Table Of ContentLecture Notes in Artificial Intelligence 5129
EditedbyR.Goebel,J.Siekmann,andW.Wahlster
Subseries of Lecture Notes in Computer Science
François Fages Francesca Rossi
Sylvain Soliman (Eds.)
Recent Advances
in Constraints
12thAnnual ERCIM InternationalWorkshop
on Constraint Solving and Constraint Logic Programming,
CSCLP 2007
Rocquencourt, France, June 7-8, 2007
Revised Selected Papers
1 3
SeriesEditors
RandyGoebel,UniversityofAlberta,Edmonton,Canada
JörgSiekmann,UniversityofSaarland,Saarbrücken,Germany
WolfgangWahlster,DFKIandUniversityofSaarland,Saarbrücken,Germany
VolumeEditors
FrançoisFages
SylvainSoliman
INRIARocquencourt
ProjetContraintes
DomainedeVoluceau,BP105,78153LeChesnayCEDEX,France
E-mail:{Francois.Fages,Sylvain.Soliman}@inria.fr
FrancescaRossi
UniversitàdiPadova
DipartimentodiMatematicaPuraedApplicata
ViaTrieste63,35121Padova,Italy
E-mail:[email protected]
LibraryofCongressControlNumber:2008940263
CRSubjectClassification(1998):I.2.3,F.3.1-2,F.4.1,D.3.3,F.2.2,G.1.6,I.2.8
LNCSSublibrary:SL7–ArtificialIntelligence
ISSN 0302-9743
ISBN-10 3-540-89811-5SpringerBerlinHeidelbergNewYork
ISBN-13 978-3-540-89811-5SpringerBerlinHeidelbergNewYork
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Preface
Constraintprogrammingsupports a greatambitionfor computer programming:
the one of making programming essentially a modeling task, with equations,
constraints,andlogicalformulas.Thisfieldemergedinthemid-1980sborrowing
conceptsfromlogicprogramming,operationsresearch,andartificialintelligence.
Itsfoundationisthe useofrelationsonmathematicalvariablestocomputewith
partial information systems. The successes of constraint programming for solv-
ing combinatorialoptimizationproblems inindustry orcommercearerelatedto
theadvancesmadeinthefieldonnewconstraintpropagationtechniquesandon
declarativelanguageswhichallowcontrolonthemixingofheterogeneousresolu-
tiontechniquessuchasnumerical,symbolic,deductive,andheuristictechniques.
Thisvolumecontainsthepapersselectedforthepost-proceedingsofthe12th
International Workshop on Constraint Solving and Constraint Logic Program-
ming (CSCLP 2007) held during June 7–8, 2008 in Rocquencourt, France. This
workshop, open to all, was organized as the 12th meeting of the working group
onConstraintsoftheEuropeanResearchConsortiumforInformaticsandMath-
ematics (ERCIM), continuinga seriesof workshopsorganizedsince the creation
of the working group in 1997. A selection of papers of these annual workshops
have been published since 2002 in a series of books which illustrate the evolu-
tionofthefield,underthetitle“RecentAdvancesinConstraints”intheLecture
Notes in Artificial Intelligence series.
This year, there were 16 submissions, most of them being extended and re-
visedversionsofpaperspresentedatthe workshop,plus somenew papers.Each
submission was reviewed by three reviewers. The Program Committee decided
to accept ten papers for publication in this book.
We would like to take the opportunity to thank all authors who submit-
ted a paper, as well as the reviewers for their useful work. CSCLP 2007 was
made possible thanks to the support of the European Research Consortium for
Informatics and Mathematics (ERCIM), the Institut National de la Recherche
en Informatique et Automatique (INRIA), and the Association for Constraint
Programming (ACP).
May 2008 Franc¸ois Fages
Francesca Rossi
Sylvain Soliman
Organization
CSCLP 2007 was organized by the ERCIM Working Group on Constraints.
