Durán, Guillermo

Liebling, Thomas M.

Matamala, Martin

Infoscience - École polytechnique fédérale de Lausanne

Traces of the Latin American Conference on Combina-torics, Graphs and ApplicationsA selection of papers from LACGA 2004, Santiago, ChileIntroductionGuillermo Dura´n a, Thomas M. Liebling b and Mart´ın Matamala aaUniversidad de Chile, Santiago, ChilebEPFL, Lausanne, SwitzerlandThe present issue comprises papers presented at the Latin American Confer-ence on Combinatorics, Graphs and Applications LACGA, held August 2004in Santiago, Chile. That conference gathered scientists from Latin America,Europe and the US sharing their interest in modern aspects of discrete appliedmathematics, its ramifications and applications. Its venue and size, its subjectdiversity, and last not least, the particularly pleasant working environmentmade the meeting into an extremely fertile interaction forum between par-ticipants, be they well established researchers or young students. In betweenstimulating presentations, many informal exchanges took place, novel ideastook shape and new projects and partnerships were started. Many excitingnew results e.g. in extremal and polyhedral combinatorics, optimization overgraphs and applications were presented. This is well documented by the col-lection of papers presented in rhis issue and we are grateful to the Editor inChief of DAM for having agreed to host it in this Journal. We thank all theanonymous referees for their careful, competent and diligent reviewing of thesubmitted papers. We gratefully acknowledge the support from the MillenniumScience Nuclei “Complex Engineering Systems” and “Information and Ran-domness” in Chile as well as the Departments of Industrial Engineering andMathematical Engineering, and the Center of Mathematical Modeling of theUniversidad de Chile, that also hosted the meeting. Here is a quick overviewof the papers, classified into the categories: Graph Theory and Combinatorics,Combinatorial Optimization and Polyhedral Combinatorics, and Applications.Finally we would like to thank Marianne Ruegg for her competent support inpreparing this issue.Graph Theory and CombinatoricsOn maximum planar induced subgraphs, by Luerbio Faria, Celina M. Herrerade Figueiredo, Sylvain Gravier, Candido F. X. de Mendonc¸a, and Jorge Stolfi,resolves complexity issues about the problem of finding, for a given graph, thesmallest number of vertices whose deletion will result in a planar graph. The1problem itself and the associated approximation problems are NP-hard.Algorithms for clique-independent sets on subclasses of circular-arc graphs, byGuillermo Dura´n, Min Chih Lin, Sergio Mera, and Jayme Luiz Szwarcfiter,gives a linear time algorithm to solve the maximum cardinality of a clique-independent set in the special case where the graph is a Helly circular-arcgraph. Previous algorithms were in O(n3).The sandwich problem for cutsets: clique cutset, k-star cutset, by Rafael B.Texeira, and Celina M. Herrera de Figueiredo, proposes polynomial algorithmsfor several particular sandwich problems. In such problems two graphs aregiven and a third, with some particular property and whose edge set lies in-between, is found.Clique-Critical Graphs: bound on the number of vertices and recognition, byLiliana Alco´n, establishes that if graph G has m edges, then any clique-criticalgraph in the class of graphs whose clique-graph is G has at most 2m vertices.She also shows in this paper that recognizing a clique-critical graph is NP-complete.Some basic properties of multiple Hamiltonian covers, by Hans L. Fetter, in-troduces the concept of multiple Hamiltonian cover and studies it on cubic3-connected planar graphs. It also relates this notion to problems in geome-try.A Concentration Bound for the Longest Increasing Subsequence of a Ran-domly Chosen Involution, by Marcos Kiwi, provides a concentration result forthe length of the longest increasing sub-sequence of a randomly and uniformlychosen involution of the integers {1, . . . , s}.NP-completeness results for edge modification problems, by Pablo Burzyn,Flavia Bonomo, and Guillermo Dura´n, addresses the problem of endowinga graph with some given property by edge modifications. They present NP-completeness results for several classes of graphs such as interval, circular-arc,permutation and circle graphs.Combinatorial Optimization and Polyhedral CombinatoricsOn the Commutativity of antiblocker diagrams under lift-and-project operators,by Mariana Escalante, Graciela L. Nasini, and M.C. Varaldo, provides explicitproofs from the non-commutativity of various antiblocker duality diagramsassociated with the stable set polytope of a graph. To do so, they look at aparticular case of complements of line graphs of complete graphs.On a certain class of non-ideal clutters, by Gabriela R. Argiroffo, Silvia M.Bianchi, and Graciela L. Nasini, introduces the class of near-ideal clutterswhich is analogous to those introduced by Shepherd for near-perfect graphs.They give a similar polyhedral characterization for the former as Shepherddid for the latter. They show in particular that near-ideal blockers of graphsare blockers of near-bipartite graphs.On the Combinatorial Structure of Chromatic Scheduling Polytopes, by JavierMarenco, and Annegret Wagler, studies the structure of this polytope whicharises as solution set of the bandwidth allocation problem in radio access2networks and the like. In particular they study what happens to the polytopefor increasing frequency bands.Some Formulations for the Group Steiner Tree Problem, by Carlos E. Ferreira,and Fernando M. de Oliveira Filho. They are interested in a problem whichis a slide generalization of the original Steiner problem in graphs. New facetsdefining in equalities are presented in this problem.ApplicationsOn the Characterization of the Domination of a Diameter Constrained Net-work Reliability Model, by He´ctor Cancela, and Louis Petingi, deals with aproblem which is important in the context of reliable network design. Theproblem is that of designing a network whose arcs are subject to failure, suchthat the probability that the surviving arcs span a graph of given (s,K)-diameter exceeds some value. The (s,K)-diameter is the length of the longestsimple path from a node s to any node in the set K.Reoptimization Gaps versus Model Errors in Online-Dispatching of ServiceUnits for ADAC, by Benjamin Hiller, Sven O. Krumke, and Jo¨rg Rambau,considers the difficult online optimization problem of continuously assigningrescue vehicles to new emergency sites. The algorithms must be particularlyfast. They compare the methods implemented for the German AutomobileAssociation with “optimal solutions” found using an oracle.Online-Optimization of Multi-Elevator Transport Systems with Reoptimiza-tion Algorithms based on Set-Partitioning Models, by Philipp Friese, and Jo¨rgRambau. The authors develop, experiment and compare a control policies fora set of K elevators with unit capacity. This is a idealist version of a situationencountered in a large German inventory system.Maximizing breaks and bounding solutions to the mirrored traveling tourna-ment problem, by Sebastia´n Urrutia, and Celso Ribeiro, investigates the re-lation between two aspects of round robin tournament scheduling problems:breaks and distances and they present new heuristics for approximate solutionsof this problem.Santiago, LausanneOctober 20053

