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On Treewidth and Stable Marriage [article]

Sushmita Gupta, Saket Saurabh, Meirav Zehavi
2017 arXiv   pre-print
Four well-known NP-hard optimization versions of this problem are the Sex-Equal Stable Marriage (SESM), Balanced Stable Marriage (BSM), max-Stable Marriage with Ties (max-SMT) and min-Stable Marriage with  ...  We thus present a comprehensive, complete picture of the behavior of central optimization versions of Stable Marriage with respect to treewidth.  ...  Accordingly, books on Parameterized Complexity devote several complete chapters solely to the study of treewidth (see [5, 8, 40, 11] ).  ... 
arXiv:1707.05404v1 fatcat:wvzfalp4rzd4nn2atrxfzj47j4

Stable Matching Games: Manipulation via Subgraph Isomorphism

Sushmita Gupta, Sanjukta Roy
2017 Algorithmica  
Our algorithm is a nontrivial combination of a parameterized algorithm for Subgraph Isomorphism, a relationship between stable matching and finding an out-branching in an appropriate graph and enumerating  ...  This algorithm is widely used in both practice and theory, and it exists in two versions: the men-optimal and the women-optimal, so named to emphasise the fact that one side prefers one over the other.  ...  To the best of our knowledge, Cseh and Manlove [4] initiated this type of analysis by studying an NP-hard variant of the stable marriage and stable roommate problems 1 , where the input consists of each  ... 
doi:10.1007/s00453-017-0382-5 fatcat:txog53msovgvxlpc7mvtw5x67q

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

Robert Bredereck, Klaus Heeger, Dušan Knop, Rolf Niedermeier
2021 arXiv   pre-print
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  ...  of parameterized hardness as well as on the side of fixed-parameter tractability.  ...  An FPT-algorithm for a parameterized problem is treewidth tree-cut width Results for graph-structural parameterizations of Stable Roommates with Ties and Incomplete Lists.  ... 
arXiv:1911.09379v2 fatcat:7q7ykn4mnvfotav6djcpzxfngu

Pareto Optimal Allocation under Uncertain Preferences

Haris Aziz, Ronald de Haan, Baharak Rastegari
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
For both of these models, we present a number of algorithmic and complexity results highlighting the difference and similarities in the complexity of the two models.  ...  The assignment problem is one of the most well-studied settings in social choice, matching, and discrete allocation.  ...  Ronald de Haan is supported by the Austrian Science Fund (FWF), projects P26200 and J4047. Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  ... 
doi:10.24963/ijcai.2017/12 dblp:conf/ijcai/0001HR17 fatcat:ahgufohuvfcgvepontnp7nmnzm

Stable Matchings with Restricted Preferences: Structure and Complexity [article]

Christine T. Cheng, Will Rosenbaum
2021 arXiv   pre-print
Many researchers exploit the rotation poset of an instance to develop fast algorithms or to establish the hardness of stable matching problems.  ...  It is well known that every stable matching instance I has a rotation poset R(I) that can be computed efficiently and the downsets of R(I) are in one-to-one correspondence with the stable matchings of  ...  The work of Khanchandani and Wattenhofer [27] shows that stable matchings in the k-range model can be computed with less total communication than the Gale-Shapley algorithm.  ... 
arXiv:2008.08480v2 fatcat:yzo4ag3hdbf3rde257ksv5kwuq

Subject index volumes 1–200

1999 Theoretical Computer Science  
, 3107 languages, 489 stable marriage problem, 2426 man-optimal -, 2475 stable marriages, 2426 model semantics, 2040, 2797, 3392 model, ground -, 3 148 stable models, 2058. 2797, 3207 of logic  ...  2290 snapshot algorithm of Cahndy and Lamport, 964 Snir, 827, 1302 Kruskal and -, 938 Shamir and -, 262 Snir's lower bound, 1302 SNP-hard, 2697, 2734 Max -, 2710 Snyder, Gallier, Raatz and -,  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Preference Restrictions in Computational Social Choice: A Survey [article]

Edith Elkind, Martin Lackner, Dominik Peters
2022 arXiv   pre-print
Particular focus areas of our survey include algorithms for recognizing whether preferences belong to a particular preference domain, and algorithms for winner determination of voting rules that are hard  ...  Social choice becomes easier on restricted preference domains such as single-peaked, single-crossing, and Euclidean preferences.  ...  In contrast to the stable marriage setting (where agents come in two types), stable matchings need not exist for the stable roommates problem (Gale and Shapley, 1962) .  ... 
arXiv:2205.09092v1 fatcat:a4vbknzskvhotmedlaneakg2am

