Abstract
A semi-matching on a bipartite graph G=(U ∪ V, E) is a set of edges X ⊆ E such that each vertex in U is incident to exactly one edge in X. The sum of the weights of the vertices from U that are assigned (semi-matched) to some vertex v ∈ V is referred to as the load of vertex v. In this paper, we consider the problem to finding a semi-matching that minimizes the maximum load among all vertices in V. This problem has been shown to be solvable in polynomial time by Harvey et. al [3] and Fakcharoenphol et. al [5] for unweighted graphs. However, the computational complexity for the weighted version of the problem was left as an open problem. In this paper, we prove that the problem of finding a semi-matching that minimizes the maximum load among all vertices in a weighted bipartite graph is NP-complete. A \(\frac{3}{2}\)-approximation algorithm is proposed for this problem.
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Low, C.P. (2006). On Load-Balanced Semi-matchings for Weighted Bipartite Graphs. In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_15
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DOI: https://doi.org/10.1007/11750321_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34021-8
Online ISBN: 978-3-540-34022-5
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