Table Of ContentTrends in Mathematics
Research Perspectives CRM Barcelona Vol.6
Josep Díaz
Lefteris Kirousis
Luis Ortiz-Gracia
Maria Serna
Editors
Extended
Abstracts
Summer 2015
Strategic Behavior in Combinatorial
Structures; Quantitative Finance
Trends in Mathematics
Research Perspectives CRM Barcelona
Volume 6
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Extended Abstracts
Summer 2015
Strategic Behavior in Combinatorial
Structures
Josep Díaz
Lefteris Kirousis
Maria Serna
Editors
Quantitative Finance
Luis Ortiz-Gracia
Editor
Editors
JosepDíaz LefterisKirousis
DepartamentdeCieJnciesdelaComputació DepartmentofMathematics
UniversitatPoliteJcnicadeCatalunya NationalandKapodistrianUniversity
Barcelona,Spain Zografos,Greece
LuisOrtiz-Gracia MariaSerna
DepartmentofEconometrics DepartamentdeCieJnciesdelaComputació
UniversityofBarcelona UniversitatPoliteJcnicadeCatalunya
Barcelona,Spain Barcelona,Spain
ISSN2297-0215 ISSN2297-024X (electronic)
TrendsinMathematics
ISBN978-3-319-51752-0 ISBN978-3-319-51753-7 (eBook)
DOI10.1007/978-3-319-51753-7
LibraryofCongressControlNumber:2017932282
Mathematics SubjectClassification(2010):Firstpart:05C80,34E10,37N99,52C45,60C05,68W40,
68Q32, 68W20, 82B26, 90B15, 90B60, 91B15; Second part: 62P05, 60G07, 60E10, 65T60, 91B02,
91G60,91G80
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Contents
PartI StrategicBehaviorinCombinatorialStructures
OnthePush&PullProtocolforRumourSpreading.......................... 3
Hüseyin Acan, Andrea Collevecchio, Abbas Mehrabian,
andNickWormald
RandomWalksThatFindPerfectObjectsandtheLovász
LocalLemma..................................................................... 11
DimitrisAchlioptasandFotisIliopoulos
LogitDynamicswithConcurrentUpdatesforLocal
InteractionGames ............................................................... 17
Vincenzo Auletta, Diodato Ferraioli, Francesco Pasquale,
PaoloPenna,andGiuseppePersiano
TheSetChromaticNumberofRandomGraphs............................. 23
AndrzejDudek,DieterMitsche,andPawełPrałat
CarpoolinginSocialNetworks ................................................. 29
AmosFiat,AnnaR.Karlin,EliasKoutsoupias,ClaireMathieu,
andRotemZach
WhotoTrustforTruthfulFacilityLocation?................................. 35
DimitrisFotakis,ChristosTzamos,andEmmanouilZampetakis
Metric and SpectralPropertiesof Dense Inhomogeneous
RandomGraphs.................................................................. 41
NicolasFraimanandDieterMitsche
On-LineListColouringofRandomGraphs.................................. 47
Alan Frieze, Dieter Mitsche, Xavier Pérez-Giménez,
andPawełPrałat
v
vi Contents
ApproximationAlgorithmsforComputingMaximin
ShareAllocations................................................................. 55
GeorgiosAmanatidis, EvangelosMarkakis, Afshin Nikzad,
andAminSaberi
AnAlternateProofoftheAlgorithmicLovászLocalLemma .............. 61
Ioannis Giotis, Lefteris Kirousis, Kostas I. Psaromiligkos,
andDimitriosM.Thilikos
LearningGame-TheoreticEquilibriaViaQueryProtocols................. 67
PaulW.Goldberg
TheLowerTail:PoissonApproximationRevisited........................... 73
SvanteJansonandLutzWarnke
PopulationProtocolsforMajorityinArbitraryNetworks.................. 77
George B. Mertzios, Sotiris E. Nikoletseas,
ChristoforosL.Raptopoulos,andPaulG.Spirakis
TheAsymptoticValueinFiniteStochasticGames........................... 83
MiquelOliu-Barton
AlmostAll5-RegularGraphsHavea3-Flow................................. 89
PawełPrałatandNickWormald
PartII QuantitativeFinance
OntheShort-TimeBehaviouroftheImpliedVolatilitySkew
forSpreadOptionsandApplications.......................................... 97
ElisaAlòsandJorgeA.León
An Alternative to CARMA Models via Iterations
ofOrnstein–UhlenbeckProcesses.............................................. 101
ArgimiroArratia,AlejandraCabaña,andEnriqueM.Cabaña
Euler–PoissonSchemesforLévyProcesses ................................... 109
AlbertFerreiro-Castilla
OnTime-ConsistentPortfolioswithTime-InconsistentPreferences....... 115
JesúsMarín-Solano
AGenericDecompositionFormulaforPricingVanillaOptions
UnderStochasticVolatilityModels ............................................ 121
RaúlMerinoandJosepVives
AHighlyEfficientPricingMethodforEuropean-StyleOptions
BasedonShannonWavelets .................................................... 127
LuisOrtiz-GraciaandCornelisW.Oosterlee
ANewPricingMeasureintheBarndorff-Nielsen–Shephard
ModelforCommodityMarkets ................................................ 133
SalvadorOrtiz-Latorre
Part I
Strategic Behavior in Combinatorial
Structures
Foreword
The Workshop on Strategic Behavior and Phase Transitions in Random and
ComplexCombinatorialStructureswasheldinthe CentredeRecercaMatemàtica
(CRM) in Bellaterra (Barcelona) from June 8th to 12th, 2015. This workshop
was part of a research activity in CRM under the umbrella name Algorithmic
PerspectivesinEconomicsandPhysicsextendedfromApril7thtoJune19th,2015.
