Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Faster scaling algorithms for network problems
SIAM Journal on Computing
SIAM Journal on Computing
Faster scaling algorithms for general graph matching problems
Journal of the ACM (JACM)
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Geometric matching under noise: combinatorial bounds and algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
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
Approximate congruence in nearly linear time
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
A Divide-and-Conquer Algorithm for Min-Cost Perfect Matching in the Plane
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
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
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Perfect matchings in o(n log n) time in regular bipartite graphs
Proceedings of the forty-second ACM symposium on Theory of computing
Approximating Maximum Weight Matching in Near-Linear Time
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Algorithms for the transportation problem in geometric settings
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A sub-quadratic algorithm for bipartite matching of planar points with bounded integer coordinates
Proceedings of the twenty-ninth annual symposium on Computational geometry
Linear-Time Approximation for Maximum Weight Matching
Journal of the ACM (JACM)
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For point sets A,B ⊂ Rd, |A|=|B|=n, and for a parameter ε 0, we present an algorithm that computes, in O(n poly(log n, 1/ε)) time, an ε-approximate perfect matching of A and B with high probability; the previously best known algorithm takes Ω(n3/2) time. We approximate the Lp-norm using a distance function, d(•,•) based on a randomly shifted quad-tree. The algorithm iteratively generates an approximate minimum-cost augmenting path under d(•,•) in time proportional to the length of the path. We show that the total length of the augmenting paths generated by the algorithm is O((n/ε)log n), implying that the running time of our algorithm is O(n poly(log n,1/ε)).