The "Stable Roommates" Problem with Random Preferences
نویسندگان
چکیده
منابع مشابه
Stable Roommates Problem with Random Preferences
Matching under preferences is a topic of great practical importance, deep mathematical structure, and elegant algorithmics [Manlove 2013; Gusfield and Irving 1989]. The most famous example is the stable marriage problem, where n men and n women compete with each other in the “marriage market.” Each man ranks all the women according to his individual preferences, and each woman does the same wit...
متن کاملThe Stable Roommates Problem with Ties
We study the variant of the well-known Stable Roommates problem in which participants are permitted to express ties in their preference lists. In this setting, more than one definition of stability is possible. Here we consider two of these stability criteria, so-called super-stability and weak stability. We present a linear-time algorithm for finding a super-stable matching if one exists, give...
متن کاملThe Strongly Stable Roommates Problem
An instance of the strongly stable roommates problem with incomplete lists and ties (srti) is an undirected non-bipartite graph G = (V,E), with an adjacency list being a linearly ordered list of ties, which are vertices equally good for a given vertex. Ties are disjoint and may contain one vertex. A matching M is a set of vertex-disjoint edges. An edge {x, y} ∈ E \M is a blocking edge for M if ...
متن کامل"Almost Stable" Matchings in the Roommates Problem
An instance of the classical Stable Roommates problem (sr) need not admit a stable matching. This motivates the problem of finding a matching that is “as stable as possible”, i.e. admits the fewest number of blocking pairs. In this paper we prove that, given an sr instance with n agents, in which all preference lists are complete, the problem of finding a matching with the fewest number of bloc...
متن کاملSolutions for the Stable Roommates Problem with Payments
The stable roommates problem with payments has as input a graph G = (V,E) with an edge weighting w : E → R≥0 and the problem is to find a stable solution. A solution is a matching M with a vector p ∈ R≥0 that satisfies pu + pv = w(uv) for all uv ∈ M and pu = 0 for all u unmatched in M . A solution is stable if it prevents blocking pairs, i.e., pairs of adjacent vertices u and v with pu + pv < w...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1993
ISSN: 0091-1798
DOI: 10.1214/aop/1176989126