Geometric algorithms for the minimum cost assignment problem

Authors:
Takeshi Tokuyama;Jun Nakano
Affiliations:
IBM Research, Tokyo Research Laboratory, 1623‐14, Shimo‐tsuruma, Yamato‐shi, Kanagawa 242, Japan;IBM Research, Tokyo Research Laboratory, 1623‐14, Shimo‐tsuruma, Yamato‐shi, Kanagawa 242, Japan
Venue:
Random Structures & Algorithms
Year:
1995

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Abstract

We consider the minimum‐cost λ‐assignment problem, which is equivalent to the minimum‐weight one‐to‐many matching problem on a complete bipartite graph Γ = (A, B), where A and B have n and k nodes (n ⩾ k), respectively. Formulating the problem geometrically, we given an O(kn + k2.5n0.5 log1.5 n) time randomized algorithm, which is better than the existing O(kn2 + n2 log n) time algorithm if n k log k. © 1995 Wiley Periodicals, Inc.