NDLI: A divide-and-conquer algorithm for min-cost perfect matching in the plane

Content Provider	IEEE Xplore Digital Library
Author	Varadarajan, K.R.
Copyright Year	1998
Description	Author affiliation: Dept. of Comput. Sci., Duke Univ., Durham, NC, USA (Varadarajan, K.R.)
Abstract	Given a set V of 2n points in the plane, the min-cost perfect matching problem is to pair up the points (into n pairs) so that the sum of the Euclidean distances between the paired points is minimized. We present an O(n/sup 3/2/log/sup 5/ n)-time algorithm for computing a min-cost perfect matching in the plane, which is an improvement over the previous best algorithm of Vaidya [1989) by nearly a factor of n. Vaidya's algorithm is an implementation of the algorithm of Edmonds (1965), which runs in n phases, and computes a matching with i edges at the end of the i-th phase. Vaidya shows that geometry can be exploited to implement a single phase in roughly O(n/sup 3/2/) time, thus obtaining an O(n/sup 5/2/log/sup 4/ n)-time algorithm. We improve upon this in two major ways. First, we develop a variant of Edmonds algorithm that uses geometric divide-and-conquer, so that in the conquer step we need only O(/spl radic/n) phases. Second, we show that a single phase can be implemented in O(n log/sup 5/ n) time.
Starting Page	320
Ending Page	329
File Size	176827
Page Count	10
File Format	PDF
ISBN	0818691727
ISSN	02725428
DOI	10.1109/SFCS.1998.743466
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1998-11-08
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Costs Geometry Electrical capacitance tomography Programmable logic arrays Euclidean distance Computer science Application software Operations research Pattern recognition Statistics
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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