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On the (Parameterized) Complexity of Almost Stable Marriage [article]

Sushmita Gupta, Pallavi Jain, Sanjukta Roy, Saket Saurabh, Meirav Zehavi
2020 arXiv   pre-print
We study this question in the realm of parameterized complexity with respect to several natural parameters, k,t,d, where d is the maximum length of a preference list.  ...  In the Stable Marriage problem. when the preference lists are complete, all agents of the smaller side can be matched. However, this need not be true when preference lists are incomplete.  ...  We define the Almost Stable Marriage problem as follows.  ... 
arXiv:2005.08150v1 fatcat:yjrxu2ea6jd6dpdw6ertrymstu

On the (Parameterized) Complexity of Almost Stable Marriage

Sushmita Gupta, Pallavi Jain, Sanjukta Roy, Saket Saurabh, Meirav Zehavi, Nitin Saxena, Sunil Simon
2020
We study this question in the realm of parameterized complexity with respect to several natural parameters, k,t,d, where d is the maximum length of a preference list.  ...  In the Stable Marriage problem, when the preference lists are complete, all agents of the smaller side can be matched. However, this need not be true when preference lists are incomplete.  ...  F S T T C S 2 0 2 0 24:4 On the (Parameterized) Complexity of Almost Stable Marriage Unsurprisingly perhaps, the existence of a stable matching in the proximity of which we wish to find a solution does  ... 
doi:10.4230/lipics.fsttcs.2020.24 fatcat:kac4d7r4anfb3neugqhmn6wq4y

Theory, Computers and the Parameterization of Demographic Behavior [chapter]

Thomas K. Burch
2017 Demographic Research Monographs  
It is not mentioned in the United Nations Manual X in the section on 'Nuptiality Models,' and is mentioned only briefly if at all in many other treatments of marriage in recent demographic literature.  ...  The two models are the Coale-McNeil (1972) and the Hernes (1972) models of first marriage. Developed at roughly the same time, the models have experienced rather different fates.  ...  Theory, Computers and the Parameterization of Demographic Behavior While this view still seems valid, it may need to be qualified to take account of measurement error in complex multivariate models  ... 
doi:10.1007/978-3-319-65433-1_6 fatcat:lo4s2x7nrjfjnajgkrf3wjlhxm

Parameterized Complexity of Manipulating Sequential Allocation [article]

Michele Flammini, Hugo Gilbert
2019 arXiv   pre-print
In this work, we take a parameterized approach to provide several new complexity results on this manipulation problem.  ...  More precisely, we give a complete picture of its parameterized complexity w.r.t. the following three parameters: the number n of agents, the number μ(a_1) of times the manipulator a_1 picks in the picking  ...  We are grateful to Jérôme Lang and Paolo Serafino for helpful comments and stimulating conversations on this work.  ... 
arXiv:1909.08920v4 fatcat:pqqovy7o4baynkizxisc3ivspq

Deepening the (Parameterized) Complexity Analysis of Incremental Stable Matching Problems [article]

Niclas Boehmer, Klaus Heeger, Rolf Niedermeier
2022 arXiv   pre-print
As they showed that Incremental Stable Roommates and Incremental Stable Marriage with Ties are NP-hard, we focus on the parameterized complexity of these problems.  ...  that Incremental Stable Roommates and Incremental Stable Marriage with Ties parameterized by the number of different preference lists are W[1]-hard.  ...  Setting F := ∅ now results in an NP-complete problem by the same proof as the one of Theorem 1. Incremental Stable Marriage with Ties Parameterized by the Number of Ties Bredereck et al.  ... 
arXiv:2208.01563v1 fatcat:paldebwm6bfqxh3s2rfbj5mt7a

Parameterized Complexity Results for Exact Bayesian Network Structure Learning

S. Ordyniak, S. Szeider
2013 The Journal of Artificial Intelligence Research  
In this paper we study the computational worst-case complexity of exact Bayesian network structure learning under graph theoretic restrictions on the (directed) super-structure.  ...  The super-structure is an undirected graph that contains as subgraphs the skeletons of solution networks.  ...  The parameterized complexity class W [1] is considered as the parameterized analog to NP.  ... 
doi:10.1613/jair.3744 fatcat:4vxjfnzavnapxkujvl6eqqorhe

Theory of and Experiments on Minimally Invasive Stability Preservation in Changing Two-Sided Matching Markets

Niclas Boehmer, Klaus Heeger, Rolf Niedermeier
2022 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Our theoretical extensions include the study of new problems (that is, incremental variants of Almost Stable Marriage and Hospital Residents), focusing on their (parameterized) computational complexity  ...  and the equivalence of various change types (thus simplifying algorithmic and complexity-theoretic studies for various natural change scenarios).  ...  They referred to this as the "incremental" scenario and studied the computational complexity of this question for STABLE MARRIAGE and STABLE ROOMMATES (both being one-to-one matching problems).  ... 
doi:10.1609/aaai.v36i5.20413 fatcat:is6evlda65aivpcpesnt2kvw6u

