A linear time randomized approximation algorithm for Euclidean matching

We study the problem of computing Euclidean minimum weight matching which investigates the minimum weight perfect matching in a complete geometric graph on a set of 2 n points in the plane. We propose a simple randomized approximation algorithm based on the geometrical aspect of the problem with O (...

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Published in:The Journal of supercomputing Vol. 75; no. 5; pp. 2648 - 2664
Main Authors: Imanparast, Mahdi, Hashemi, Seyed Naser
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2019
Springer Nature B.V
Subjects:
Algorithms
Approximation
Compilers
Computer Science
Euclidean geometry
Interpreters
Matching
Mathematical analysis
Minimum weight
Processor Architectures
Programming Languages
Randomization
Approximation algorithms
Point sets
Hash table
Expected time
Euclidean matching
ISSN:0920-8542, 1573-0484
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Abstract We study the problem of computing Euclidean minimum weight matching which investigates the minimum weight perfect matching in a complete geometric graph on a set of 2 n points in the plane. We propose a simple randomized approximation algorithm based on the geometrical aspect of the problem with O ( n ) expected time. The proposed algorithm computes a matching within at most 3 factors of the optimal solution. We also do some experimental tests to evaluate the performance of the proposed algorithm which indicate the efficiency of the proposed algorithm in finding the approximate matching in the practice.
AbstractList We study the problem of computing Euclidean minimum weight matching which investigates the minimum weight perfect matching in a complete geometric graph on a set of 2 n points in the plane. We propose a simple randomized approximation algorithm based on the geometrical aspect of the problem with O ( n ) expected time. The proposed algorithm computes a matching within at most 3 factors of the optimal solution. We also do some experimental tests to evaluate the performance of the proposed algorithm which indicate the efficiency of the proposed algorithm in finding the approximate matching in the practice.
We study the problem of computing Euclidean minimum weight matching which investigates the minimum weight perfect matching in a complete geometric graph on a set of 2n points in the plane. We propose a simple randomized approximation algorithm based on the geometrical aspect of the problem with O(n) expected time. The proposed algorithm computes a matching within at most 3 factors of the optimal solution. We also do some experimental tests to evaluate the performance of the proposed algorithm which indicate the efficiency of the proposed algorithm in finding the approximate matching in the practice.
Author Imanparast, Mahdi
Hashemi, Seyed Naser
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CitedBy_id crossref_primary_10_1016_j_petrol_2020_107934
crossref_primary_10_1155_2023_7761902
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Point sets
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Euclidean matching
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Snippet We study the problem of computing Euclidean minimum weight matching which investigates the minimum weight perfect matching in a complete geometric graph on a...
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SubjectTerms Algorithms
Approximation
Compilers
Computer Science
Euclidean geometry
Interpreters
Matching
Mathematical analysis
Minimum weight
Processor Architectures
Programming Languages
Randomization
Title A linear time randomized approximation algorithm for Euclidean matching
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