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Stable marriage and roommates problems with restricted edges: complexity and approximability [article]

Ágnes Cseh, David F. Manlove
2016 arXiv   pre-print
In the stable marriage and roommates problems, a set of agents is given, each of them having a strictly ordered preference list over some or all of the other agents.  ...  For the non-bipartite stable roommates instances, case (2) yields an NP-hard problem.  ...  of the open problems that feature in Section 5.  ... 
arXiv:1412.0271v6 fatcat:m56t3tusijf3jpcngoees5gv6u

Stable Marriage and Roommates problems with restricted edges: Complexity and approximability

Ágnes Cseh, David F. Manlove
2016 Discrete Optimization  
In the Stable Marriage and Roommates problems, a set of agents is given, each of them having a strictly ordered preference list over some or all of the other agents.  ...  For non-bipartite Stable Roommates instances, case (2) yields an NP-hard but (under some cardinality assumptions) 2-approximable problem.  ...  of the open problems that feature in Section 5.  ... 
doi:10.1016/j.disopt.2016.03.002 fatcat:x2fr2o7yynd7xhq22pgzjzl2ni

Stable Marriage and Roommates Problems with Restricted Edges: Complexity and Approximability [chapter]

Ágnes Cseh, David F. Manlove
2015 Lecture Notes in Computer Science  
In the Stable Marriage and Roommates problems, a set of agents is given, each of them having a strictly ordered preference list over some or all of the other agents.  ...  For non-bipartite Stable Roommates instances, case (2) yields an NP-hard but (under some cardinality assumptions) 2-approximable problem.  ...  of the open problems that feature in Section 5.  ... 
doi:10.1007/978-3-662-48433-3_2 fatcat:z2sgva74evblhg2r4hned3huvy

The complexity of approximately counting stable roommate assignments

Prasad Chebolu, Leslie Ann Goldberg, Russell Martin
2012 Journal of computer and system sciences (Print)  
Exactly counting the number of assignments is #P-complete, since Irving and Leather demonstrated #P-completeness for the special case of the stable marriage problem.  ...  We show that counting the number of stable roommate assignments in the k-attribute model (k ≥ 4) and the 3-Euclidean model(k ≥ 3) is interreducible, in an approximation-preserving sense, with counting  ...  An example We give the following example to illustrate the definitions from Section 3 and the two-phase algorithm for finding a stable roommate assignment. Consider the following preference lists.  ... 
doi:10.1016/j.jcss.2012.02.003 fatcat:ypyssptg6rdfxb2pq5cmfcww6u

How Hard Is It to Satisfy (Almost) All Roommates?

Jiehua Chen, Danny Hermelin, Manuel Sorge, Harel Yedidsion, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
The classic Stable Roommates problem (the non-bipartite generalization of the well-known Stable Marriage problem) asks whether there is a stable matching for a given set of agents, i.e. a partitioning  ...  Keywords and phrases NP-hard problems Data reduction rules Kernelizations Parameterized complexity analysis and algorithmics  ...  Stable Marriage and Stable Roommates.  ... 
doi:10.4230/lipics.icalp.2018.35 dblp:conf/icalp/ChenHSY18 fatcat:azg3db35irajld2gfy5jceoweq

Parameterized Complexity of Stable Roommates with Ties and Incomplete Lists Through the Lens of Graph Parameters

Robert Bredereck, Klaus Heeger, Dusan Knop, Rolf Niedermeier, Michael Wagner
2019 International Symposium on Algorithms and Computation  
Other than for its famous sister problem Stable Marriage which focuses on a bipartite scenario, Stable Roommates with Incomplete Lists allows for arbitrary acceptability graphs whose edges specify the  ...  We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side  ...  6 Parameterized Complexity of Stable Roommates with Ties and Incomplete Lists A parameterized problem consists of the problem instance I (in our setting the Stable Roommate instance) and a parameter value  ... 
doi:10.4230/lipics.isaac.2019.44 dblp:conf/isaac/BredereckHKN19 fatcat:5pian5zjszdlndrndzadk7wv2q

Popular Matchings in the Marriage and Roommates Problems [chapter]

Péter Biró, Robert W. Irving, David F. Manlove
2010 Lecture Notes in Computer Science  
In this paper we study popular matchings in the context of the Roommates Problem, including its special (bipartite) case, the Marriage Problem.  ...  Here, we are interested in the Marriage and Roommates scenarios, where each participant expresses preferences over some or all of the others, but we focus on matchings that are popular rather than stable  ...  An instance of the Marriage Problem with Ties (mpt) may be viewed as an instance of rpt in which the underlying graph G is bipartite. The Marriage Problem (mp) is the analogous restriction of rp.  ... 
doi:10.1007/978-3-642-13073-1_10 fatcat:dw62fkijmvb4hiyf62gk42gznq

