Counting spanning trees using modular decomposition

TL;DR: An accurate analysis of the reliability of Ethernet multiple-ring mesh networks will be performed by a novel approach named the spanning tree set method, and the availability of the ring networks with imperfect coverage and online repair assumptions will be analyzed using a hierarchical model.

TL;DR: Performance evaluations demonstrate that the proposed approach provides significant improvement in network reliability compared to the representative approaches.

TL;DR: In this paper, the authors present an algorithm for drawing an undirected graph G which takes advantage of the structure of the modular decomposition tree of G. In order to achieve aesthetically pleasing results, they use grid and circular placement techniques, and utilize an appropriate modification of a well-known spring embedder algorithm.

TL;DR: A new method for accelerating matrix multiplication asymptotically is presented, by using a basic trilinear form which is not a matrix product, and making novel use of the Salem-Spencer Theorem.

TL;DR: It is proved that this is also the case for graphs of clique-width at most k, where this complexity measure is associated with hierarchical decompositions of another type, and where logical formulas are no longer allowed to use edge set quantifications.

TL;DR: It is shown that sparse Gaussian elimination is efficient for any class of graphs which have good separator, and conversely that graphs without good separators are not amenable to sparse GaRussian elimination.