research-article

Analyzing Node-Weighted Oblivious Matching Problem via Continuous LP with Jump Discontinuity

Authors:

T.-H. Hubert Chan,

Xiaowei WuAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 14, Issue 2

Article No.: 12, Pages 1 - 25

https://doi.org/10.1145/3168008

Published: 16 April 2018 Publication History

Abstract

We prove the first non-trivial performance ratio strictly above 0.5 for the weighted Ranking algorithm on the oblivious matching problem where nodes in a general graph can have arbitrary weights.

We have discovered a new structural property of the ranking algorithm: if a node has two unmatched neighbors, then it will still be matched even when its rank is demoted to the bottom. This property allows us to form LP constraints for both the weighted and the unweighted versions of the problem.

Using a new class of continuous linear programming (LP), we prove that the ratio for the weighted case is at least 0.501512, and we improve the ratio for the unweighted case to 0.526823 (from the previous best 0.523166 in SODA 2014). Unlike previous continuous LP, in which the primal solution must be continuous everywhere, our new continuous LP framework allows the monotone component of the primal function to have jump discontinuities, and the other primal components to take non-conventional forms, such as the Dirac δ function.

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Cited By

Xiao SLi CGuo BXiao H(2020)A radix sorting parallel algorithm suitable for graphic processing unit computingConcurrency and Computation: Practice and Experience10.1002/cpe.581833:6Online publication date: 30-Sep-2020
https://doi.org/10.1002/cpe.5818
Huang ZTang ZWu XZhang Y(2019)Online Vertex-Weighted Bipartite MatchingACM Transactions on Algorithms10.1145/332616915:3(1-15)Online publication date: 17-Jun-2019
https://dl.acm.org/doi/10.1145/3326169

Index Terms

Analyzing Node-Weighted Oblivious Matching Problem via Continuous LP with Jump Discontinuity
1. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 14, Issue 2

April 2018

339 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/3196491

Editor:
Aravind Srinivasan
University of Maryland, USA

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Copyright © 2018 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 16 April 2018

Accepted: 01 November 2017

Received: 01 November 2016

Published in TALG Volume 14, Issue 2

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Cited By

Xiao SLi CGuo BXiao H(2020)A radix sorting parallel algorithm suitable for graphic processing unit computingConcurrency and Computation: Practice and Experience10.1002/cpe.581833:6Online publication date: 30-Sep-2020
https://doi.org/10.1002/cpe.5818
Huang ZTang ZWu XZhang Y(2019)Online Vertex-Weighted Bipartite MatchingACM Transactions on Algorithms10.1145/332616915:3(1-15)Online publication date: 17-Jun-2019
https://dl.acm.org/doi/10.1145/3326169

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