Adapting Stable Matchings to Evolving Preferences

Robert Bredereck, Jiehua Chen, Dušan Knop, Junjie Luo, Rolf Niedermeier
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
After formalizing these incremental versions, we provide a fairly comprehensive picture of the computational complexity landscape of Incremental Stable Marriage and Incremental Stable Roommates.  ...  Adaptivity to changing environments and constraints is key to success in modern society. We address this by proposing "incrementalized versions" of Stable Marriage and Stable Roommates.  ...  Main work was done while DK was with TU Berlin, supported by the DFG project MaMu (NI 369/19). JL was supported by the DFG project AFFA (BR 5207/1 and NI 369/15).  ... 
doi:10.1609/aaai.v34i02.5550 fatcat:tz6wrhsjavaadfqe5envvd5cmi

How hard is it to satisfy (almost) all roommates? [article]

Jiehua Chen and Danny Hermelin and Manuel Sorge and Harel Yedidsion
2018 arXiv   pre-print
The classic Stable Roommates problem (which is the non-bipartite generalization of the well-known Stable Marriage problem) asks whether there is a stable matching for a given set of agents, i.e. a partitioning  ...  Since stable matchings may not be unique, we study an NP-hard optimization variant of Stable Roommates, called Egal Stable Roommates, which seeks to find a stable matching with a minimum egalitarian cost  ...  Stable Marriage and Stable Roommates An instance of the Stable Marriage problem consists of two disjoint sets of n men and n women (collectively called agents), who are each equipped with his or her own  ... 
arXiv:1707.04316v3 fatcat:txjrfu5z75gkldf33423yr7hgq

The Stable Roommates Problem with Short Lists

Ágnes Cseh, Robert W. Irving, David F. Manlove
2017 Theory of Computing Systems  
We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists (sri) that are degree constrained, i.e., preference lists are of bounded length  ...  We also consider the "most stable" version of this problem and prove a strong inapproximability bound for the d = 3 case.  ...  Such a subgraph therefore gives rise to the restriction of srti called the Stable Marriage problem with Ties and Incomplete lists (smti).  ... 
doi:10.1007/s00224-017-9810-9 fatcat:zr4d5bq625autlqlpoa47uqbru

A new fixed point approach for stable networks and stable marriages

Tomás Feder
1992 Journal of computer and system sciences (Print)  
express as special cases stable marriage and stable roommate problems.  ...  In this paper we study the sequential and parallel complexity of network stability on networks with restricted fanout.  ...  I also had valuable discussions with Dan Gustield, who introduced me to several of the questions on stable matching, and my advisor Donald Knuth.  ... 
doi:10.1016/0022-0000(92)90048-n fatcat:2iaiqjwkezelfoz3dbz3tirvhy

The Stable Roommates problem with short lists [article]

Ágnes Cseh, Robert W. Irving, David F. Manlove
2017 arXiv   pre-print
We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists SRI that are degree constrained, i.e., preference lists are of bounded length.  ...  We also consider the "most stable" version of this problem and prove a strong inapproximability bound for the d=3 case.  ...  Acknowledgements We thank the anonymous reviewers of this paper and an earlier version of it for their valuable comments, which helped to improve the presentation.  ... 
arXiv:1605.04609v3 fatcat:brg76s5bfnettdlxnauc3vmvim

The Stable Roommates Problem with Short Lists [chapter]

Ágnes Cseh, Robert W. Irving, David F. Manlove
2016 Lecture Notes in Computer Science  
We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists (sri) that are degree constrained, i.e., preference lists are of bounded length  ...  We also consider the "most stable" version of this problem and prove a strong inapproximability bound for the d = 3 case.  ...  Such a subgraph therefore gives rise to the restriction of srti called the Stable Marriage problem with Ties and Incomplete lists (smti).  ... 
doi:10.1007/978-3-662-53354-3_17 fatcat:gtawkxfre5agznu4wdms7yjwgi

Adapting Stable Matchings to Evolving Preferences [article]

Robert Bredereck, Jiehua Chen, Dušan Knop, Junjie Luo, Rolf Niedermeier
2019 arXiv   pre-print
After formalizing these incremental versions, we provide a fairly comprehensive picture of the computational complexity landscape of Incremental Stable Marriage and Incremental Stable Roommates.  ...  Adaptivity to changing environments and constraints is key to success in modern society. We address this by proposing "incrementalized versions" of Stable Marriage and Stable Roommates.  ...  Algorithms for Incremental Stable Marriage and Roommates As a warm-up, we first show that our most restricted problem variant, Incremental Stable Marriage without ties, can be solved in polynomial time  ... 
arXiv:1907.01375v2 fatcat:eyi62oa7xngzxhc5dhrgth2qpi

Locally Stable Marriage with Strict Preferences

Martin Hoefer, Lisa Wagner
2017 SIAM Journal on Discrete Mathematics  
Finally, we conclude with results on approximating maximum locally stable matchings. Supported by DFG Cluster of Excellence MMCI and grant Ho 3831/3-1.  ...  We consider convergence of dynamics to locally stable matchings that are stable with respect to their imposed information structure in the network.  ...  Our model extends the stable marriage problem, in which we have sets U and W of men and women.  ... 
doi:10.1137/151003854 fatcat:qfrebjfkvfh5fpwolyzduvkyqi
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