Traces of the Latin American Conference on Combinatorics, Graphs and Applications. A selection of papers from LACGA 2004, Santiago, Chile, editorial

Matamala, Martín

Elsevier - Publisher Connector 

Discrete Applied Mathematics 154 (2006) 1771–1772
www.elsevier.com/locate/dam
Editorial
Traces of the Latin American Conference on Combinatorics,
Graphs and Applications
A selection of papers from LACGA 2004, Santiago, Chile
The present issue comprises papers presented at the Latin American Conference on Combinatorics, Graphs and
Applications LACGA, held inAugust 2004 in Santiago, Chile. That conference gathered scientists from LatinAmerica,
Europe and the US sharing their interest in modern aspects of discrete applied mathematics, its ramiﬁcations and
applications. Its venue and size, its subject diversity, and last not least, the particularly pleasant working environment
made the meeting into an extremely fertile interaction forum between participants, be they well established researchers
or young students. In between stimulating presentations, many informal exchanges took place, novel ideas took shape
andnewprojects and partnershipswere started.Many exciting new results e.g. in extremal and polyhedral combinatorics,
optimization over graphs and applicationswere presented. This is well documented by the collection of papers presented
in this issue and we are grateful to the Editor in Chief of Discrete Applied Mathematics for having agreed to host it in
this Journal. We thank all the anonymous referees for their careful, competent and diligent reviewing of the submitted
papers. We gratefully acknowledge the support from the Millennium Science Nuclei “Complex Engineering Systems”
and “Information and Randomness” in Chile as well as the Departments of Industrial Engineering and Mathematical
Engineering, and the Center of Mathematical Modeling of the Universidad de Chile, that also hosted the meeting.
Here is a quick overview of the papers, classiﬁed into the categories: Graph theory and combinatorics, Combinatorial
optimization and polyhedral combinatorics, and Applications. Finally we would like to thank Marianne Ruegg for her
competent support in preparing this issue.
Graph theory and combinatorics
On maximum planar induced subgraphs, by Luerbio Faria, Celina M. Herrera de Figueiredo, Sylvain Gravier,
Candido F.X. de Mendonça, and Jorge Stolﬁ, resolves complexity issues about the problem of ﬁnding, for a given
graph, the smallest number of vertices whose deletion will result in a planar graph. The problem itself and the associated
approximation problems are NP-hard.
Algorithms for clique-independent sets on subclasses of circular-arc graphs, by Guillermo Durán, Min Chih Lin,
Sergio Mera, and Jayme Luiz Szwarcﬁter, gives a linear time algorithm to solve the maximum cardinality of a clique-
independent set in the special case where the graph is a Helly circular-arc graph. Previous algorithm was in O(n2).
The sandwich problem for cutsets: clique cutset, k-star cutset, by Rafael B. Texeira, and Celina M. Herrera de
Figueiredo, proposes polynomial algorithms for several particular sandwich problems. In such problems two graphs
are given and a third, with some particular property and whose edge set lies in-between, is found.
Clique-Critical Graphs: Maximum Size and Recognition, by Liliana Alcón, establishes that if graph G has m edges,
then any clique-critical graph in the class of graphs whose clique-graph is G has at most 2m vertices. She also shows
in this paper that recognizing a clique-critical graph is NP-complete.
Some basic properties of multiple Hamiltonian covers, by Hans L. Fetter, introduces the concept of multiple Hamil-
tonian cover and studies it on cubic 3-connected planar graphs. It also relates this notion to problems in geometry.
0166-218X/$ - see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.dam.2006.03.019
1772 Editorial /Discrete Applied Mathematics 154 (2006) 1771–1772
