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On the proper intervalization of colored caterpillar trees

Carme Àlvarez, Maria Serna (2009)

RAIRO - Theoretical Informatics and Applications

This paper studies the computational complexity of the proper interval colored graph problem (PICG), when the input graph is a colored caterpillar, parameterized by hair length. In order prove our result we establish a close relationship between the PICG and a graph layout problem the proper colored layout problem (PCLP). We show a dichotomy: the PICG and the PCLP are NP-complete for colored caterpillars of hair length ≥2, while both problems are in P for colored caterpillars of hair length <2. For...

On the weighted Euclidean matching problem in ℝ d

Birgit Anthes, Ludger Rüschendorf (2001)

Applicationes Mathematicae

A partitioning algorithm for the Euclidean matching problem in ℝ d is introduced and analyzed in a probabilistic model. The algorithm uses elements from the fixed dissection algorithm of Karp and Steele (1985) and the Zig-Zag algorithm of Halton and Terada (1982) for the traveling salesman problem. The algorithm runs in expected time n ( l o g n ) p - 1 and approximates the optimal matching in the probabilistic sense.

One-way communication complexity of symmetric boolean functions

Jan Arpe, Andreas Jakoby, Maciej Liśkiewicz (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We study deterministic one-way communication complexity of functions with Hankel communication matrices. Some structural properties of such matrices are established and applied to the one-way two-party communication complexity of symmetric Boolean functions. It is shown that the number of required communication bits does not depend on the communication direction, provided that neither direction needs maximum complexity. Moreover, in order to obtain an optimal protocol, it is in any case sufficient...

One-way communication complexity of symmetric Boolean functions

Jan Arpe, Andreas Jakoby, Maciej Liśkiewicz (2010)

RAIRO - Theoretical Informatics and Applications

We study deterministic one-way communication complexity of functions with Hankel communication matrices. Some structural properties of such matrices are established and applied to the one-way two-party communication complexity of symmetric Boolean functions. It is shown that the number of required communication bits does not depend on the communication direction, provided that neither direction needs maximum complexity. Moreover, in order to obtain an optimal protocol, it is in any case sufficient...

On-line models and algorithms for max independent set

Bruno Escoffier, Vangelis Th. Paschos (2006)

RAIRO - Operations Research

In on-line computation, the instance of the problem dealt is not entirely known from the beginning of the solution process, but it is revealed step-by-step. In this paper we deal with on-line independent set. On-line models studied until now for this problem suppose that the input graph is initially empty and revealed either vertex-by-vertex, or cluster-by-cluster. Here we present a new on-line model quite different to the ones already studied. It assumes that a superset of the final graph is initially...

Optimal edge ranking of complete bipartite graphs in polynomial time

Ruo-Wei Hung (2006)

Discussiones Mathematicae Graph Theory

An edge ranking of a graph is a labeling of edges using positive integers such that all paths connecting two edges with the same label visit an intermediate edge with a higher label. An edge ranking of a graph is optimal if the number of labels used is minimum among all edge rankings. As the problem of finding optimal edge rankings for general graphs is NP-hard [12], it is interesting to concentrate on special classes of graphs and find optimal edge rankings for them efficiently. Apart from trees...

Ordres médians et ordres de Slater des tournois

Irène Charon, Olivier Hudry, Frédéric Woirgard (1996)

Mathématiques et Sciences Humaines

Dans cet article, nous essayons de faire le point sur les résultats concernant les aspects combinatoires et algorithmiques des ordres médians et des ordres de Slater des tournois. La plupart des résultats recensés sont tirés de différentes publications ; plusieurs sont originaux.

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