Organizing and Program Committee
Franc¸ois Fages INRIA Rocquencourt, France
Francesca Rossi University of Padova, Italy
Sylvain Soliman INRIA Rocquencourt, France
Additional Reviewers
Erika Abraham Christian Herde
Krzysztof Apt Boutheina Jlifi
Pedro Barahona Ulrich Junker
Roman Barta´k Chavalit Likitvivatanavong
Thierry Benoist Pedro Meseguer
Hariolf Betz Barry O’Sullivan
Stefano Bistarelli Gregory Provan
Ismel Brito Igor Razgon
Ondrej Cepek Francesco Santini
Marco Correia Pierre Schaus
Yves Deville Pavel Surynek
Gregoire Dooms Tino Teige
Thom Fru¨hwirth Kristen Brent Venable
Martin Fra¨nzle Ruben Viegas
Khaled Ghedira Roland Yap
Daniel Goossens St´ephane Zampelli
Martin Hejna
Sponsoring Institutions
European Research Consortium for Informatics and Mathematics (ERCIM)
TheInstitutNationaldelaRechercheenInformatiqueetAutomatique(INRIA)
The Association for Constraint Programming (ACP)
Table of Contents
A Comparison of the Notions of Optimality in Soft Constraints and
Graphical Games ................................................ 1
Krzysztof R. Apt, Francesca Rossi, and K. Brent Venable
Temporal Reasoning in Nested Temporal Networks with Alternatives ... 17
Roman Bart´ak, Ondˇrej Cˇepek, and Martin Hejna
SCLP for Trust Propagationin Small-World Networks................ 32
Stefano Bistarelli and Francesco Santini
Improving ABT Performance by Adding Synchronization Points ....... 47
Ismel Brito and Pedro Meseguer
On the Integration of Singleton Consistencies and Look-Ahead
Heuristics....................................................... 62
Marco Correia and Pedro Barahona
Combining Two Structured Domains for Modeling Various Graph
Matching Problems .............................................. 76
Yves Deville, Gr´egoire Dooms, and St´ephane Zampelli
Quasi-Linear-Time Algorithms by Generalisation of Union-Find in
CHR ........................................................... 91
Thom Fru¨hwirth
Preference-Based Problem Solving for Constraint Programming........ 109
Ulrich Junker
Generalizing Global Constraints Based on Network Flows ............. 127
Igor Razgon, Barry O’Sullivan, and Gregory Provan
A Global Filtration for Satisfying Goals in Mutual Exclusion
Networks ....................................................... 142
Pavel Surynek
Author Index.................................................. 159
A Comparison of the Notions of Optimality in
Soft Constraints and Graphical Games
Krzysztof R. Apt1,2, Francesca Rossi3, and K. Brent Venable3
1 CWI Amsterdam, Amsterdam, The Netherlands
2 Universityof Amsterdam, Amsterdam, TheNetherlands
3 University of Padova, Padova, Italy
[email protected], {frossi,kvenable}@math.unipd.it
Abstract. The notion of optimality naturally arises in many areas of
appliedmathematicsandcomputerscienceconcernedwithdecisionmak-
ing. Here we consider this notion in the context of two formalisms used
for different purposes and in different research areas: graphical games
andsoft constraints.Werelate thenotion ofoptimality usedinthearea
ofsoftconstraintsatisfactionproblems(SCSPs)tothatusedingraphical
games, showing that for a large class of SCSPs that includes weighted
constraints every optimal solution corresponds to a Nash equilibrium
that is also a Pareto efficient joint strategy.
Wealsostudyalternativemappingsincludingonethatmapsgraphical
games to SCSPs, for which Pareto efficient joint strategies and optimal
solutions coincide.
1 Introduction
The concept of optimality is prevalent in many areas of applied mathematics
and computer science. It is of relevance whenever we need to choose among
several alternatives that are not equally preferable. For example, in constraint
optimization,eachsolutionofaconstraintproblemhasaqualitylevelassociated
with it and the aim is to choose an optimal solution, that is, a solution with an
optimal quality level.
Theaimofthispaperistoclarifytherelationbetweenthenotionsofoptimal-
ity usedin game theory,commonly usedto modelmulti-agentsystems,andsoft
constraints. This allows us to gain new insights into these notions which hope-
fully willleadtofurthercross-fertilizationamongthesetwodifferentapproaches
to model optimality.
Game theory, notably the theory of strategic games, captures the idea of an
interaction between agents (players). Each player chooses one among a set of
strategies,andithasa payofffunction onthe game’sjointstrategiesthatallows
the player to take action (simultaneously with the other players) with the aim
of maximizing its payoff. A commonly used concept of optimality in strategic
games is that of a Nash equilibrium. Intuitively, it is a joint strategy that is
optimal for each player under the assumption that only he may reconsider his
action. Another concept of optimality concerns Pareto efficient joint strategies,
F.Fages,F.Rossi,andS.Soliman(Eds.):CSCLP2007,LNAI5129,pp.1–16,2008.
(cid:1)c Springer-VerlagBerlinHeidelberg2008
2 K.R. Apt,F. Rossi, and K.B. Venable
whicharethoseinwhichnoplayercanimproveitspayoffwithoutdecreasingthe
payoffof some other player.Sometimes it is useful to consider constrainedNash
equilibria,that is,Nash equilibria that satisfy some additionalrequirements [6].
For example, Pareto efficient Nash equilibria are Nash equilibria which are also
Pareto efficient among the Nash equilibria.
