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On-line algorithms for weighted bipartite matching and stable marriages

Samir Khuller, Stephen G. Mitchell, Vijay V. Vazirani
1994 Theoretical Computer Science  
Mitchell and V.V. Vazirani, On-line algorithms for weighted bipartite matching and stable marriages, Theoretical Computer Science 127 (1994) 255-267.  ...  We give an on-line deterministic algorithm for the weighted bipartite matching problem that achieves a competitive ratio of (2n-1) in any metric space (where n is the number of vertices).  ...  In this paper we study two related problems -on-line weighted bipartite matching, and on-line stable marriages. .l.  ... 
doi:10.1016/0304-3975(94)90042-6 fatcat:xyb2zeumn5bovoz7fdv3zuknvi

On-line algorithms for weighted bipartite matching and stable marriages [chapter]

Samir Khuller, Stephen G. Mitchell, Vijay V. Vazirani
1991 Lecture Notes in Computer Science  
In this paper we study two related problems -on-line weighted bipartite matching, and on-line stable marriages.  ...  An optimal randomized on-line algorithm for bipartite matching (without weights) was given in [KVV].  ...  Acknowledgments: We would like to thank Amotz Bar-Noy, Omer Berkman and Baruch Schieber for useful discussions. We would also like to thank the referees for their comments.  ... 
doi:10.1007/3-540-54233-7_178 fatcat:gvu7b6r5zfeytauyl7pvzdbosy

Statistical Behaviors of Distributed Transition Planning [chapter]

Ning Wu, Alva L. Couch
2008 Lecture Notes in Computer Science  
Prior work shows that the transition planning problem can be reduced to a bipartite matching problem and the stable marriage algorithm can be used to approximate a minimum cost transition in a distributed  ...  We discuss the relationship between algorithm performance and the distribution of the input data.  ...  Acknowledgement We wish to thank Marc Chiarini for reading several versions of the paper and making timely comments.  ... 
doi:10.1007/978-3-540-70587-1_7 fatcat:6in472qxkzcurpkkuakda2jmo4

Brief announcement

Patrik Floréen, Petteri Kaski, Valentin Polishchuk, Jukka Suomela
2010 Proceeding of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '10  
We study the stable marriage problem in a distributed setting. The communication network is a bipartite graph, with men on one side and women on the other.  ...  The classical Gale-Shapley algorithm could be simulated in such a network to find a stable matching.  ...  , and by the Foundation of Nokia Corporation.  ... 
doi:10.1145/1835698.1835765 dblp:conf/podc/FloreenKPS10 fatcat:x4xbahgo55e2xmbnwxaix4tj2q

On the stable b-matching polytope

Tamás Fleiner
2003 Mathematical Social Sciences  
Our proof uses the comparability theorem of Roth and Sotomayor [13] and follows a similar line as Rothblum did in [14] for the stable matching polytope.  ...  We characterize the bipartite stable b-matching polytope in terms of linear constraints.  ...  I thank Gábor Maróti for the discussions on the topic.  ... 
doi:10.1016/s0165-4896(03)00074-x fatcat:dnalvap4t5hkriz4ntc6njs27y

Note on an Auction Procedure for a Matching Game in Polynomial Time [chapter]

Winfried Hochstättler, Hui Jin, Robert Nickel
2006 Lecture Notes in Computer Science  
As a special case we derive an O(nm) algorithm for bipartite matching that does not seem to have appeared in the literature yet.  ...  We derive a polynomial time algorithm to compute a stable solution in a mixed matching market from an auction procedure as presented by Eriksson and Karlander [5] .  ...  [4] ) and the classical algorithm for weighted bipartite matching, namely the Hungarian Method of Kuhn [14] , is not as prominent in game theory as it is in combinatorial optimization.  ... 
doi:10.1007/11775096_36 fatcat:g77l2f7ydbg7vfzn3egdxu2axa

Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

Patrik Floréen, Petteri Kaski, Valentin Polishchuk, Jukka Suomela
2009 Algorithmica  
We apply our results to give a distributed (2+ϵ)-approximation algorithm for maximum-weight matching in bicoloured graphs and a centralised randomised constant-time approximation scheme for estimating  ...  We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose--accept rounds executed by the Gale--Shapley algorithm for the stable marriage problem.  ...  We acknowledge email exchange with the members of the Algorithms and Complexity Research at Glasgow group, and thank the organisers of ALGO 2008 for the creative atmosphere at the conference.  ... 
doi:10.1007/s00453-009-9353-9 fatcat:husrbyw5p5hkzhrjk6urryeley

The weighted stable matching problem [article]

Linda Farczadi, Natália Guričanová
2017 arXiv   pre-print
Previously Chen et al. have shown that the stable matching polytope is integral if and only if the subgraph obtained after running phase one of Irving's algorithm is bipartite.  ...  We complement these results with a 2-approximation algorithm for the minimum weight stable matching problem for instances where each agent has at most two possible partners in any stable matching.  ...  We then consider approximation algorithms for the minimum weight stable matching problem.  ... 
arXiv:1703.09083v1 fatcat:w6grhf3eqjhafjzsrbqyx35sgi

