NDLI: A Simpler Max-Product Maximum Weight Matching Algorithm and the Auction Algorithm

Content Provider	IEEE Xplore Digital Library
Author	Bayati, M. Shah, D. Sharma, M.
Copyright Year	2006
Description	Author affiliation: Dept. of EE, Stanford Univ., CA (Bayati, M.)
Abstract	The max-product "belief propagation" algorithm has received a lot of attention recently due to its spectacular success in many application areas such as iterative decoding, computer vision and combinatorial optimization. There is a lot of ongoing work investigating the theoretical properties of the algorithm. In our previous work (2005) we showed that the max-product algorithm can be used to solve the problem of finding the maximum weight matching (MWM) in a weighted complete bipartite graph. However, for a graph with n nodes the max-product algorithm requires $O(n^{4})$ operations to find the MWM compared to $O(n^{3})$ for best known algorithms such as those proposed by Edmonds and Karp (1972) and Bertsekas (1988). In this paper, we simplify the max-product algorithm to reduce the number of operations required to $O(n^{3}).$ The simplified algorithm has very similar dynamics to the well-known auction algorithm of Bertsekas (1988). To make this connection precise, we show that the max-product and auction algorithms, when slightly modified, are equivalent. We study the correctness of this modified algorithm. There is a tantalizing similarity between this connection and a recently observed connection between the max-product and LP-based algorithms for iterative decoding by Vontobel and Koetter
Starting Page	557
Ending Page	561
File Size	240545
Page Count	5
File Format	PDF
ISBN	142440505X
DOI	10.1109/ISIT.2006.261778
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-07-09
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Iterative algorithms Bipartite graph Iterative decoding Electrostatic discharge Belief propagation Application software Computer vision Graphical models Random variables Probability distribution
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
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
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in