Good Edge, Bad Edge: How Network Structure Affects a Group’s Ability to Coordinate

Coordination is a core concern in social science. Problems as diverse as deciding where to go to dinner, what price to charge for a good or service, which political candidate to support or what regulatory policy to adopt all contain coordination as a core element. Most coordination problems arise among actors connected in a network, and these connections can both improve and impede a group’s ability to achieve coordination. To model how links influence coordination we distinguish between “constraining edges” that make coordination harder by reducing the number of equilibrium outcomes, and “redundant edges” that make coordination easier by merely increasing communication without affecting the number of equilibria. We show experimentally that the addition of constraining edges reduces coordination, while redundant edges improve subjects’ ability to solve a coordination problem

Variations on Memetic Algorithms for Graph Coloring Problems

11 pages, 8 figures, 3 tables, 2 algorithmsInternational audienceGraph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem.The most effective methods to solve this problem are proved to be hybrid algorithms such as memetic algorithms or quantum annealing. Those hybrid algorithms use a powerful local search inside a population-based algorithm.This paper presents a new memetic algorithm based on one of the most effective algorithms: the Hybrid Evolutionary Algorithm HEA from Galinier and Hao (1999).The proposed algorithm, denoted HEAD - for HEA in Duet - works with a population of only two individuals.Moreover, a new way of managing diversity is brought by HEAD.These two main differences greatly improve the results, both in terms of solution quality and computational time.HEAD has produced several good results for the popular DIMACS benchmark graphs, such as 222-colorings for , 81-colorings for and even 47-colorings for and 82-colorings for

Two decomposition algorithms for solving a minimum weight maximum clique model for the air conflict resolution problem

International audienceIn this article, we tackle the conflict resolution problem using a new variant of the minimum-weight maximum-clique model. The problem involves identifying maneuvers that maintain the required separation distance between all pairs of a set of aircraft while minimizing fuel costs. We design a graph in which the vertices correspond to a finite set of maneuvers and the edges connect conflict-free maneuvers. A maximum clique of minimal weight yields a conflict-free situation that involves all the aircraft and minimizes the costs induced. The innovation of the model is its cost structure: the costs of the vertices cannot be determined a priori, since they depend on the vertices in the clique. We formulate the problem as a mixed integer linear program. Since the modeling of the aircraft dynamics and the computation of trajectories is separated from the solution process, the model is flexible. As a consequence, our mathematical framework is valid for any hypotheses. In particular, the aircraft can perform dynamic velocity, heading, and flight-level changes. To solve instances involving a large number of aircraft spread over several flight levels, we introduce two decomposition algorithms. The first is a sequential mixed integer linear optimization procedure that iteratively refines the discretization of the maneuvers to yield a trade-off between computational time and cost. The second is a large neighborhood search heuristic that uses the first procedure as a subroutine. The best solutions for the available set of maneuvers are obtained in less than 10 seconds for instances with up to 250 aircraft randomly allocated to 20 flight levels

Graph Coloring via Degeneracy in Streaming and Other Space-Conscious Models

We study the problem of coloring a given graph using a small number of colors in several well-established models of computation for big data. These include the data streaming model, the general graph query model, the massively parallel computation (MPC) model, and the CONGESTED-CLIQUE and the LOCAL models of distributed computation. On the one hand, we give algorithms with sublinear complexity, for the appropriate notion of complexity in each of these models. Our algorithms color a graph $G$ using about $\kappa(G)$ colors, where $\kappa(G)$ is the degeneracy of $G$: this parameter is closely related to the arboricity $\alpha(G)$. As a function of $\kappa(G)$ alone, our results are close to best possible, since the optimal number of colors is $\kappa(G)+1$. On the other hand, we establish certain lower bounds indicating that sublinear algorithms probably cannot go much further. In particular, we prove that any randomized coloring algorithm that uses $\kappa(G)+1$ many colors, would require $\Omega(n^2)$ storage in the one pass streaming model, and $\Omega(n^2)$ many queries in the general graph query model, where $n$ is the number of vertices in the graph. These lower bounds hold even when the value of $\kappa(G)$ is known in advance; at the same time, our upper bounds do not require $\kappa(G)$ to be given in advance.Comment: 26 page

Problems and applications of Discrete and Computational Geometry concerning graphs, polygons, and points in the plane

