Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Computational geometry: an introduction
Computational geometry: an introduction
A sweepline algorithm for Voronoi diagrams
SCG '86 Proceedings of the second annual symposium on Computational geometry
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
An Efficient Implementation of Edmonds' Algorithm for Maximum Matching on Graphs
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Solving query-retrieval problems by compacting Voronoi diagrams
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Faster scaling algorithms for general graph matching problems
Journal of the ACM (JACM)
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
High-performance clock routing based on recursive geometric matching
DAC '91 Proceedings of the 28th ACM/IEEE Design Automation Conference
New techniques for some dynamic closest-point and farthest-point problems
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Robust Character Image Retrieval Method Using Bipartite Matching and Pseudo-bipartite Matching
AISA '02 Proceedings of the First International Workshop on Advanced Internet Services and Applications
Limitations of passive protection of quantum information
Quantum Information & Computation
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Non-crossing matchings of points with geometric objects
Computational Geometry: Theory and Applications
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A set of 2n points on the plane induces a complete weighted undirected graph as follows: The points are the vertices of the graph and the weight of an edge between any two points is the distance between the points under some metric. We study the problem of finding a minimum weight complete matching (MWCM) in such a graph. We give an &Ogr;(n23 (logn)4) algorithm for finding an MWCM in such a graph, for the L1 (manhattan), the L2 (euclidean), and the L∞ metrics. We also study the bipartite version of the problem, where half the points are painted with one color and the other half are painted with another color, and the restriction is that a point of one color may be matched only to a point of another color. We present an &Ogr;(n2.5 logn) algorithm for the bipartite version, for the L1, L2, and L∞, metrics. The running time for the bipartite version can be further improved to &Ogr;(n2 (logn)3) for the L1 and L∞ metrics.