On Load-Balanced Semi-matchings for Weighted Bipartite Graphs

  • Chor Ping Low
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3959)


A semi-matching on a bipartite graph G=(UV, 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 vV 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.


semi-matching bipartite graphs load balancing NP-hard approximation algorithm 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Chor Ping Low
    • 1
  1. 1.School of Electrical and Electronic EngineeringNanyang Technological UniversitySingapore

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