Esta tesistratasobreproblemasyaplicacionesdelageometríadiscretay computacional enelplano,relacionadosconpolígonos,conjuntosdepuntos y grafos. Después deunprimercapítulointroductorio,enelcapítulo 2 estudiamos una generalizacióndeunfamosoproblemadevisibilidadenelámbitodela O-convexidad. Dadounconjuntodeorientaciones(ángulos) O, decimosque una curvaes O-convexa si suintersecciónconcualquierrectaparalelaauna orientaciónde O es conexa.Cuando O = {0◦, 90◦}, nosencontramosenel caso delaortoconvexidad,consideradodeespecialrelevancia.El O-núcleo de unpolígonoeselconjuntodepuntosdelmismoquepuedenserconectados con cualquierotropuntodelpolígonomedianteunacurva O-convexa.En este trabajoobtenemos,para O = {0◦} y O = {0◦, 90◦}, unalgoritmopara calcular ymantenerel O-núcleodeunpolígonoconformeelconjuntode orientaciones O rota. Dichoalgoritmoproporciona,además,losángulosde rotación paralosqueel O-núcleotieneáreayperímetromáximos. En elcapítulo 3 consideramos unaversiónbicromáticadeunproblema combinatorioplanteadoporNeumann-LarayUrrutia.Enconcreto,de- mostramos quetodoconjuntode n puntosazulesy n puntosrojosenel plano contieneunparbicromáticodepuntostalquetodocírculoquelos tenga ensufronteracontieneensuinterioralmenos n(1− 1 √2 )−o(n) puntos del conjunto.Esteproblemaestáfuertementeligadoalcálculodelosdiagra- mas deVoronoideordensuperiordelconjuntodepuntos,pueslasaristas de estosdiagramascontienenprecisamentetodosloscentrosdeloscírculos que pasanpordospuntosdelconjunto.Porello,nuestralíneadetrabajo actual enesteproblemaconsisteenexplorarestaconexiónrealizandoun estudio detalladodelaspropiedadesdelosdiagramasdeVoronoideorden superior. En loscapítulos 4 y 5, planteamosdosaplicacionesdelateoríadegrafos 6 7 al análisissensorialyalcontroldeltráficoaéreo,respectivamente.Enel primer caso,presentamosunnuevométodoquecombinatécnicasestadísti- cas ygeométricasparaanalizarlasopinionesdelosconsumidores,recogidas a travésdemapeoproyectivo.Estemétodoesunavariacióndelmétodo SensoGraph ypretendecapturarlaesenciadelmapeoproyectivomediante el cálculodelasdistanciaseuclídeasentrelosparesdemuestrasysunor- malización enelintervalo [0, 1]. Acontinuación,aplicamoselmétodoaun ejemplo prácticoycomparamossusresultadosconlosobtenidosmediante métodosclásicosdeanálisissensorialsobreelmismoconjuntodedatos. En elsegundocaso,utilizamoslatécnicadelespectro-coloreadodegrafos para plantearunmodelodecontroldeltráficoaéreoquepretendeoptimizar el consumodecombustibledelosavionesalmismotiempoqueseevitan colisiones entreellos.This thesisdealswithproblemsandapplicationsofdiscreteandcomputa- tional geometryintheplane,concerningpolygons,pointsets,andgraphs. After afirstintroductorychapter,inChapter 2 westudyageneraliza- tion ofafamousvisibilityproblemintheframeworkof O-convexity. Given a setoforientations(angles) O, wesaythatacurveis O-convex if itsin- tersection withanylineparalleltoanorientationin O is connected.When O = {0◦, 90◦}, wefindourselvesinthecaseoforthoconvexity,consideredof specialrelevance.The O-kernel of apolygonisthesubsetofpointsofthe polygonthatcanbeconnectedtoanyotherpointofthepolygonwithan O-convexcurve.Inthisworkweobtain,for O = {0◦} and O = {0◦, 90◦}, an algorithm tocomputeandmaintainthe O-kernelofapolygonasthesetof orientations O rotates. Thisalgorithmalsoprovidestheanglesofrotation that maximizetheareaandperimeterofthe O-kernel. In Chapter 3, weconsiderabichromaticversionofacombinatorialprob- lem posedbyNeumann-LaraandUrrutia.Specifically,weprovethatevery set of n blue and n red pointsintheplanecontainsabichromaticpairof pointssuchthateverycirclehavingthemonitsboundarycontainsatleast n(1 − 1 √2 ) − o(n) pointsofthesetinitsinterior.Thisproblemisclosely related toobtainingthehigherorderVoronoidiagramsofthepointset.The edges ofthesediagramscontain,precisely,allthecentersofthecirclesthat pass throughtwopointsoftheset.Therefore,ourcurrentlineofresearch on thisproblemconsistsonexploringthisconnectionbystudyingindetail the propertiesofhigherorderVoronoidiagrams. In Chapters 4 and 5, weconsidertwoapplicationsofgraphtheoryto sensory analysisandairtrafficmanagement,respectively.Inthefirstcase, weintroduceanewmethodwhichcombinesgeometricandstatisticaltech- niques toanalyzeconsumeropinions,collectedthroughprojectivemapping. This methodisavariationofthemethodSensoGraph.Itaimstocapture 4 5 the essenceofprojectivemappingbycomputingtheEcuclideandistances betweenpairsofsamplesandnormalizingthemtotheinterval [0, 1]. Weap- ply themethodtoareal-lifescenarioandcompareitsperformancewiththe performanceofclassicmethodsofsensoryanalysisoverthesamedataset. In thesecondcase,weusetheSpectrumGraphColoringtechniquetopro- poseamodelforairtrafficmanagementthataimstooptimizetheamount of fuelusedbytheairplanes,whileavoidingcollisionsbetweenthem

