Adapting Stable Matchings to Evolving Preferences

Bredereck, Robert; Knop, Dušan; Luo, Jiaqi; Niedermeier, Rolf

doi:10.1609/aaai.v34i02.5550

Cited by 15 publications

(40 citation statements)

References 20 publications

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“…First, to better understand the NPcompleteness result, one may study the parameterized complexity with respect to the "degree" of incompleteness of the input preferences, such as the number of ties or the number of agents that are in the same equivalence class of the tie-relation. We refer to some recent papers on the parameterized complexity of preference-based stable matching problems [1,11,12,[14][15][16]29,[40][41][42]45] for this line of research. Second, we were not able to settle the computational complexity for complete preferences that are also single-peaked and single-crossing.…”

Section: Resultsmentioning

confidence: 99%

Stable roommates with narcissistic, single-peaked, and single-crossing preferences

Bredereck

Finnendahl

Niedermeier

2020

Auton Agent Multi-Agent Syst

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The classical Stable Roommates problem is to decide whether there exists a matching of an even number of agents such that no two agents which are not matched to each other would prefer to be with each other rather than with their respectively assigned partners. We investigate Stable Roommates with complete (i.e., every agent can be matched with any other agent) or incomplete preferences, with ties (i.e., two agents are considered of equal value to some agent) or without ties. It is known that in general allowing ties makes the problem NP-complete. We provide algorithms for Stable Roommates that are, compared to those in the literature, more efficient when the input preferences are complete and have some structural property, such as being narcissistic, single-peaked, and single-crossing. However, when the preferences are incomplete and have ties, we show that being single-peaked and single-crossing does not reduce the computational complexity—Stable Roommates remains NP-complete.

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Section: Resultsmentioning

confidence: 99%

Stable roommates with narcissistic, single-peaked, and single-crossing preferences

Bredereck

Finnendahl

Niedermeier

2020

Auton Agent Multi-Agent Syst

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“…We are closest to the purely theoretical work of Bredereck et al [2020], using their formulation of incremental stable matching problems (we refer to their related work section for an extensive discussion of related and motivating literature before 2020). Among others, they proved that INCREMENTAL STABLE MARRIAGE is polynomial-time solvable but is -hard parameterized by the allowed change between the two matchings) if the preferences may contain ties.…”

Section: Related Workmentioning

confidence: 99%

“…One wants to find a "stable" assignment of each resident to at most one hospital such that a given capacity for each hospital is respected. To model the task of adjusting a matching to change, Bredereck et al [2020] introduced the problem, given a stable matching with respect to some initial preference profile, to find a new matching which is stable with respect to an updated preference profile (where some agents performed swaps in their preferences) and which is as similar as possible to the given matching. 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).…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we address multiple so-far unstudied aspects of our introductory school choice example. First, we theoretically and experimentally relate different types of changes to each other, including swapping two agents in some preference list (as studied by Bredereck et al [2020]) and deleting an agent (as in our introductory example). Second, we initiate the study of the incremental variant of many-toone stable matchings (HOSPITAL RESIDENTS).…”

Section: Introductionmentioning

confidence: 99%

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

Boehmer¹,

Heeger²,

Niedermeier³

2021

Preprint

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Following up on purely theoretical work of Bredereck et al. [AAAI 2020], we contribute further theoretical insights into adapting stable two-sided matchings to change. Moreover, we perform extensive empirical studies hinting at numerous practically useful properties. Our theoretical extensions include the study of new problems (that is, incremental variants of ALMOST STABLE MAR-RIAGE 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). Our experimental findings reveal, for instance, that allowing the new matching to be blocked by a few pairs significantly decreases the necessary differences between the old and the new stable matching.

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“…Bredereck et al [4] designed a polynomial-time algorithm for the following problem: given a bipartite graph G, a pair L and L ′ of preference lists for G, a stable matching M of (G, L) and a natural number k, decide whether (G, L ′ ) has a stable matching M ′ such that the symmetric difference of M and M ′ is at most k.…”

Section: Introductionmentioning

confidence: 99%

Preference Swaps for the Stable Matching Problem

Eiben¹,

Gutin²,

Neary³

et al. 2021

Preprint

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An instance I of the Stable Matching Problem (SMP) is given by a bipartite graph with a preference list of neighbors for every vertex. A swap in I is the exchange of two consecutive vertices in a preference list. A swap can be viewed as a smallest perturbation of I. Boehmer et al. (2021) designed a polynomial-time algorithm to find the minimum number of swaps required to turn a given maximal matching into a stable matching. To generalize this result to the many-to-many version of SMP, we introduce a new representation of SMP as an extended bipartite graph and reduce the problem to submodular minimization. It is a natural problem to establish computational complexity of deciding whether at most k swaps are enough to turn I into an instance where one of the maximum matchings is stable. Using a hardness result of Gupta et al. (2020), we prove that it is NP-hard to decide whether at most k swaps are enough to turn I into an instance with a stable perfect matching. Moreover, this problem parameterized by k is W[1]-hard. We also obtain a lower bound on the running time for solving the problem using the Exponential Time Hypothesis.

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Adapting Stable Matchings to Evolving Preferences

Cited by 15 publications

References 20 publications

Stable roommates with narcissistic, single-peaked, and single-crossing preferences

Stable roommates with narcissistic, single-peaked, and single-crossing preferences

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

Preference Swaps for the Stable Matching Problem

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