Graph Classes based on Interval Structures: Combinatorial Optimization and Recognition of Graph Classes with Applications to Related Models - Couverture souple

Mertzios, George B.

 
9783838111957: Graph Classes based on Interval Structures: Combinatorial Optimization and Recognition of Graph Classes with Applications to Related Models
Couverture souple
ISBN 10 : 3838111958 ISBN 13 : 9783838111957
Editeur : Suedwestdeutscher Verlag fuer Hochschulschriften, 2010

Synopsis

Interval structures arise naturally in many applications, as in genetics, molecular biology, resource allocation, and scheduling, among others. Such structures are often modeled with graphs, such as interval and tolerance graphs, which have been widely studied. In this book we mainly investigate these classes of graphs, as well as a scheduling problem. We present solutions to some open problems, along with some new representation models that enable the design of new efficient algorithms. In the context of interval graphs, we present the first polynomial algorithm for the longest path problem, whose complexity status was an open question. Furthermore, we introduce two matrix representations for both interval and proper interval graphs, which can be used to derive efficient algorithms. In the context of tolerance graphs, we present the first non-trivial intersection model, given by three-dimensional parallelepipeds, which enables the design of efficient algorithms for some NP-hard optimization problems. Furthermore, we prove that both recognition problems for tolerance and bounded tolerance graphs are NP-complete, thereby settling a long standing open question since 1982.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Interval structures arise naturally in many applications, as in genetics, molecular biology, resource allocation, and scheduling, among others. Such structures are often modeled with graphs, such as interval and tolerance graphs, which have been widely studied. In this book we mainly investigate these classes of graphs, as well as a scheduling problem. We present solutions to some open problems, along with some new representation models that enable the design of new efficient algorithms. In the context of interval graphs, we present the first polynomial algorithm for the longest path problem, whose complexity status was an open question. Furthermore, we introduce two matrix representations for both interval and proper interval graphs, which can be used to derive efficient algorithms. In the context of tolerance graphs, we present the first non-trivial intersection model, given by three-dimensional parallelepipeds, which enables the design of efficient algorithms for some NP-hard optimization problems. Furthermore, we prove that both recognition problems for tolerance and bounded tolerance graphs are NP-complete, thereby settling a long standing open question since 1982.

Biographie de l'auteur

George Mertzios, born in Greece (1983), has studied Applied Mathematics and Informatics at the National Technical Univ. of Athens and the Technische Univ. München. In 2009 he received his Ph.D. on Computer Science at the RWTH Aachen University. During his school years he received the Gold Medal at the 2nd Junior Balkan Mathematical Olympiad (1998).

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Suedwestdeutscher Verlag fuer Hochschulschriften
Date d'édition
2010
Langue
anglais
ISBN 10 
3838111958
ISBN 13 
9783838111957
Reliure
Broché
Nombre de pages
164
Coordonnées du fabricant
non disponible
Personne responsable
non disponible