195,681 research outputs found
Finding robust solutions to stable marriage
We study the notion of robustness in stable matching problems. We first define robustness by introducing (a,b)-supermatches. An (a,b)-supermatch is a stable matching in which if a pairs break up it is possible to find another stable matching by changing the partners of those a pairs and at most b other pairs. In this context, we define the most robust stable matching as a (1,b)-supermatch where b is minimum. We show that checking whether a given stable matching is a (1,b)-supermatch can be done in polynomial time. Next, we use this procedure to design a constraint programming model, a local search approach, and a genetic algorithm to find the most robust stable matching. Our empirical evaluation on large instances show that local search outperforms the other approaches
Local search for stable marriage problems
The stable marriage (SM) 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. In the
classical formulation, n men and n women express their preferences (via a
strict total order) over the members of the other sex. Solving a SM problem
means finding a stable marriage where stability is an envy-free notion: no man
and woman who are not married to each other would both prefer each other to
their partners or to being single. We consider both the classical stable
marriage problem and one of its useful variations (denoted SMTI) where the men
and women express their preferences in the form of an incomplete preference
list with ties over a subset of the members of the other sex. Matchings are
permitted only with people who appear in these lists, an we try to find a
stable matching that marries as many people as possible. Whilst the SM problem
is polynomial to solve, the SMTI problem is NP-hard. We propose to tackle both
problems via a local search approach, which exploits properties of the problems
to reduce the size of the neighborhood and to make local moves efficiently. We
evaluate empirically our algorithm for SM problems by measuring its runtime
behaviour and its ability to sample the lattice of all possible stable
marriages. We evaluate our algorithm for SMTI problems in terms of both its
runtime behaviour and its ability to find a maximum cardinality stable
marriage.For SM problems, the number of steps of our algorithm grows only as
O(nlog(n)), and that it samples very well the set of all stable marriages. It
is thus a fair and efficient approach to generate stable marriages.Furthermore,
our approach for SMTI problems is able to solve large problems, quickly
returning stable matchings of large and often optimal size despite the
NP-hardness of this problem.Comment: 12 pages, Proc. COMSOC 2010 (Third International Workshop on
Computational Social Choice
Local search for stable marriage problems with ties and incomplete lists
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 stable marriage problem, where the men and women express their
preferences using a preference list with ties over a subset of the members of
the other sex. Matchings are permitted only with people who appear in these
preference lists. In this setting, we study the problem of finding a stable
matching that marries as many people as possible. Stability is an envy-free
notion: no man and woman who are not married to each other would both prefer
each other to their partners or to being single. This problem is NP-hard. We
tackle this problem using local search, exploiting properties of the problem to
reduce the size of the neighborhood and to make local moves efficiently.
Experimental results show that this approach is able to solve large problems,
quickly returning stable matchings of large and often optimal size.Comment: 12 pages, Proc. PRICAI 2010 (11th Pacific Rim International
Conference on Artificial Intelligence), Byoung-Tak Zhang and Mehmet A. Orgun
eds., Springer LNA
Distributed Relay Selection for Heterogeneous UAV Communication Networks Using A Many-to-Many Matching Game Without Substitutability
This paper proposes a distributed multiple relay selection scheme to maximize
the satisfaction experiences of unmanned aerial vehicles (UAV) communication
networks. The multi-radio and multi-channel (MRMC) UAV communication system is
considered in this paper. One source UAV can select one or more relay radios,
and each relay radio can be shared by multiple source UAVs equally. Without the
center controller, source UAVs with heterogeneous requirements compete for
channels dominated by relay radios. In order to optimize the global
satisfaction performance, we model the UAV communication network as a
many-to-many matching market without substitutability. We design a potential
matching approach to address the optimization problem, in which the optimizing
of local matching process will lead to the improvement of global matching
results. Simulation results show that the proposed distributed matching
approach yields good matching performance of satisfaction, which is close to
the global optimum result. Moreover, the many-to-many potential matching
approach outperforms existing schemes sufficiently in terms of global
satisfaction within a reasonable convergence time.Comment: 6 pages, 4 figures, conferenc
An Extended Stable Marriage Problem Algorithm for Clone Detection
Code cloning negatively affects industrial software and threatens
intellectual property. This paper presents a novel approach to detecting cloned
software by using a bijective matching technique. The proposed approach focuses
on increasing the range of similarity measures and thus enhancing the precision
of the detection. This is achieved by extending a well-known stable-marriage
problem (SMP) and demonstrating how matches between code fragments of different
files can be expressed. A prototype of the proposed approach is provided using
a proper scenario, which shows a noticeable improvement in several features of
clone detection such as scalability and accuracy.Comment: 20 pages, 10 figures, 6 table
Random multi-index matching problems
The multi-index matching problem (MIMP) generalizes the well known matching
problem by going from pairs to d-uplets. We use the cavity method from
statistical physics to analyze its properties when the costs of the d-uplets
are random. At low temperatures we find for d>2 a frozen glassy phase with
vanishing entropy. We also investigate some properties of small samples by
enumerating the lowest cost matchings to compare with our theoretical
predictions.Comment: 22 pages, 16 figure
Genetic embedded matching approach to ground states in continuous-spin systems
Due to an extremely rugged structure of the free energy landscape, the
determination of spin-glass ground states is among the hardest known
optimization problems, found to be NP-hard in the most general case. Owing to
the specific structure of local (free) energy minima, general-purpose
optimization strategies perform relatively poorly on these problems, and a
number of specially tailored optimization techniques have been developed in
particular for the Ising spin glass and similar discrete systems. Here, an
efficient optimization heuristic for the much less discussed case of continuous
spins is introduced, based on the combination of an embedding of Ising spins
into the continuous rotators and an appropriate variant of a genetic algorithm.
Statistical techniques for insuring high reliability in finding (numerically)
exact ground states are discussed, and the method is benchmarked against the
simulated annealing approach.Comment: 17 pages, 12 figures, 1 tabl
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