We demonstrate the applicability of bandwidth and wavefront reduction algorithms to static variable ordering. In symbolic model checking event locality plays a major role in time and memory usage. For example, in Petri nets event locality can be captured by dependency matrices, where nonzero entries indicate whether a transition modifies a place. The quality of event locality has been expressed...

Due to the availability of required information in the web, as multiple documents, the need for summarizing these multiple documents and ordering of the sentences in the summary in an efficient way become a relevant task in data mining. We present a novel sentence ordering method based on maximum cost spanning tree algorithm to improve the readability and cohesion of the summary obtained by ext...

It is known that the problem of computing adjacency dimension a graph NP-hard. This suggests finding for special classes graphs or obtaining good bounds on this invariant. In work we obtain general G in terms parameters . We discuss tightness these and, some particular graphs, closed formulae. particular, show close relationships exist between and other parameters, like domination number, locat...

Felsner, Li and Trotter showed that the dimension of adjacency poset an outerplanar graph is at most 5, gave example whose has 4. We improve their upper bound to 4, which then best possible.

In this paper, we show that the dimension of the adjacency poset of a planar graph is at most 8. From below, we show that there is a planar graph whose adjacency poset has dimension 5. We then show that the dimension of the adjacency poset of an outerplanar graph is at most 5. From below, we show that there is an outerplanar graph whose adjacency poset has dimension 4. We also show that the dim...

We look at problems involving finding subgraphs in larger graphs, such as the maximum clique problem, the subgraph isomorphism problem, and the maximum common subgraph problem. We investigate variable and value ordering heuristics, different inference strategies, intelligent backtracking search (backjumping), and bitand thread-parallelism to exploit modern hardware.