Alternative Algorithms for Counting All Matchings in Graphs [chapter]

Piotr Sankowski
2003 Lecture Notes in Computer Science  
Then an algorithm used for determining maximu m matchings in b ipartite graphs is discussed and examples of its execut ion are explored.  ...  The Marriage Algorith m is also discussed as are stable marriages and examp les of the execut ion of the Marriage A lgorith m are provided.  ...  Vassilev during the work on this paper.  ... 
doi:10.1007/3-540-36494-3_38 fatcat:oq43kaeug5dxpd5vp2sftyvji4

Analysis of ground state in random bipartite matching [article]

Gui-Yuan Shi, Yi-Xiu Kong, Hao Liao, Yi-Cheng Zhang
2015 arXiv   pre-print
In human society, a lot of social phenomena can be concluded into a mathematical problem called the bipartite matching, one of the most well known model is the marriage problem proposed by Gale and Shapley  ...  Furthermore, we discover that the connectivity in the bipartite matching problem has a great impact on the stability of the ground state, and the system will become more unstable if there were more connections  ...  Acknowledgements The authors would like to thank Zhuo-Ming Ren for his valuable comments on this work.  ... 
arXiv:1502.02163v1 fatcat:7ga2biqybzcstdaqcxi4spu23m

Protein Structure Comparison Using Bipartite Graph Matching and Its Application to Protein Structure Classification

William R. Taylor
2002 Molecular & Cellular Proteomics  
The main algorithm used was the "stable marriage" algorithm, which works on the ranked "preferences" of one interaction for another.  ...  The matching used a fast bipartite graphmatching algorithm that avoids the computational complexity of searching for the full subgraph isomorphism between the two sets of interactions.  ...  Acknowledgments-Darrell Conklin and Kjell Petersen are thanked for useful discussion, and Alex May and Jaap Heringa are thanked for comments on the manuscript. * The costs of publication of this article  ... 
doi:10.1074/mcp.t200001-mcp200 pmid:12096115 fatcat:2cxam4l3urh5tpr5ft4psl2yhe

NC Algorithms for Popular Matchings in One-Sided Preference Systems and Related Problems [article]

Changyong Hu, Vijay K. Garg
2019 arXiv   pre-print
Moreover, we give an NC algorithm for a weaker version of the stable matching problem, that is, the problem of finding the "next" stable matching given a stable matching.  ...  We also give an NC algorithm that solves the maximum-cardinality popular matching problem. No NC or RNC algorithms were known for the matching problem in preference systems prior to this work.  ...  The problem of finding an NC algorithm for the stable marriage problem has been open for a long time. Mayr and Subramanian [15] showed that the stable marriage problem is CC-complete.  ... 
arXiv:1910.13386v2 fatcat:guldjmmgarekrnaaxs6e2qp3ai

Stable Matching Beyond Bipartite Graphs

Jie Wu
2016 2016 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)  
Gale and Shapley showed that a stable marriage exists for any set of preferences in any complete and balanced bipartite graphs.  ...  We use a solution for the stable roommates problem to illustrate the matching identification process if one exists.  ...  For example, in maximum-weighted bipartite matching [1] , the objective is to maximize the total utility (or happiness) of matching pairs, represented as the total edge weight of matching pairs.  ... 
doi:10.1109/ipdpsw.2016.207 dblp:conf/ipps/000116 fatcat:ewgxntxovvg7nkm7eqvzu5rtty

Stable Marriage with Covering Constraints–A Complete Computational Trichotomy [chapter]

Matthias Mnich, Ildikó Schlotter
2017 Lecture Notes in Computer Science  
We consider Stable Marriage with Covering Constraints (SMC): in this variant of Stable Marriage, we distinguish a subset of women as well as a subset of men, and we seek a matching with fewest number of  ...  We investigate how a set of natural parameters, namely the maximum length of preference lists for men and women, the number of distinguished men and women, and the number of blocking pairs allowed determine  ...  bipartite matching in G .  ... 
doi:10.1007/978-3-319-66700-3_25 fatcat:5fwbpapi2bbmfdvawirfrsoghe

The stable marriage problem with ties and restricted edges

Ágnes Cseh, Klaus Heeger
2020 Discrete Optimization  
Ties in the preferences allow for three different definitions for a stable matching: weak, strong and super-stability.  ...  In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class.  ...  Acknowledgments The authors thank David Manlove, Rolf Niedermeier, and the anonymous reviewers for useful suggestions that improved the presentation of this paper.  ... 
doi:10.1016/j.disopt.2020.100571 fatcat:tr35jy4oxbg43nz7ezkiewpz7u
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