Soft constraints, see e.g. [2], are a quantitative formalism which allow us to
express constraints and preferences. While constraints state what is acceptable
for a certain subset of the objects of the problem, preferences (also called soft
constraints) allow for several levels of acceptance. An example are fuzzy con-
straints, see [4] and [11], where acceptance levels are between 0 and 1, and
where the quality of a solution is the minimal level over all the constraints. An
optimalsolutionistheonewiththehighestquality.Theresearchinthisareafo-
cusesmainly onalgorithmsforfinding optimalsolutionsandonthe relationship
between modelling formalisms (see [9]).
We consider the notions of optimality in soft constraints and in strategic
games. Although apparently the only connection between these two formalisms
is that they both model preferences, we show that there is in fact a strong
relationship.Thisissurprisingandinterestingonitsown.Moreover,itmightbe
exploited for a cross-fertilizationamong these frameworks.
In considering the relationship between strategic games and soft constraints,
theappropriatenotionofastrategicgameisherethatofagraphicalgame,see[7].
Thisisduetothefactthatsoftconstraintsusuallyinvolveonlyasmallsubsetof
the problem variables.This is in analogywith the fact that in a graphicalgame
a player’s payoff function depends only on a (usually small) number of other
players.
We consider a ‘local’ mapping that associates with eachsoft constraint satis-
factionproblem(inshort,asoftCSP,oranSCSP)agraphicalgame.Forstrictly
monotonic SCSPs (which include, for example, weighted constraints), every op-
timal solution of the SCSP is mapped to a Nash equilibrium of the game. We
also show that this local mapping, when applied to a consistent CSP (that is, a
classical constraint satisfaction problem), maps the solutions of the CSP to the
Nash equilibria of the corresponding graphical game. This relationship between
the optimal solutions and Nash equilibria holds in general, and not just for a
subclass, if we consider a ‘global’ mapping from the SCSPs to the graphical
games, which is independent of the constraint structure.
We then consider the relationship between optimal solutions of the SCSPs
and Pareto efficiency in graphical games. First we show that the above local
mapping maps every optimal solution of a strictly monotonic SCSP to a Pareto
efficient joint strategy. We then exhibit a mapping from the graphical games to
theSCSPsforwhichtheoptimalsolutionsoftheSCSPcoincidewiththePareto
efficient joint strategies of the game.
In [5] a mapping from graphical games to classical CSPs has been defined,
and it has been shown that the Nash equilibria of the games coincide with the
solutions of the CSPs. We can use this mapping, together with our mapping
from the graphical games to the SCSPs, to identify the Pareto efficient Nash
A Comparison of theNotions of Optimality 3
equilibriaofthegivengraphicalgame.Infact,theseequilibriacorrespondtothe
optimalsolutionsof the SCSP obtainedby joining the softand hardconstraints
generated by the two mappings.
The study of the relations among preference models coming from different
fields such as AI and game theory has only recently gained attention. In [1] we
have considered the correspondence between optimality in CP-nets of [3] and
pure Nash equilibria in so-called parametrized strategic games, showing that
there is a precise correspondence between these two concepts.
As mentioned above, a mapping from strategic, graphical and other types of
gamesto classicalCSPshas beenconsideredin [5], leadingto interestingresults
on the complexity of deciding whether a game has a pure Nash equilibria or
other kinds of desirable joint strategies.
In [12] a mapping from the distributed constraint optimization problems to
strategic graphical games is introduced, where the optimization criteria is to
maximizethesumofutilities.Byusingthismapping,itisshownthattheoptimal
solutions of the given problem are Nash equilibria of the generated game. This
result is in line with our findings regarding strictly monotonic SCSPs, which
include the class of problems considered in [12].
2 Preliminaries
Inthissectionwerecallthemainnotionsregardingsoftconstraintsandstrategic
games.
2.1 Soft Constraints
Soft constraints,see e.g.[2], allow to express constraintsand preferences.While
constraints state what is acceptable for a certain subset of the objects of the
problem, preferences (also called soft constraints) allow for several levels of ac-
ceptance. A technical way to describe soft constraints is via the use of an alge-
braic structure called a c-semiring.
A c-semiring is a tuple (cid:1)A,+,×,0,1(cid:2), where:
• A is a set, called the carrier of the semiring, and 0,1∈A;
• +is commutative,associative,idempotent,0 isits unitelement,and1is its
absorbing element;
• × is associative, commutative, distributes over +, 1 is its unit element and
0 is its absorbing element.
Elements 0 and 1 represent, respectively, the highest and lowest preference.
While the operator × is used to combine preferences, the operator + induces a
partial ordering on the carrier A defined by
a≤b iff a+b=b.
Given a c-semiringS =(cid:1)A,+,×,0,1(cid:2),anda set ofvariables V,eachvariable
x with a domain D(x), a soft constraint is a pair (cid:1)def,con(cid:2), where con ⊆ V
