NDLI: Csc5160: combinatorial optimization and approximation algorithms topic: perfect matching polytope date: 22/02/2008.

Please wait, while we are loading the content...

Csc5160: combinatorial optimization and approximation algorithms topic: perfect matching polytope date: 22/02/2008.

Content Provider	CiteSeerX
Author	Wu, Xiaobing Chan, Hei Ding, Ling Lau, Chi Lap, Lecturer Yuk, Scribe
Abstract	In this lecture, the focus is on general perfect matching problem where the goal is to prove that it can be solved in polynomial time by linear programming. Based on the LP formulation for bipartite matching studied in Lecture 10, we add some valid inequalities to establish a new formulation. Then we prove that for general perfect matching, all vertex solutions of the linear program are integral. This shows that the new formulation defines the matching polytope, and the general perfect matching problem can be solved by linear programming. Finally, we will show that this linear program can be solved in polynomial time, by providing a polynomial time separation oracle. 12.1 Formulation of General Perfect Matching Given a weighted general graph G = (V, E), for any edge e, we represents the weight of the edge and xe is the indicator variable of e. If an edge e is in the matching, we set xe = 1, otherwise xe = 0. Base on these definitions, the weighted perfect matching problem can be formulated as follows: max � e∈δ(v) e∈E
File Format	PDF
Access Restriction	Open
Subject Keyword	General Perfect Matching Given Combinatorial Optimization Linear Program Perfect Matching Polytope Date General Perfect Matching Problem Polynomial Time Linear Programming Polynomial Time Separation Oracle General Perfect Indicator Variable Valid Inequality Weighted General Graph Approximation Algorithm Topic Lp Formulation General Perfect Matching New Formulation Vertex Solution Weighted Perfect
Content Type	Text

Central Library (ISO-9001:2015 Certified)
Indian Institute of Technology Kharagpur
Kharagpur, West Bengal, India | PIN - 721302

See location in the Map
03222 282435
Mail: support@ndl.gov.in

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