Modeling Stable Matching Problems with Answer Set Programming

The Stable Marriage Problem (SMP) is a well-known matching problem first introduced and solved by Gale and Shapley (1962). Several variants and extensions to this problem have since been investigated to cover a wider set of applications. Each time a new variant is considered, however, a new algorithm needs to be developed and implemented. As an alternative, in this paper we propose an encoding of the SMP using Answer Set Programming (ASP). Our encoding can easily be extended and adapted to the needs of specific applications. As an illustration we show how stable matchings can be found when individuals may designate unacceptable partners and ties between preferences are allowed. Subsequently, we show how our ASP based encoding naturally allows us to select specific stable matchings which are optimal according to a given criterion. Each time, we can rely on generic and efficient off-the-shelf answer set solvers to find (optimal) stable matchings.Comment: 26 page

Stable marriage and roommates problems with restricted edges: complexity and approximability

In the Stable Marriage and Roommates problems, a set of agents is given, each of them having a strictly ordered preference list over some or all of the other agents. A matching is a set of disjoint pairs of mutually acceptable agents. If any two agents mutually prefer each other to their partner, then they block the matching, otherwise, the matching is said to be stable. We investigate the complexity of finding a solution satisfying additional constraints on restricted pairs of agents. Restricted pairs can be either forced or forbidden. A stable solution must contain all of the forced pairs, while it must contain none of the forbidden pairs. Dias et al. (2003) gave a polynomial-time algorithm to decide whether such a solution exists in the presence of restricted edges. If the answer is no, one might look for a solution close to optimal. Since optimality in this context means that the matching is stable and satisfies all constraints on restricted pairs, there are two ways of relaxing the constraints by permitting a solution to: (1) be blocked by as few as possible pairs, or (2) violate as few as possible constraints n restricted pairs. Our main theorems prove that for the (bipartite) Stable Marriage problem, case (1) leads to View the MathML source-hardness and inapproximability results, whilst case (2) can be solved in polynomial time. For non-bipartite Stable Roommates instances, case (2) yields an View the MathML source-hard but (under some cardinality assumptions) 2-approximable problem. In the case of View the MathML source-hard problems, we also discuss polynomially solvable special cases, arising from restrictions on the lengths of the preference lists, or upper bounds on the numbers of restricted pairs

Signal-Jamming in a Sequential Auction

In a recurring auction early bids may reveal bidders’ types, which in turn affects bidding in later auctions. Bidders take this into account and may bid in a way that conceals their private information until the last auction is played. The present paper analyzes the equilibrium of a sequence of ?rst-price auctions assuming bidders have stable private values. We show that signal-jamming occurs and explore the dynamics of equilibrium prices

Coherence Time Effects on J/psi Production and Suppression in Relativistic Heavy Ion Collisions

Using a coherence time extracted from high precision proton-nucleus Drell-Yan measurements and a nuclear absorption cross section extracted from pA charmonium production experiments, we study J/psi production and absorption in nucleus-nucleus collisions. We find that coherence time effects are large enough to affect the measured J/psi-to-Drell-Yan ratio. The S+U data at 200A GeV/c measured by NA38 are reproduced quantitatively without the introduction of any new parameters. However, when compared with recent NA50 measurements for Pb+Pb at 158A GeV/c, the data is not reproduced in trend or in magnitude.Comment: 8 pages, 2 figure

Coherence Time in High Energy Proton-Nucleus Collisions

Precisely measured Drell-Yan cross sections for 800 GeV protons incident on a variety of nuclear targets exhibit a deviation from linear scaling in the atomic number A. We show that this deviation can be accounted for by energy degradation of the proton as it passes through the nucleus if account is taken of the time delay of particle production due to quantum coherence. We infer an average proper coherence time of 0.4 +- 0.1 fm/c, corresponding to a coherence path length of 8 +- 2 fm in the rest frame of the nucleus.Comment: 11 pages in LaTeX. Includes 6 eps figures. Uses epsf.st

On the imaginary parts and infrared divergences of two-loop vector boson self-energies in thermal QCD

We calculate the imaginary part of the retarded two-loop self-energy of a static vector boson in a plasma of quarks and gluons of temperature T, using the imaginary time formalism. We recombine various cuts of the self-energy to generate physical processes. We demonstrate how cuts containing loops may be reinterpreted in terms of interference between Order $\alpha$ tree diagrams and the Born term along with spectators from the medium. We apply our results to the rate of dilepton production in the limit of dilepton invariant mass E>>T. We find that all infrared and collinear singularities cancel in the final result obtained in this limit.Comment: references added, typos corrected, slightly abridged, version accepted for publication in Phys. Rev.

The effects of meson mixing on dilepton spectra

The effect of scalar and vector meson mixing on the dilepton radiation from hot and dense hadronic matter is estimated in different isospin channels. In particular, we study the effect of $\sigma$-$\omega$ and $\rho-a_0$ mixing and calculate the corresponding rates. Effects are found to be significant compared to standard $\pi$-$\pi$ and $K$-${\bar K}$ annihilations. While the mixing in the isoscalar channel mostly gives a contribution in the invariant mass range between the two-pion threshold and the $\omega$ peak, the isovector channel mixing induces an additional peak just below that of the $\phi$. Experimentally, the dilepton signals from $\rho$-$a_0$ mixing seem to be more tractable than those from $\sigma$-$\omega$ mixing.Comment: 10 pages, 9 figure