325 research outputs found
The game of go as a complex network
We study the game of go from a complex network perspective. We construct a
directed network using a suitable definition of tactical moves including local
patterns, and study this network for different datasets of professional
tournaments and amateur games. The move distribution follows Zipf's law and the
network is scale free, with statistical peculiarities different from other real
directed networks, such as e. g. the World Wide Web. These specificities
reflect in the outcome of ranking algorithms applied to it. The fine study of
the eigenvalues and eigenvectors of matrices used by the ranking algorithms
singles out certain strategic situations. Our results should pave the way to a
better modelization of board games and other types of human strategic scheming.Comment: 6 pages, 9 figures, final versio
Algorithmic Aspects of a General Modular Decomposition Theory
A new general decomposition theory inspired from modular graph decomposition
is presented. This helps unifying modular decomposition on different
structures, including (but not restricted to) graphs. Moreover, even in the
case of graphs, the terminology ``module'' not only captures the classical
graph modules but also allows to handle 2-connected components, star-cutsets,
and other vertex subsets. The main result is that most of the nice algorithmic
tools developed for modular decomposition of graphs still apply efficiently on
our generalisation of modules. Besides, when an essential axiom is satisfied,
almost all the important properties can be retrieved. For this case, an
algorithm given by Ehrenfeucht, Gabow, McConnell and Sullivan 1994 is
generalised and yields a very efficient solution to the associated
decomposition problem
Hamilton cycles in graphs and hypergraphs: an extremal perspective
As one of the most fundamental and well-known NP-complete problems, the
Hamilton cycle problem has been the subject of intensive research. Recent
developments in the area have highlighted the crucial role played by the
notions of expansion and quasi-randomness. These concepts and other recent
techniques have led to the solution of several long-standing problems in the
area. New aspects have also emerged, such as resilience, robustness and the
study of Hamilton cycles in hypergraphs. We survey these developments and
highlight open problems, with an emphasis on extremal and probabilistic
approaches.Comment: to appear in the Proceedings of the ICM 2014; due to given page
limits, this final version is slightly shorter than the previous arxiv
versio
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