相关论文: A New Version of the Menages Problem

We address the problem of enumeration of seating arrangements of married couples around a circular table such that no spouses sit next to each other and no k consecutive persons are of the same gender. While the case of k=2 corresponds to…

We give a solution of the following combinatorial problem: "Let one from $n$ married couples in the m\'enage problem (see Problem 1) be a couple of a known mathematician $M$ and his wife. After the ladies are seated at every other chair,…

We present a fascinating model that has lately caught attention among physicists working in complexity related fields. Though it originated from mathematics and later from economics, the model is very enlightening in many aspects that we…

The Stable Marriage Problem is to find a one-to-one matching for two equally sized sets of agents. Due to its widespread applications in the real world, especially the unique importance to the centralized match maker, a very large number of…

The stable marriage problem has been introduced in order to describe a complex system where individuals attempt to optimise their own satisfaction, subject to mutually conflicting constraints. Due to the potential large applicability of…

The stable marriage problem is a well-known problem of matching men to women so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from…

A king invites n couples to sit around a round table with 2n+1 seats. For each couple, the king decides a prescribed distance d between 1 and n which the two spouses have to be seated from each other (distance d means that they are…

The classical stable marriage problem asks for a matching between a set of men and a set of women with no blocking pairs, which are pairs formed by a man and a woman who would both prefer switching from their current status to be paired up…

The stable marriage problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. We consider a useful variation of the…

Most of the mammal species hold polygynous mating systems. The majority of the marriage systems of mankind were also polygynous over civilized history, however, socially imposed monogamy gradually prevails throughout the world. This is…

The problem of the malicious ma\^{i}tre d' is introduced and solved by Peter Winkler in his book Mathematical Puzzles: A Connoisseur's Collection [1]. This problem is about a ma\^{i}tre d' seating diners around a table, trying to maximize…

The napkin problem was first posed by John H. Conway, and written up as a `toughie' in "Mathematical Puzzles: A Connoisseur's Collection," by Peter Winkler. To paraphrase Winkler's book, there is a banquet dinner to be served at a…

We consider two river crossing problems, about jealous husbands and about missionaries and cannibals. The missionaries and cannibals problem arose a thousand years after the jealous husbands problem, although its solution had actually…

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…

We investigate the hardness of establishing as many stable marriages (that is, marriages that last forever) in a population whose memory is placed in some arbitrary state with respect to the considered problem, and where traitors try to…

In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of…

In the stable marriage problem N men and N women have to be matched by pairs under the constraint that the resulting matching is stable. We study the statistical properties of stable matchings in the large N limit using both numerical and…

In this paper, we begin by discussing different types of preference profiles related to the stable marriage problem. We then introduce the concept of soulmates, which are a man and a woman who rank each other first. Inversely, we examine…

This paper has two objectives. One is to give a linear time algorithm that solves the stable roommates problem (i.e., obtains one stable matching) using the stable marriage problem. The idea is that a stable matching of a roommate instance…

We study the classical, two-sided stable marriage problem under pairwise preferences. In the most general setting, agents are allowed to express their preferences as comparisons of any two of their edges and they also have the right to…