A Concentration Bound for the Longest Increasing Subsequence of a Randomly Chosen Involution, by Marcos Kiwi,
provides a concentration result for the length of the longest increasing sub-sequence of a randomly and uniformly
chosen involution of the integers {1, . . . , s}.
NP-completeness results for edge modiﬁcation problems, by Pablo Burzyn, Flavia Bonomo, and Guillermo Durán,
addresses the problem of endowing a graph with some given property by edge modiﬁcations. They present NP-
completeness results for several classes of graphs such as interval, circular-arc, permutation and circle graphs.
Combinatorial optimization and polyhedral combinatorics
On the Commutativity of antiblocker diagrams under lift-and-project operators, by Mariana Escalante, Graciela L.
Nasini, and M.C. Varaldo, provides explicit proofs of the non-commutativity of various antiblocker duality diagrams
associated with the stable set polytope of a graph. To do so, they look at a particular case of complements of line graphs
of complete graphs.
Ona certain class of nonideal clutters, byGabriela R.Argiroffo, SilviaM.Bianchi, andGraciela L.Nasini, introduces
the class of near-ideal clutters which is analogous to those introduced by Shepherd for near-perfect graphs. They give a
similar polyhedral characterization for the former as Shepherd did for the latter. They show in particular that near-ideal
blockers of graphs are blockers of near-bipartite graphs.
On theCombinatorial Structure of Chromatic Scheduling Polytopes, by JavierMarenco, andAnnegretWagler, studies
the structure of this polytope which arises as solution set of the bandwidth allocation problem in radio access networks
and the like. In particular they study what happens to the polytope for increasing frequency bands.
Some Formulations for the Group Steiner Tree Problem, by Carlos E. Ferreira, and Fernando M. de Oliveira Filho.
They are interested in a problem which is a slide generalization of the original Steiner problem in graphs. New facets
deﬁning in equalities are presented in this problem.
Applications
On theCharacterization of theDomination of aDiameter-ConstrainedNetworkReliabilityModel, byHéctorCancela,
and Louis Petingi, deals with a problem which is important in the context of reliable network design. The problem is
that of designing a network whose arcs are subject to failure, such that the probability that the surviving arcs span a
graph of given (s,K)-diameter exceeds some value. The (s,K)-diameter is the length of the longest simple path from
a node s to any node in the set K.
Reoptimization Gaps versus Model Errors in Online-Dispatching of Service Units for ADAC, by Benjamin Hiller,
SvenO.Krumke, and JörgRambau, considers the difﬁcult online optimization problemof continuously assigning rescue
vehicles to new emergency sites. The algorithms must be particularly fast. They compare the methods implemented for
the German Automobile Association with “optimal solutions” found using an oracle.
Online-Optimization of Multi-Elevator Transport Systems with Reoptimization Algorithms based on Set-Partitioning
Models, by Philipp Friese, and Jörg Rambau. The authors develop, experiment and compare a control policies for a
set of K elevators with unit capacity. This is a idealist version of a situation encountered in a large German inventory
system.
Maximizing breaks and bounding solutions to the mirrored traveling tournament problem, by Sebastián Urrutia, and
Celso Ribeiro, investigates the relation between two aspects of round robin tournament scheduling problems: breaks
and distances and they present new heuristics for approximate solutions of this problem.
Guest Editors
Guillermo Durán
Thomas M. Liebling
Martín Matamala


Traces of the Latin American Conference on Combinatorics, Graphs and Applications A selection of papers from LACGA 2004, Santiago, Chile

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