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

The influence of parathyroid hormone upon bone formation in xenopus laevis

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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

The Stable Roommates problem with short lists

We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists SRI that are degree constrained, i.e., preference lists are of bounded length. The first variant, EGAL d-SRI, involves finding an egalitarian stable matching in solvable instances of SRI with preference lists of length at most d. We show that this problem is NP-hard even if d=3. On the positive side we give a (2d+3)/7-approximation algorithm for d={3,4,5} which improves on the known bound of 2 for the unbounded preference list case. In the second variant of SRI, called d-SRTI, preference lists can include ties and are of length at most d. We show that the problem of deciding whether an instance of d-SRTI admits a stable matching is NP-complete even if d=3. We also consider the "most stable" version of this problem and prove a strong inapproximability bound for the d=3 case. However for d=2 we show that the latter problem can be solved in polynomial time.Comment: short version appeared at SAGT 201

Manipulation Strategies for the Rank Maximal Matching Problem

We consider manipulation strategies for the rank-maximal matching problem. In the rank-maximal matching problem we are given a bipartite graph $G = (A \cup P, E)$ such that $A$ denotes a set of applicants and $P$ a set of posts. Each applicant $a \in A$ has a preference list over the set of his neighbours in $G$, possibly involving ties. Preference lists are represented by ranks on the edges - an edge $(a,p)$ has rank $i$, denoted as $rank(a,p)=i$, if post $p$ belongs to one of $a$'s $i$-th choices. A rank-maximal matching is one in which the maximum number of applicants is matched to their rank one posts and subject to this condition, the maximum number of applicants is matched to their rank two posts, and so on. A rank-maximal matching can be computed in $O(\min(c \sqrt{n},n) m)$ time, where $n$ denotes the number of applicants, $m$ the number of edges and $c$ the maximum rank of an edge in an optimal solution. A central authority matches applicants to posts. It does so using one of the rank-maximal matchings. Since there may be more than one rank- maximal matching of $G$, we assume that the central authority chooses any one of them randomly. Let $a_1$ be a manipulative applicant, who knows the preference lists of all the other applicants and wants to falsify his preference list so that he has a chance of getting better posts than if he were truthful. In the first problem addressed in this paper the manipulative applicant $a_1$ wants to ensure that he is never matched to any post worse than the most preferred among those of rank greater than one and obtainable when he is truthful. In the second problem the manipulator wants to construct such a preference list that the worst post he can become matched to by the central authority is best possible or in other words, $a_1$ wants to minimize the maximal rank of a post he can become matched to

Calculation of Finite Size Effects on the Nucleon Mass in Unquenched QCD using Chiral Perturbation Theory

The finite size effects on nucleon masses are calculated in relativistic chiral perturbation theory. Results are compared with two-flavor lattice results.Comment: talk at Confinement03, 5 pages latex, 3 figures. Assignment of 2 data points to incorrect data sets in plot 1 and of 1 data point in plot 2 corrected. 1 fm lattice result updated. Conclusions unchange

Grid computing technologies for renewable electricity generator monitoring and control

In this paper we discuss the use of real-time Grid computing for the monitoring, control and simulation of renewable electricity generators and their associated electrical networks. We discuss briefly the architectural design of GRIDCC and how we have integrated a number of real (solar, CHP) and simulated conventional power generators into the GRIDCC environment. A local weather station has also been attached to an Instrument Manager to alert experts appropriately when the Solar Array is not generating. The customised remote control and monitoring environment (a virtual control room), distributed using a standard web server, is discussed

The lithospheric mantle and lower crust-mantle relationships under Scotland: a xenolithic perspective

In the British Isles the majority of volcanic rocks containing upper mantle and lower crustal xenoliths occur in Scotland. Most of the occurrences are of Carboniferous–Permian age. This paper presents new data on the mineral chemistry of spinel lherzolite xenoliths from the five principal Scottish tectonic terranes. Compositional variations among the minerals emphasize the broad lateral heterogeneity of the subcontinental lithospheric mantle across the region. The remarkable range of Al2O3 v. CaO exhibited by the clinopyroxenes compared with data from other ‘xenolith provinces' emphasizes the extremely complex tectonomagmatic history of the Scottish lithosphere. The generalized age increase from southern and central Scotland to the Northern Highland and Hebridean terranes of the north and NW, with concomitant complexity of geological history, is reflected also by trace element and isotopic studies. Reaction relationships in lherzolites from the Hebridean Terrane, owing to pervasive metasomatism, involve secondary growth of sodic feldspar. This, and light REE enrichment of clinopyroxenes, points to involvement of a natro-carbonatitic melt. Most pyroxenitic xenoliths are inferred to form a basal crustal layer with a generally sharp discontinuity above the underlying (dominantly lherzolitic) mantle. A second discontinuity is inferred to separate these ultramafic cumulates from overlying, broadly cognate metagabbroic cumulates

Series Expansions for the Massive Schwinger Model in Hamiltonian lattice theory

It is shown that detailed and accurate information about the mass spectrum of the massive Schwinger model can be obtained using the technique of strong-coupling series expansions. Extended strong-coupling series for the energy eigenvalues are calculated, and extrapolated to the continuum limit by means of integrated differential approximants, which are matched onto a weak-coupling expansion. The numerical estimates are compared with exact results, and with finite-lattice results calculated for an equivalent lattice spin model with long-range interactions. Both the heavy fermion and the light fermion limits of the model are explored in some detail.Comment: RevTeX, 10 figures, add one more referenc

Infectious Disease Risks to Transmigrant Communities in Indonesia : a Survey in Lampung Province, Sumatra

This study was supported in part by funds provided by the Indonesian Ministry of Health and The Naval Medical Research and Development Command, Navy Department for Work Unit MR041. 05-0052. The opinions and assertions contained herein are those of the authors and are not to be construed as official or as reflecting the views of the Indonesian Ministry of Health and the Navy De­partment or the Naval Service at large