Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Faster scaling algorithms for network problems
SIAM Journal on Computing
SIAM Journal on Computing
Approximation algorithms for bipartite and non-bipartite matching in the plane
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Vertical Decomposition of Shallow Levels in 3-Dimensional Arrangements and Its Applications
SIAM Journal on Computing
A near-linear constant-factor approximation for euclidean bipartite matching?
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
A near linear time constant factor approximation for Euclidean bichromatic matching (cost)
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for the transportation problem in geometric settings
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A near-linear time ε-approximation algorithm for geometric bipartite matching
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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Let A, B ∈ [Δ]2, |A|=|B|=n, be point sets where each point has a positive integer coordinate bounded by Δ. For an arbitrary small constant δ 0, we design an algorithm to compute a minimum-cost Euclidean bipartite matching of A,B in O(n{3/2+δlog (nΔ)) time; all previous exact algorithms for the Euclidean bipartite matching, even when the point sets have bounded integer coordinates take Ω(n2) time. First, we compute in O(n{3/2+δlog nΔ) time, a candidate set Ε ⊆ A x B such that M* ⊆ Ε and the graph G(A∪B, Ε) is planar; here M* is a minimum-cost matching of A and B. Next, we compute M* from this weighted bipartite planar graph in O(n3/2log n) using the algorithm described in [6].