9,659 research outputs found
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
Labeled Directed Acyclic Graphs: a generalization of context-specific independence in directed graphical models
We introduce a novel class of labeled directed acyclic graph (LDAG) models
for finite sets of discrete variables. LDAGs generalize earlier proposals for
allowing local structures in the conditional probability distribution of a
node, such that unrestricted label sets determine which edges can be deleted
from the underlying directed acyclic graph (DAG) for a given context. Several
properties of these models are derived, including a generalization of the
concept of Markov equivalence classes. Efficient Bayesian learning of LDAGs is
enabled by introducing an LDAG-based factorization of the Dirichlet prior for
the model parameters, such that the marginal likelihood can be calculated
analytically. In addition, we develop a novel prior distribution for the model
structures that can appropriately penalize a model for its labeling complexity.
A non-reversible Markov chain Monte Carlo algorithm combined with a greedy hill
climbing approach is used for illustrating the useful properties of LDAG models
for both real and synthetic data sets.Comment: 26 pages, 17 figure
- …