM INDEPENDENT SET and MINIMUM VERTEX COVER, respectively, so by allowing the value of W to vary, we obtain a new generalization of the two latter problems.
Submitted: May 2014.
Reviewed: July 2015.
Revised: August 2015.
Accepted: September 2015.
Final: September 2015.
Published: October 2015.
Communicated by Ken-ichi Kawarabayashi