Algoritmos para teste de perfeição de grafos

Orientador : Prof. André Luiz Pires GuedesDissertação (mestrado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Informática. Defesa: Curitiba, 26/08/2004Inclui referências : f. 65-67Resumo: Esta dissertação apresenta e discute os dois recentemente descobertos algoritmos de teste de perfeição de grafos. A parte central dos dois algoritmos e a mesma. Este núcleo que os dois algoritmos compartilham, que certamente e a parte mais complexa dos mesmos, foi discutido detalhadamente e implementado. Ate o momento, o autor desta dissertação não tem notícias de outras implementações destes algoritmos. A apresentação do algoritmo foi dividida em três partes distintas. A primeira parte agrupa vários algoritmos que testam pela presença de subgrafos específicos. A segunda parte estuda em detalhes o núcleo que os dois algoritmos compartilham. A terceira parte apresenta os dois algoritmos de teste de perfeição de grafos propriamente ditos. Adicionalmente, nesta dissertação foram definidos quatro parâmetros que podem ser associados a um grafo para exprimir seu grau de imperfeição. Estes parâmetros foram denotados p 1, p2, p3 e p4. O autor relacionou estes parâmetros com algumas operações que podem ser aplicadas a um grafo imperfeito para torna-lo perfeito. As operações utilizadas para definir estes parâmetros de foram a remoção de arestas do grafo (pi), a inversão de arestas no grafo (p2), a execução de remoção e inserção de arestas no grafo (p 3) e, finalmente, a remoção de vértices do grafo (p4). Mostrou-se que para qualquer grafo temos p4 < p3 < p1 e p4 < p3 < p2. Alem disso foram apresentados exemplos de grafos em que cada uma destas desigualdades pode ser estrita. O autor apresentou também alguns limitantes inferiores e superiores para estes parâmetros. Finalmente, utilizando um dos limitantes inferiores para p4, mostrou-se que existem grafos que são "bastante imperfeitos" . Mais especificamente, foi demonstrado que existem grafos com n vértices para os quais o número de vértices que deve ser removido n para tornás-lo perfeitos é pelo menos --;- - - lg (2n ). lg (2n) Palavras-chave: teoria dos grafos, algoritmos, teoria algorítmica dos grafos, grafos perfeitos, otimização combinatória.Abstract: This dissertation presents and discusses two recently discovered algorithms th a t test if a graph is perfect. The core shared by the two algorithms is discussed in details and the results of its implementation are presented. It is worthwhile to mention th a t no other similar implementation is known so far. The presentation of the algorithms is divided into three parts. The first part presents several algorithms th a t test some particular subgraphs. The second part reviews the core of the algorithms and the third part presents the two algorithms for perfectness. Additionally, in this work it is defined four parameters th a t can measure how imperfect a graph is. These parameters are denoted p1, p2, p3 and p4. The defined parameters are related to some operations th a t can be applied to a graph to make it perfect. The following operations are considered: edge deletion (pi), edge insertion (p2), both deletion and insertion of edges (p 3) and, finally, vertex deletion (p4). It is shown th a t for any graph it holds th a t p4 < p3 < p 1 and p4 < p3 < p2. It is also shown examples of graphs where such inequalities are strict. Finally, some lower bounds and upper bounds for these paramenters are shown. As a consequence of a lower bound for p4 , the author shows th a t there are "highly" imperfect graphs. More precisely, there are graphs with n vertices where n , . . Keywords: graph theory, algorithms, algorithmic graph theory, perfect graphs, combinatorial optimization

Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications

The success of new scientific areas can be assessed by their potential for contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely well in both of these aspects, with their sound theoretical basis developed over the years and with a variety of applications. In this survey, we analyze the applications of complex networks to real-world problems and data, with emphasis in representation, analysis and modeling, after an introduction to the main concepts and models. A diversity of phenomena are surveyed, which may be classified into no less than 22 areas, providing a clear indication of the impact of the field of complex networks.Comment: 103 pages, 3 figures and 7 tables. A working manuscript, suggestions are welcome