Besides CRM, this research activity was funded by several Catalan organizations
(Institutd’EstudisCatalans,InstitucióCentresdeRecercadeCatalunya,Universitat
AutònomadeBarcelona,andGeneralitatdeCatalunya)andbytheSimonsInstitute
fortheTheoryofComputing.Theorganizercommitteefortheprogramconsistedof
DimitrisAchlioptas(DepartmentofComputerScience,UCSantaCruz),JosepDíaz
(Departmentof ComputerScience, UniversitatPolitècnica de Catalunya),Lefteris
Kirousis (Department of Mathematics, National and Kapodistrian University of
Athens), and María Serna (Department of Computer Science, Universitat Politèc-
nicadeCatalunya).
Themainresearchthemeoftheworkshopwastoexplorepossibletiesbetween
phasetransitionsononehand,andgametheoryon theother.To bemorespecific,
notethatanimportantresearchareaofthelastdecadeishowatomicagents,acting
locallyandmicroscopically,leadtodiscontinuousmacroscopicchanges.Thispoint
of view has proved to be especially useful in studying the evolution of random
and usually complex combinatorial objects (typically, networks) with respect to
discontinuouschangesin globalparameterslike connectivity.Naturally, there is a
strategicelementintheformationofatransition:theatomicagentsseek“selfishly"
to optimize a local microscopic parameter aiming at macroscopic changes that
optimize their utility. Investigating the question of whether the connection of
microscopic strategic behavior with macroscopic phase transitions is a legitimate
andmeaningfulresearchobjectivewasthescopeoftheworkshop.
The workshopwas attendedby morethan thirtyregisteredparticipants,several
ofwhichwerePh.D.studentsorearlycareerpost-doctoralresearchers.Becauseof
theno-fee,openaccesspolicythattheorganizersoptedfor,thereweremanymore
2 I StrategicBehaviorinCombinatorialStructures
non-registeredparticipants.Theconferencefollowedaratherrelaxedtimetablethat
encouragedimpromptudiscussionsandinteractions.
The formal program comprised of some twenty presentations, more or less
equally divided between the areas of random graphs and phase transitions on
one hand, and game theory on the other. The organizers actively sought to have
renownedresearchersgivesomeofthetalksandatthesametimetodrawfromthe
poolofearlycareer,promisingresearcherstopresenttheircurrentwork.Giventhe
diversebackgroundoftheaudience,presentationsatatrans-thematicstyleandata
nonspecialized,highlevelwereencouraged.
Barcelona,Spain JosepDíaz
Athens,Greece LefterisKirousis
Barcelona,Spain MariaSerna
September2015
On the Push&Pull Protocol for Rumour
Spreading
HüseyinAcan,AndreaCollevecchio,AbbasMehrabian,andNickWormald
Abstract The asynchronous push&pull protocol, a randomized distributed algo-
rithm for spreading a rumour in a graph G, is defined as follows. Independent
exponentialclocksofrate1areassociatedwiththeverticesofG,onetoeachvertex.
Initially,onevertexofGknowstherumour.Whenevertheclockofavertexxrings,
itcallsarandomneighboury:ifxknowstherumourandydoesnot,thenx tellsy
therumour(apushoperation),andifxdoesnotknowtherumourandyknowsit,y
tellsxtherumour(apulloperation).TheaveragespreadtimeofGistheexpected
timeittakesforallverticestoknowtherumour,andtheguaranteedspreadtimeof
G is thesmallest time t such thatwith probabilityatleast 1(cid:2)1=n,aftertime t all
verticesknowtherumour.Thesynchronousvariantofthisprotocol,inwhicheach
clockringspreciselyattimes1;2;:::,hasbeenstudiedextensively.
We prove the following results for any n-vertex graph: in either version, the
average spread time is at most linear even if only the pull operation is used, and
theguaranteedspreadtimeiswithinalogarithmicfactoroftheaveragespreadtime,
so it is O.nlogn/. In the asynchronous version, both the average and guaranteed
spreadtimesare(cid:2).logn/.Wegiveexamplesofgraphsillustratingthatthesebounds
arebestpossibleuptoconstantfactors.
We also prove the first theoretical relationshipsbetween the guaranteedspread
times in the two versions. Firstly, in all graphs the guaranteed spread time in the
asynchronousversioniswithinanO.logn/factorofthatinthesynchronousversion,
andthisistight.Next,wefindexamplesofgraphswhoseasynchronousspreadtimes
are logarithmic, but the synchronousversions are polynomially large. Finally, we
H.Acan((cid:2))(cid:129)N.Wormald
SchoolofMathematicalSciences,MonashUniversity,Clayton,VIC,Australia
e-mail:[email protected];[email protected]
A.Collevecchio
SchoolofMathematicalSciences,MonashUniversity,Clayton,VIC,Australia
Ca’FoscariUniversity,Venice,Italy
e-mail:[email protected]
A.Mehrabian
DepartmentofCombinatoricsandOptimization,UniversityofWaterloo,Waterloo,ON,Canada
e-mail:[email protected]
©SpringerInternationalPublishingAG2017 3
J.Díazetal.(eds.),ExtendedAbstractsSummer2015,TrendsinMathematics6,
DOI10.1007/978-3-319-51753-7_1
