Stable Matchings with Restricted Preferences: Structure and Complexity

Cheng, Chih-Hsien; Rosenbaum, Will

doi:10.1145/3465456.3467618

Cited by 4 publications

(4 citation statements)

References 27 publications

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“…In a recent paper [5], we considered stable matching instances with "k-range preferences." That is, there is an objective ranking for each group of agents, and each person ranks agents from the other group to within k of their objective ranks.…”

Section: Counting and Sampling Elements In A Distributive Latticementioning

confidence: 99%

“…The stable matchings can be succinctly represented as the family of downsets in the "rotation digraph" of an instance, which itself can be computed in near-linear time. In a companion paper [5], we show that for a natural parameterizationthe "k-range model" introduced by Bhatnagar et al [2]-instances have rotation digraphs whose pathwidths are bounded by a function of range of the instance, and that a path decomposition of the rotation digraph can be computed efficiently from the input. Combined with the structural result in [5], our algorithms for counting and sampling downsets give FPT algorithms for counting and sampling stable matchings parameterized by the "range" of the input.…”

Section: Introductionmentioning

confidence: 99%

“…In a companion paper [5], we show that for a natural parameterizationthe "k-range model" introduced by Bhatnagar et al [2]-instances have rotation digraphs whose pathwidths are bounded by a function of range of the instance, and that a path decomposition of the rotation digraph can be computed efficiently from the input. Combined with the structural result in [5], our algorithms for counting and sampling downsets give FPT algorithms for counting and sampling stable matchings parameterized by the "range" of the input. Specifically, for any fixed constant k and k-range stable marriage instance, it is possible to exactly count and uniformly sample stable matchings in linear time (Corollary 4.5).…”

Section: Introductionmentioning

confidence: 99%

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Simple Counting and Sampling Algorithms for Graphs with Bounded Pathwidth

Cheng,

Rosenbaum

2020

Preprint

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In this paper, we consider the problem of counting and sampling structures in graphs. We define a class of "edge universal labeling problems"-which include proper k-colorings, independent sets, and downsets-and describe simple algorithms for counting and uniformly sampling valid labelings of graphs, assuming a path decomposition is given. Thus, we show that several well-studied counting and sampling problems are fixed parameter tractable (FPT) when parameterized by the pathwidth of the input graph. We discuss connections to counting and sampling problems for distributive lattices and, in particular, we give a new FPT algorithm for exactly counting and uniformly sampling stable matchings.

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Section: Counting and Sampling Elements In A Distributive Latticementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simple Counting and Sampling Algorithms for Graphs with Bounded Pathwidth

Cheng,

Rosenbaum

2020

Preprint

Self Cite

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“…A variety of systems [10], [11], industry-related problems [12]- [14], and economical problems [15] uses the stable marriage algorithm. Although useful, the application of the algorithm still has its lapses depending on specific requirements.…”

Section: Introductionmentioning

confidence: 99%

Enhancement Of Gale-Shapley algorithm with imbalanced sets for hiring and job finding applications

Mendoza

Barbosa

Cortez

et al. 2022

IJEECS

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In this paper, <span>we discuss a modification to the Gale Shapley algorithm in this study. We concentrated on how the modified algorithm would operate if the data sets for men and women were not equal. We showed how to measure the average energies of men and women with equal and unequal sets, how the new design of the algorithm will benefit both parties by duplicating sets of data to fill the unequal sets of data, resulting in an equal set of pairings, and how to measure the average energies of men and women of the new algorithm in this paper. Having stated that, each couple will have a stable partner and/or will be queued to the algorithm's suggested stable partner.</span>

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Recognizing When a Preference System is Close to Admitting a Master List

Schlotter

2023

Lecture Notes in Computer Science

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Stable Matchings with Restricted Preferences: Structure and Complexity

Cited by 4 publications

References 27 publications

Simple Counting and Sampling Algorithms for Graphs with Bounded Pathwidth

Simple Counting and Sampling Algorithms for Graphs with Bounded Pathwidth

Enhancement Of Gale-Shapley algorithm with imbalanced sets for hiring and job finding applications

Recognizing When a Preference System is Close to Admitting a Master List

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