21,431 research outputs found
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
Hypergraph Acyclicity and Propositional Model Counting
We show that the propositional model counting problem #SAT for CNF- formulas
with hypergraphs that allow a disjoint branches decomposition can be solved in
polynomial time. We show that this class of hypergraphs is incomparable to
hypergraphs of bounded incidence cliquewidth which were the biggest class of
hypergraphs for which #SAT was known to be solvable in polynomial time so far.
Furthermore, we present a polynomial time algorithm that computes a disjoint
branches decomposition of a given hypergraph if it exists and rejects
otherwise. Finally, we show that some slight extensions of the class of
hypergraphs with disjoint branches decompositions lead to intractable #SAT,
leaving open how to generalize the counting result of this paper
Efficient preparation and detection of microwave dressed-state qubits and qutrits with trapped ions
We demonstrate a method for preparing and detecting all eigenstates of a three-level microwave dressed system with a single trapped ion. The method significantly reduces the experimental complexity of gate operations with dressed-state qubits, as well as allowing all three of the dressed states to be prepared and detected, thereby providing access to a qutrit that is well protected from magnetic field noise. In addition, we demonstrate individual addressing of the clock transitions in two ions using a strong static magnetic field gradient, showing that our method can be used to prepare and detect microwave dressed states in a string of ions when performing multi-ion quantum operations with microwave and radio frequency fields. The individual addressability of clock transitions could also allow for the control of pairwise interaction strengths between arbitrary ions in a string using lasers
Creation of macroscopic superposition states from arrays of Bose-Einstein condensates
We consider how macroscopic quantum superpositions may be created from arrays
of Bose-Einstein condensates. We study a system of three condensates in Fock
states, all with the same number of atoms and show that this has the form of a
highly entangled superposition of different quasi-momenta. We then show how, by
partially releasing these condensates and detecting an interference pattern
where they overlap, it is possible to create a macroscopic superposition of
different relative phases for the remaining portions of the condensates. We
discuss methods for confirming these superpositions.Comment: 7 pages, 5 figure
Approximation algorithms for hard variants of the stable marriage and hospitals/residents problems
When ties and incomplete preference lists are permitted in the Stable Marriage and Hospitals/Residents problems, stable matchings can have different sizes. The problem of finding a maximum cardinality stable matching in this context is known to be NP-hard, even under very severe restrictions on the number, size and position of ties. In this paper, we describe polynomial-time 5/3-approximation algorithms for variants of these problems in which ties are on one side only and at the end of the preference lists. The particular variant is motivated by important applications in large scale centralised matching schemes
Small-Scale Interstellar Na I Structure Toward M92
We have used integral field echelle spectroscopy with the DensePak
fiber-optic array on the KPNO WIYN telescope to observe the central 27" x 43"
of the globular cluster M92 in the Na I D wavelength region at a spatial
resolution of 4". Two interstellar Na I absorption components are evident in
the spectra at LSR velocities of 0 km/s (Cloud 1) and -19 km/s (Cloud 2).
Substantial strength variations in both components are apparent down to scales
limited by the fiber-to-fiber separations. The derived Na I column densities
differ by a factor of 4 across the Cloud 1 absorption map and by a factor of 7
across the Cloud 2 map. Using distance upper limits of 400 and 800 pc for Cloud
1 and Cloud 2, respectively, the absorption maps indicate structure in the ISM
down to scales of 1600 and 3200 AU. The fiber-to-fiber Na I column density
differences toward M92 are comparable to those found in a similar study of the
ISM toward the globular cluster M15. Overall, the structures in the
interstellar components toward M92 have significantly lower column densities
than those toward M15. We interpret these low column density structures as
small-scale turbulent variations in the gas and compare them to the
larger-scale, higher column density variations toward M15, which may be the
hallmarks of actual H I structures.Comment: 9 pages, 2 figures, accepted for publication in ApJ Letter
Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game
We study the variant of the stable marriage problem in which the preferences
of the agents are allowed to include indifferences. We present a mechanism for
producing Pareto-stable matchings in stable marriage markets with indifferences
that is group strategyproof for one side of the market. Our key technique
involves modeling the stable marriage market as a generalized assignment game.
We also show that our mechanism can be implemented efficiently. These results
can be extended to the college admissions problem with indifferences
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