Abstract
A degree-constrained graph orientation of an undirected graph G is an assignment of a direction to each edge in G such that the outdegree of every vertex in the resulting directed graph satisfies a specified lower and/or upper bound. Such graph orientations have been studied for a long time and various characterizations of their existence are known. In this paper, we consider four related optimization problems introduced in [4]: For any fixed non-negative integer W, the problems Max W -Light, Min W -Light, Max W -Heavy, and Min W -Heavy take as input an undirected graph G and ask for an orientation of G that maximizes or minimizes the number of vertices with outdegree at most W or at least W. The problems’ computational complexities vary with W. Here, we resolve several open questions related to their polynomial-time approximability and present a number of positive and negative results.
Supported by KAKENHI Grant Numbers 21680001, 23500020, 25104521, and 25330018 and The Hakubi Project at Kyoto University.
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Asahiro, Y., Jansson, J., Miyano, E., Ono, H. (2014). Degree-Constrained Graph Orientation: Maximum Satisfaction and Minimum Violation. In: Kaklamanis, C., Pruhs, K. (eds) Approximation and Online Algorithms. WAOA 2013. Lecture Notes in Computer Science, vol 8447. Springer, Cham. https://doi.org/10.1007/978-3-319-08001-7_3
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DOI: https://doi.org/10.1007/978-3-319-08001-7_3
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