Related papers: The Stable Matching Problem and Sudoku
In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…
We develop a new discrete mathematical model which includes the classical Sudoku puzzle, Latin Squares and gerechte designs. This problem is described by integer equations and a special type of inequality constraint. We consider solutions…
Direct solution of simultaneous linear equations is regarded to be slow for large systems of equations and requires special treatment to avoid numerical instability. A new method is proposed that addresses the numerical instability without…
We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are…
Over the last decade, Sudoku, a combinatorial number-placement puzzle, has become a favorite pastimes of many all around the world. In this puzzle, the task is to complete a partially filled $9 \times 9$ square with numbers 1 through 9,…
In the marriage problem, a variant of the bi-parted matching problem, each member has a `wish-list' expressing his/her preference for all possible partners; this list consists of random, positive real numbers drawn from a certain…
Several countries successfully use centralized matching schemes for school or higher education assignment, or for entry-level labour markets. In this paper we explore the computational aspects of a possible similar scheme for assigning…
This paper develops an integer programming approach to two-sided many-to-one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that stable matchings exist in a discrete…
Gale and Shapley introduced a matching problem between two sets of agents where each agent on one side has an exogenous preference ordering over the agents on the other side. They defined a matching as stable if no unmatched pair can both…
Suppose each of $n$ men and $n$ women is located at a point in a metric space. A woman ranks the men in order of their distance to her from closest to farthest, breaking ties at random. The men rank the women similarly. An interesting…
In this paper, we propose a model of the marriage market in which individuals meet potential partners either directly or through their friends. When socialization is exogenous, a higher arrival rate of direct meetings also implies more…
The stable marriage problem with ties is a well-studied and interesting problem in game theory. We are given a set of men and a set of women. Each individual has a preference ordering on the opposite group, which can possibly contain ties.…
We study stable matching problems where agents have multilayer preferences: There are $\ell$ layers each consisting of one preference relation for each agent. Recently, Chen et al. [EC '18] studied such problems with strict preferences,…
We study dynamic decentralized two-sided matching in which players may encounter unanticipated experiences. As they become aware of these experiences, they may change their preferences over players on the other side of the market.…
Sudoku is a famous logic puzzle where the player has to fill a number between 1 and 9 into each empty cell of a $9 \times 9$ grid such that every number appears exactly once in each row, each column, and each $3 \times 3$ block. In 2020,…
In a dynamic matching market, such as a marriage or job market, how should agents balance accepting a proposed match with the cost of continuing their search? We consider this problem in a discrete setting, in which agents have cardinal…
Given a set of $n$ men represented by $n$ points lying on a line, and $n$ women represented by $n$ points lying on another parallel line, with each person having a list that ranks some people of opposite gender as his/her acceptable…
This paper presents a comparative analysis of Sudoku-solving strategies, focusing on recursive backtracking and a heuristic-based constraint propagation method. Using a dataset of 500 puzzles across five difficulty levels (Beginner to…
The mathematical aspects of the popular logic game Sudoku incorporate a significant number of the group theory concepts. In this note, we describe all symmetric transformations of the Sudoku grid. We do not intend to obtain a new strategy…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…