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

The estimation of economic benefits of urban trees using contingent valuation method in Tasik Perdana, Kuala Lumpur

Urban trees provide a multitude of tangible and intangible services which include provisionary, regulatory, as well as cultural and support services to the community. Unfortunately, to set a monetary value on these said services is challenging to say the least. Ignorance of such monetary value is unintentional and this is mainly due to the lack of awareness and the absence of monetary value of the services itself. Hence, the quality of these urban trees degrades over time as no one appreciates its monetary value. In light of this situation, a study was initiated to determine the economic benefits of the urban trees that were planted surrounding Tasik Perdana (TP) area. For this purpose, a total of 313 respondents were interviewed in the TP area using the contingent valuation method (CVM). The objective of this study was to elicit willingness to pay (WTP) for these urban trees. WTP represents the willingness of a person to pay in monetary terms to secure and sustain these urban trees. Hence, seven bid prices were used and distributed to the respondents: RM1.00, RM5.00, RM10.00, RM15.00, RM20.00, RM25.00 and RM30.00. Logit and linear regression models were applied to predict the maximum, mean, and median WTP. The study concludes that the estimated mean WTP is RM10.32 per visit and the estimated median WTP is RM10.08 per visit

A determination of the strange quark mass for unquenched clover fermions using the AWI

Using the O(a) Symanzik improved action an estimate is given for the strange quark mass for unquenched (nf=2) QCD. The determination is via the axial Ward identity (AWI) and includes a non-perturbative evaluation of the renormalisation constant. Numerical results have been obtained at several lattice spacings, enabling the continuum limit to be taken. Results indicate a value for the strange quark mass (in the MSbar-scheme at a scale of 2GeV) in the range 100 - 130MeV.Comment: 6 pages, contribution to Lattice2005(Hadron spectrum and quark masses), uses PoS.cl

A Determination of the Lambda Parameter from Full Lattice QCD

We present a determination of the QCD parameter Lambda in the quenched approximation (n_f=0) and for two flavours (n_f=2) of light dynamical quarks. The calculations are performed on the lattice using O(a) improved Wilson fermions and include taking the continuum limit. We find Lambda_{n_f=0} = 259(1)(20) MeV and Lambda_{n_f=2} = 261(17)(26) MeV}, using r_0 = 0.467 fm to set the scale. Extrapolating our results to five flavours, we obtain for the running coupling constant at the mass of the Z boson alpha_s(m_Z) = 0.112(1)(2). All numbers refer to the MSbar scheme.Comment: 25 pages, 9 figure

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