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Related papers: Preference Swaps for the Stable Matching Problem

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We study a natural generalization of stable matching to the maximum weight stable matching problem and we obtain a combinatorial polynomial time algorithm for it by reducing it to the problem of finding a maximum weight ideal cut in a DAG.…

Data Structures and Algorithms · Computer Science 2018-04-04 Tung Mai , Vijay V. Vazirani

Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…

Computer Science and Game Theory · Computer Science 2024-08-30 Naoyuki Kamiyama

We generalize several schedule matching theorems of Baiou-Balinski (Math. Oper. Res., 27 (2002), 485) and Alkan-Gale (J. Econ. Th. 112 (2003), 289) by applying a fixed point method of Fleiner (Math. Oper. Res., 28 (2003), 103). Thanks to a…

Optimization and Control · Mathematics 2010-05-13 Vilmos Komornik , Zsolt Komornik , Christelle K. Viauroux

We introduce the notion of a stable instance for a discrete optimization problem, and argue that in many practical situations only sufficiently stable instances are of interest. The question then arises whether stable instances of NP--hard…

Computational Complexity · Computer Science 2009-06-18 Yonatan Bilu , Nathan Linial

In a graph where vertices have preferences over their neighbors, a matching is called popular if it does not lose a head-to-head election against any other matching when the vertices vote between the matchings. Popular matchings can be seen…

Discrete Mathematics · Computer Science 2022-05-05 Ildikó Schlotter , Ágnes Cseh

In the Maximum Duo-Preservation String Mapping problem we are given two strings and wish to map the letters of the former to the letters of the latter so as to maximise the number of duos. A duo is a pair of consecutive letters that is…

Data Structures and Algorithms · Computer Science 2017-05-31 Bartłomiej Dudek , Paweł Gawrychowski , Piotr Ostropolski-Nalewaja

The secret protection problem (SPP) seeks to synthesize a minimum-cost policy ensuring that every execution from an initial state to a secret state includes a sufficient number of protected events. Previous work showed that the problem is…

Formal Languages and Automata Theory · Computer Science 2025-09-19 Tomáš Masopust , Jakub Večeřa

In this paper we show that when individuals in a bipartite network exclusively choose partners and exchange valued goods with their partners, then there exists a set of exchanges that are pair-wise stable. Pair-wise stability implies that…

Computer Science and Game Theory · Computer Science 2010-11-12 Ankur Mani , Asuman Ozdaglar , Alex , Pentland

Scarf's algorithm gives a pivoting procedure to find a special vertex -- a dominating vertex -- in down-monotone polytopes. This paper studies the behavior of Scarf's algorithm when employed to find stable matchings in bipartite graphs.…

Combinatorics · Mathematics 2023-03-03 Yuri Faenza , Chengyue He , Jay Sethuraman

The qubit routing problem, also known as the swap minimization problem, is a (classical) combinatorial optimization problem that arises in the design of compilers of quantum programs. We study the qubit routing problem from the viewpoint of…

Data Structures and Algorithms · Computer Science 2023-05-16 Takehiro Ito , Naonori Kakimura , Naoyuki Kamiyama , Yusuke Kobayashi , Yoshio Okamoto

In multi-parameter persistence, the matching distance is defined as the supremum of weighted bottleneck distances on the barcodes given by the restriction of persistence modules to lines with a positive slope. In the case of finitely…

Computational Geometry · Computer Science 2023-12-06 Robyn Brooks , Celia Hacker , Claudia Landi , Barbara I. Mahler , Elizabeth R. Stephenson

Kidney exchange programs (KEP's) represent an additional possibility of transplant for patients suffering from end stage kidney disease. If a patient has a willing living donor with whom the patient is not compatible, the pair…

Computer Science and Game Theory · Computer Science 2020-12-10 Xenia Klimentova , Péter Biró , Ana Viana , Virginia Costa , João Pedro Pedroso

The study of stable matchings usually relies on the assumption that agents' preferences over the opposite side are complete and known. In many real markets, however, preferences might be uncertain and revealed only through costly…

Computer Science and Game Theory · Computer Science 2026-02-25 Moshe Babaioff , Rotem Gil , Assaf Romm

We show that \emph{Sorting by Strip Swaps} (SbSS) is NP-hard by a polynomial reduction of \emph{Block Sorting}. The key idea is a local gadget, a \emph{cage}, that replaces every decreasing adjacency $(a_i,a_{i+1})$ by a guarded triple…

Data Structures and Algorithms · Computer Science 2025-11-04 Swapnoneel Roy , Asai Asaithambi , Debajyoti Mukhopadhyay

A combinatorial trade is a pair of sets of blocks of elements that can be exchanged while preserving relevant subset intersection constraints. The class of balanced and swap-robust minimal trades was proposed in [1] for exchanging blocks of…

Data Structures and Algorithms · Computer Science 2024-06-24 Jin Sima , Chao Pan , Olgica Milenkovic

This paper considers the problem of finding an optimal order for entanglement swapping in a heterogeneous path of quantum repeaters so as to maximize the path throughput defined as the delivery rate of end-to-end entanglements. The primary…

Quantum Physics · Physics 2025-09-11 Van Sy Mai , Abderrahim Amlou , Amar Abane , Abdella Battou

We are given a bipartite graph $G = \left( A \cup B, E \right)$. In the one-sided model, every $a \in A$ (often called agents) ranks its neighbours $z \in N_{a}$ strictly, and no $b \in B$ has any preference order over its neighbours $y \in…

Computer Science and Game Theory · Computer Science 2025-10-30 Koustav De

We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of…

Data Structures and Algorithms · Computer Science 2019-04-15 Marthe Bonamy , Nicolas Bousquet , Marc Heinrich , Takehiro Ito , Yusuke Kobayashi , Arnaud Mary , Moritz Mühlenthaler , Kunihiro Wasa

Adaptivity to changing environments and constraints is key to success in modern society. We address this by proposing "incrementalized versions" of Stable Marriage and Stable Roommates. That is, we try to answer the following question: for…

Computer Science and Game Theory · Computer Science 2019-11-25 Robert Bredereck , Jiehua Chen , Dušan Knop , Junjie Luo , Rolf Niedermeier

The stable roommates problem does not necessarily have a solution, i.e. a stable matching. We had found that, for the uniformly random instance, the expected number of solutions converges to $e^{1/2}$ as $n$, the number of members, grows,…

Combinatorics · Mathematics 2017-05-24 Boris Pittel