51,475 research outputs found
Solving stable matching problems using answer set programming
Since the introduction of the stable marriage problem (SMP) by Gale and
Shapley (1962), several variants and extensions have been investigated. While
this variety is useful to widen the application potential, each variant
requires a new algorithm for finding the stable matchings. To address this
issue, we propose an encoding of the SMP using answer set programming (ASP),
which can straightforwardly be adapted and extended to suit the needs of
specific applications. The use of ASP also means that we can take advantage of
highly efficient off-the-shelf solvers. To illustrate the flexibility of our
approach, we show how our ASP encoding naturally allows us to select optimal
stable matchings, i.e. matchings that are optimal according to some
user-specified criterion. To the best of our knowledge, our encoding offers the
first exact implementation to find sex-equal, minimum regret, egalitarian or
maximum cardinality stable matchings for SMP instances in which individuals may
designate unacceptable partners and ties between preferences are allowed.
This paper is under consideration in Theory and Practice of Logic Programming
(TPLP).Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP). arXiv admin note: substantial text overlap with arXiv:1302.725
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 Design of the Fifth Answer Set Programming Competition
Answer Set Programming (ASP) is a well-established paradigm of declarative
programming that has been developed in the field of logic programming and
nonmonotonic reasoning. Advances in ASP solving technology are customarily
assessed in competition events, as it happens for other closely-related
problem-solving technologies like SAT/SMT, QBF, Planning and Scheduling. ASP
Competitions are (usually) biennial events; however, the Fifth ASP Competition
departs from tradition, in order to join the FLoC Olympic Games at the Vienna
Summer of Logic 2014, which is expected to be the largest event in the history
of logic. This edition of the ASP Competition series is jointly organized by
the University of Calabria (Italy), the Aalto University (Finland), and the
University of Genova (Italy), and is affiliated with the 30th International
Conference on Logic Programming (ICLP 2014). It features a completely
re-designed setup, with novelties involving the design of tracks, the scoring
schema, and the adherence to a fixed modeling language in order to push the
adoption of the ASP-Core-2 standard. Benchmark domains are taken from past
editions, and best system packages submitted in 2013 are compared with new
versions and solvers.
To appear in Theory and Practice of Logic Programming (TPLP).Comment: 10 page
Logic Programming Applications: What Are the Abstractions and Implementations?
This article presents an overview of applications of logic programming,
classifying them based on the abstractions and implementations of logic
languages that support the applications. The three key abstractions are join,
recursion, and constraint. Their essential implementations are for-loops, fixed
points, and backtracking, respectively. The corresponding kinds of applications
are database queries, inductive analysis, and combinatorial search,
respectively. We also discuss language extensions and programming paradigms,
summarize example application problems by application areas, and touch on
example systems that support variants of the abstractions with different
implementations
Solving Hard Stable Matching Problems Involving Groups of Similar Agents
Many important stable matching problems are known to be NP-hard, even when
strong restrictions are placed on the input. In this paper we seek to identify
structural properties of instances of stable matching problems which will allow
us to design efficient algorithms using elementary techniques. We focus on the
setting in which all agents involved in some matching problem can be
partitioned into k different types, where the type of an agent determines his
or her preferences, and agents have preferences over types (which may be
refined by more detailed preferences within a single type). This situation
would arise in practice if agents form preferences solely based on some small
collection of agents' attributes. We also consider a generalisation in which
each agent may consider some small collection of other agents to be
exceptional, and rank these in a way that is not consistent with their types;
this could happen in practice if agents have prior contact with a small number
of candidates. We show that (for the case without exceptions), several
well-studied NP-hard stable matching problems including Max SMTI (that of
finding the maximum cardinality stable matching in an instance of stable
marriage with ties and incomplete lists) belong to the parameterised complexity
class FPT when parameterised by the number of different types of agents needed
to describe the instance. For Max SMTI this tractability result can be extended
to the setting in which each agent promotes at most one `exceptional' candidate
to the top of his/her list (when preferences within types are not refined), but
the problem remains NP-hard if preference lists can contain two or more
exceptions and the exceptional candidates can be placed anywhere in the
preference lists, even if the number of types is bounded by a constant.Comment: Results on SMTI appear in proceedings of WINE 2018; Section 6
contains work in progres
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