41,004 research outputs found
Algorithmic Aspects of Switch Cographs
This paper introduces the notion of involution module, the first
generalization of the modular decomposition of 2-structure which has a unique
linear-sized decomposition tree. We derive an O(n^2) decomposition algorithm
and we take advantage of the involution modular decomposition tree to state
several algorithmic results. Cographs are the graphs that are totally
decomposable w.r.t modular decomposition. In a similar way, we introduce the
class of switch cographs, the class of graphs that are totally decomposable
w.r.t involution modular decomposition. This class generalizes the class of
cographs and is exactly the class of (Bull, Gem, Co-Gem, C_5)-free graphs. We
use our new decomposition tool to design three practical algorithms for the
maximum cut, vertex cover and vertex separator problems. The complexity of
these problems was still unknown for this class of graphs. This paper also
improves the complexity of the maximum clique, the maximum independant set, the
chromatic number and the maximum clique cover problems by giving efficient
algorithms, thanks to the decomposition tree. Eventually, we show that this
class of graphs has Clique-Width at most 4 and that a Clique-Width expression
can be computed in linear time
A survey on algorithmic aspects of modular decomposition
The modular decomposition is a technique that applies but is not restricted
to graphs. The notion of module naturally appears in the proofs of many graph
theoretical theorems. Computing the modular decomposition tree is an important
preprocessing step to solve a large number of combinatorial optimization
problems. Since the first polynomial time algorithm in the early 70's, the
algorithmic of the modular decomposition has known an important development.
This paper survey the ideas and techniques that arose from this line of
research
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Action selection in modular reinforcement learning
textModular reinforcement learning is an approach to resolve the curse of dimensionality problem in traditional reinforcement learning. We design and implement a modular reinforcement learning algorithm, which is based on three major components: Markov decision process decomposition, module training, and global action selection. We define and formalize module class and module instance concepts in decomposition step. Under our framework of decomposition, we train each modules efficiently using SARSA() algorithm. Then we design, implement, test, and compare three action selection algorithms based on different heuristics: Module Combination, Module Selection, and Module Voting. For last two algorithms, we propose a method to calculate module weights efficiently, by using standard deviation of Q-values of each module. We show that Module Combination and Module Voting algorithms produce satisfactory performance in our test domain.Computer Science
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
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