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.  ...  We address this by proposing "incrementalized versions" of Stable Marriage and Stable Roommates.  ...  Main work was done while JC was with University of Warsaw, supported by ERC Horizon 2020 research and innovation programme (677651). JC was also supported by the WWTF research project (VRG18-012).  ... 
doi:10.1609/aaai.v34i02.5550 fatcat:tz6wrhsjavaadfqe5envvd5cmi

Report on BCTCS & AlgoUK 2019

Matthew Johnson, Barnaby Martin, George B. Mertzios, Daniël Paulusma
2019 Bulletin of the European Association for Theoretical Computer Science  
Within BCTCS there were two invited talks, one on graph theory and perfect graphs and one on logic. Abstracts for all of the talks are provided below.  ...  AlgoUK is a research network for Algorithms and Complexity in the UK, which is funded by an EPSRC network grant.  ...  Frances Cooper Rank-maximal stable matchings in the Stable Marriage problem In 1962, Gale and Shapley described the Stable Marriage problem (SM) in their seminal paper â ȂIJCollege Admissions and the Stability  ... 
dblp:journals/eatcs/JohnsonMMP19 fatcat:mzd35uzlerfzjntkhlxdxt4vem

Mitigation of the double ITCZ syndrome in BCC-CSM2-MR through improving parameterizations of boundary-layer turbulence and shallow convection

Yixiong Lu, Tongwen Wu, Yubin Li, Ben Yang
2021 Geoscientific Model Development  
The spurious double Intertropical Convergence Zone (ITCZ) is one of the most prominent systematic biases in coupled atmosphere–ocean general circulation models (CGCMs), and the underestimated marine stratus  ...  The study suggests that improving parameterizations of boundary-layer turbulence and shallow convection is effective for mitigating the double ITCZ syndrome in CGCMs.  ...  simulation of the ITCZ-cold tongue complex.  ... 
doi:10.5194/gmd-14-5183-2021 fatcat:hlxnozosonc25hvkb42it3gxfm

Guest Editorial: Special Issue on Matching Under Preferences

David F. Manlove, Robert W. Irving, Kazuo Iwama
2010 Algorithmica  
preference lists may be incomplete and may include ties, in "Parameterized Complexity and Local Search Approaches for the Stable Marriage Problem with Ties".  ...  Cheng studies the complexity of finding generalized median stable matchings in instances of the Stable Marriage problem in "Understanding the Generalized Median Stable Matchings".  ... 
doi:10.1007/s00453-010-9415-z fatcat:qp4iuv3ffjdffblw2stnoxaqyu

Recent Advances on the Graph Isomorphism Problem [article]

Martin Grohe, Daniel Neuen
2021 arXiv   pre-print
We give an overview of recent advances on the graph isomorphism problem.  ...  Our main focus will be on Babai's quasi-polynomial time isomorphism test and subsequent developments that led to the design of isomorphism algorithms with a quasi-polynomial parameterized running time  ...  The question whether GI parameterized by maximum degree is fixed parameter tractable has already been raised more than twenty years ago in Downey and Fellow's monograph on parameterized complexity [24  ... 
arXiv:2011.01366v2 fatcat:drrbl2cx3zabtkxo75f6nc5jlq

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 also classify all cases of one-sided constraints where only women may be distinguished.  ...  To investigate how these aspects affect the complexity of SMC, we use the framework of parameterized complexity, which deals with computationally hard problems and focuses on how certain parameters of  ... 
doi:10.1007/978-3-319-66700-3_25 fatcat:5fwbpapi2bbmfdvawirfrsoghe

Fitting the HIV Epidemic in Zambia: A Two-Sex Micro-Simulation Model

Pauline M. Leclerc, Alan P. Matthews, Michel L. Garenne, Nitika Pant Pai
2009 PLoS ONE  
Particular attention was paid to precise age-specific estimates of exposure to risk through the modelling of the formation and dissolution of relationships: marriage (stable union), casual partnership,  ...  This study is based on a micro-simulation model (individual-based) of the spread of the HIV epidemic in the population of Zambia, where women tend to marry early and where divorces are not frequent.  ...  This parameterization allows one to compute transition rates by week or month. Transitions to first marriage are given by a Picrate model [19] , also fitted on DHS data.  ... 
doi:10.1371/journal.pone.0005439 pmid:19415113 pmcid:PMC2673026 fatcat:qpnlbh4jtjfejgm6nofe3542xi

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  ...  Our main result is that Egal Stable Roommates parameterized by γ is fixed-parameter tractable, while Min-Block-Pair Stable Roommates parameterized by β is W[1]-hard, even if the length of each preference  ...  We analyze both Egal Stable Roommates and Min-Block-Pair Stable Roommates from the perspective of parameterized complexity, under the natural parameterization of each problem (i.e. the egalitarian cost  ... 
doi:10.4230/lipics.icalp.2018.35 dblp:conf/icalp/ChenHSY18 fatcat:azg3db35irajld2gfy5jceoweq
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