Determinantal Point Processes for Machine Learning

Alex Kulesza
2012 Foundations and Trends® in Machine Learning  
In contrast to traditional structured models like Markov random fields, which become intractable and hard to approximate in the presence of negative correlations, DPPs offer efficient and exact algorithms  ...  We provide a gentle introduction to DPPs, focusing on the intuitions, algorithms, and extensions that are most relevant to the machine learning community, and show how DPPs can be applied to real-world  ...  Algorithm 7 is essentially the Summation Algorithm, which is both asymptotically faster and numerically more stable than the other two, since it uses only sums and does not rely on precise cancellation  ... 
doi:10.1561/2200000044 fatcat:qqq2fvo6tfcnbd73ee2oa43num

Exploring parameter spaces in coping with computational intractability [article]

Sepp Hartung, Technische Universität Berlin, Technische Universität Berlin, Rolf Niedermeier
In a nutshell, parameterized algorithmics deals with identifying parameters in computationally hard problems (mostly, so-called NP-hard problems) and exploits them in order to design parameterized algorithms  ...  Exploiting small parameter values that are implied by these structures for the development of exact and "efficient" solving algorithms is the central concern of parameterized algorithmics.  ...  In this way we take a closer look at parameterization aspects that help in better understanding and exploiting problem-specific properties.  ... 
doi:10.14279/depositonce-3922 fatcat:ynttmtrybfh2xbdcw3ot7zw43a

Computational Geometry (Dagstuhl Seminar 13101) Scheduling (Dagstuhl Seminar 13111) Future Internet (Dagstuhl Seminar 13131)

Otfried Cheong, Kurt Mehlhorn, Monique, Susanne Albers, Onno Boxma, Kirk, Erik Demaine, Fedor Fomin, Mohammadtaghi Hajiaghayi, Dimitrios, Jon Crowcroft, Markus Fidler (+2 others)
2013 unpublished
Then a dynamic programming algorithm for Planar Completion to Bounded Diameter on graphs of bound treewidth would result in the construction of the desired algorithm.  ...  The resulting parameter special treewidth falls somewhere between treewidth and pathwidth.  ...  One simple hope for SDN might be to take research results in policy routing (e.g. metarouting) and do a one-time replacement of BGP. We also considered SDN in data plane. 1.  ... 

Multivariate complexity analysis of team management problems [article]

Robert Bredereck, Technische Universität Berlin, Technische Universität Berlin, Rolf Niedermeier
On the negative side, we show W[2]-hardness for the parameter "size of the solution" and NP-hardness for various special cases.  ...  To this end, we perform a multivariate complexity analysis of the underlying problems and test some of our algorithms on synthetic and empirical data.  ...  Finally, our studies and results basically focused on "single parameterizations", yielding several hardness results.  ... 
doi:10.14279/depositonce-4450 fatcat:5kaiaeadcvbvbj3ph26auyksce

Property testing of graphs and the role of neighborhood distributions

Hendrik Fichtenberger, Technische Universität Dortmund
Hence, decision problems are relaxed by introducing a gap between "yes" and "no" instances: A property tester for a property Π (e. g., planarity) is a randomized algorithm with constant error probability  ...  properties with constant testing complexity in graphs with bounded (maximum vertex) degree and a connection between testers with constant complexity for general graphs and testers with logarithmic space  ...  The main impetus of classic approximation algorithms comes as hardness results regarding the computational complexity of a problem.  ... 
doi:10.17877/de290r-21116 fatcat:yfwvazz3jzeffdqkacxuawydry

OASIcs, Volume 69, SOSA'19, Complete Volume [article]

Jeremy T. Fineman, Michael Mitzenmacher
OASIcs, Volume 69, SOSA'19, Complete Volume  ...  on our results. 5:21 Seth Pettie and Vijaya Ramachandran.  ...  Acknowledgements Mohsen Ghaffari is grateful to Gregory Schwartzman for sharing a write-up of [9], and to Ami Paz and Gregory Schwartzman for feedback on an earlier draft of this article.  ... 
doi:10.4230/oasics.sosa.2019 fatcat:qjz3tl5ccfe3nprcrv6msbfwbq

Dagstuhl Reports, Volume 12, Issue 1, January 2019, Complete Issue [article]

Dagstuhl Reports, Volume 12, Issue 1, January 2019, Complete Issue  ...  First-order logic (FO) can express many algorithmic problems on graphs, such as the independent set and dominating set problem parameterized by solution size.  ...  On the other hand, FO cannot express the very simple algorithmic question whether two vertices are connected.  ... 
doi:10.4230/dagrep.12.1 fatcat:7yrxmj6zhve4zgcdpffp4uhtnu