Subquadratic Algorithms for Succinct Stable Matching

Künnemann, Marvin; Moeller, Daniel; Paturi, Ramamohan; Schneider, Stefan

doi:10.1007/s00453-019-00564-x

Cited by 4 publications

(7 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This conjecture is consistent with the results of Chebolu et al [5], who show that #SM is #BIS-complete in the -attributed model for any ≥ 3. Chebolu et al [5] and Künnemann et al [25] also consider the -Euclidean preference model defined by Bogomolnaia and Laslier [3]. In this model, each agent is also associated with a point in R .…”

Section: Discussion and Questionsmentioning

confidence: 99%

See 1 more Smart Citation

Stable Matchings with Restricted Preferences: Structure and Complexity

Cheng

Rosenbaum

2021

Proceedings of the 22nd ACM Conference on Economics and Computation

View full text Add to dashboard Cite

Section: Discussion and Questionsmentioning

confidence: 99%

“…We note that Künnemann et al[25] had similar difficulty with the -list model, and posed as an open question whether or not 2-list preferences admit an ( 2 )-time algorithm for finding a stable matching.Technical Program Presentation • EC '21, July 18-23, 2021, Budapest, Hungary…”

mentioning

confidence: 91%

Stable Matchings with Restricted Preferences: Structure and Complexity

Cheng

Rosenbaum

2021

Proceedings of the 22nd ACM Conference on Economics and Computation

View full text Add to dashboard Cite

“…Finding (and verifying) stable matchings with restricted preferences has also been studied in the centralized [31] and distributed [27] settings. Künnemann et al [31] showed that for the k-attribute, k-list, k-Euclidean, and "single-peaked" preference models, stable matchings can be computed in o(n 2 ) time when k = O (1). For k = ω(log n), however, k-attribute and k-Euclidean preferences require Ω(n 2 ) time, assuming the strong exponential time hypothesis.…”

Section: Related Workmentioning

confidence: 99%

“…Chebolu et al [5] and Künnemann et al [31] also consider the k-Euclidean preference model defined by Bogomolnaia and Laslier [3]. In this model, each agent is also associated with a point in R k .…”

Section: Finding Sex-equal and Balanced Stable Matchingsmentioning

confidence: 99%

See 1 more Smart Citation

Stable Matchings with Restricted Preferences: Structure and Complexity

Cheng¹,

Rosenbaum²

2020

Preprint

View full text Add to dashboard Cite

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 I. Furthermore, for every poset P, an instance I(P) can be constructed efficiently so that the rotation poset of I(P) is isomorphic to P. In this case, we say that I(P) realizes P. Many researchers exploit the rotation poset of an instance to develop fast algorithms or to establish the hardness of stable matching problems.To make the problem of sampling stable matchings more tractable, Bhatnagar et al.[1] introduced stable matching instances whose preference lists are restricted but nevertheless model situations that arise in practice. In this paper, we study four such parameterized restrictions; our goal is to characterize the rotation posets that arise from these models:1. k-bounded, where each agent has at most k acceptable partners; 2. k-attribute, where each agent has an associated k dimensional profile and her preferences are determined by a linear function of the others' profiles;3. (k 1 , k 2 )-list, where the men and women can be partitioned into k 1 and k 2 sets (respectively) such that within each set all agents have identical preferences;4. k-range, where there is an objective ranking for each set of agents, and each person ranks agents from the other group within k of the others' objective ranks.We prove that there is a constant k so that every rotation poset is realized by some instance in models 1-3 (k ≥ 3 for k-bounded, k ≥ 6 for k-attribute, and k 1 ≥ 2, k 2 = ∞ for (k 1 , k 2 )-list, respectively). We describe efficient algorithms for constructing such instances given the Hasse diagram of a poset. As a consequence, the fundamental problem of counting stable matchings remains #BIS-complete even for these restricted instances.For k-range preferences, we show that a poset P is realizable if and only if the Hasse diagram of P has pathwidth bounded by functions of k. Using this characterization, we show that the following problems are fixed parameter tractable when parametrized by the range of the instance: exactly counting and uniformly sampling stable matchings, finding median, sex-equal, and balanced stable matchings.

show abstract

A Fine-Grained Perspective on Approximating Subset Sum and Partition

Bringmann

Nakos

2021

Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA)

View full text Add to dashboard Cite

Subset Sum Ratio is the following optimization problem: Given a set of n positive numbers I, find disjoint subsets X, Y Ď I minimizing the ratio maxtΣpXq{ΣpY q, ΣpY q{ΣpXqu, where ΣpZq denotes the sum of all elements of Z. Subset Sum Ratio is an optimization variant of the Equal Subset Sum problem. It was introduced by Woeginger and Yu in '92 and is known to admit an FPTAS [Bazgan, Santha, Tuza '98]. The best approximation schemes before this work had running time Opn 4 {εq [Melissinos, Pagourtzis '18], r Opn 2.3 {ε 2.6 q and r Opn 2 {ε 3 q [Alonistiotis et al. '22].In this work, we present an improved approximation scheme for Subset Sum Ratio running in time Opn{ε 0.9386 q. Here we assume that the items are given in sorted order, otherwise we need an additional running time of Opn log nq for sorting. Our improved running time simultaneously improves the dependence on n to linear and the dependence on 1{ε to sublinear.For comparison, the related Subset Sum problem admits an approximation scheme running in time Opn{εq [Gens, Levner '79]. If one would achieve an approximation scheme with running time r Opn{ε 0.99 q for Subset Sum, then one would falsify the Strong Exponential Time Hypothesis [Abboud, Bringmann, Hermelin, Shabtay '19] as well as the Min-Plus-Convolution Hypothesis [Bringmann, Nakos '21]. We thus establish that Subset Sum Ratio admits faster approximation schemes than Subset Sum. This comes as a surprise, since at any point in time before this work the best known approximation scheme for Subset Sum Ratio had a worse running time than the best known approximation scheme for Subset Sum.

show abstract

Subquadratic Algorithms for Succinct Stable Matching

Cited by 4 publications

References 41 publications

Stable Matchings with Restricted Preferences: Structure and Complexity

Stable Matchings with Restricted Preferences: Structure and Complexity

Stable Matchings with Restricted Preferences: Structure and Complexity

A Fine-Grained Perspective on Approximating Subset Sum and Partition

Contact Info

Product

Resources

About