Search results for "Comparability graph"
showing 6 items of 6 documents
Potential approach in marginalizing Gibbs models
1999
Abstract Given an undirected graph G or hypergraph potential H model for a given set of variables V , we introduce two marginalization operators for obtaining the undirected graph G A or hypergraph H A associated with a given subset A ⊂ V such that the marginal distribution of A factorizes according to G A or H A , respectively. Finally, we illustrate the method by its application to some practical examples. With them we show that potential approach allow defining a finer factorization or performing a more precise conditional independence analysis than undirected graph models. Finally, we explain connections with related works.
Two graphs with a common edge
2014
Let G = G1 ∪ G2 be the sum of two simple graphs G1,G2 having a common edge or G = G1 ∪ e1 ∪ e2 ∪ G2 be the sum of two simple disjoint graphs G1,G2 connected by two edges e1 and e2 which form a cycle C4 inside G. We give a method of computing the determinant det A(G) of the adjacency matrix of G by reducing the calculation of the determinant to certain subgraphs of G1 and G2. To show the scope and effectiveness of our method we give some examples
P-matrix completions under weak symmetry assumptions
2000
An n-by-n matrix is called a Π-matrix if it is one of (weakly) sign-symmetric, positive, nonnegative P-matrix, (weakly) sign-symmetric, positive, nonnegative P0,1-matrix, or Fischer, or Koteljanskii matrix. In this paper, we are interested in Π-matrix completion problems, that is, when a partial Π-matrix has a Π-matrix completion. Here, we prove that a combinatorially symmetric partial positive P-matrix has a positive P-matrix completion if the graph of its specified entries is an n-cycle. In general, a combinatorially symmetric partial Π-matrix has a Π-matrix completion if the graph of its specified entries is a 1-chordal graph. This condition is also necessary for (weakly) sign-symmetric …
A tabu thresholding algorithm for arc crossing minimization in bipartite graphs
1996
Acyclic directed graphs are commonly used to model complex systems. The most important criterion to obtain a readable map of an acyclic graph is that of minimizing the number of arc crossings. In this paper, we present a heuristic for solving the problem of minimizing the number of arc crossings in a bipartite graph. It consists of a novel and easier implementation of fundamental tabu search ideas without explicit use of memory structures (a tabu thresholding approach). Computational results are reported on a set of 250 randomly generated test problems. Our algorithm has been compared with the two best heuristics published in the literature and with the optimal solutions for the test proble…
Stochastic Learning for SAT- Encoded Graph Coloring Problems
2010
The graph coloring problem (GCP) is a widely studied combinatorial optimization problem due to its numerous applications in many areas, including time tabling, frequency assignment, and register allocation. The need for more efficient algorithms has led to the development of several GC solvers. In this paper, the authors introduce a team of Finite Learning Automata, combined with the random walk algorithm, using Boolean satisfiability encoding for the GCP. The authors present an experimental analysis of the new algorithm’s performance compared to the random walk technique, using a benchmark set containing SAT-encoding graph coloring test sets.
Biased graph walks for RDF graph embeddings
2017
Knowledge Graphs have been recognized as a valuable source for background information in many data mining, information retrieval, natural language processing, and knowledge extraction tasks. However, obtaining a suitable feature vector representation from RDF graphs is a challenging task. In this paper, we extend the RDF2Vec approach, which leverages language modeling techniques for unsupervised feature extraction from sequences of entities. We generate sequences by exploiting local information from graph substructures, harvested by graph walks, and learn latent numerical representations of entities in RDF graphs. We extend the way we compute feature vector representations by comparing twel…