Message routing strategies are given for any network that can be decomposed by a separator of size at most a small constant c into two networks with the same property. These strategies use a total of O(cnlogn) items of routing information, keep node names to O(log n) bits, and still route along near-shortest paths. If the names generated from a separator-based hierarchical decomposition of the ...

The problem of determining shortest paths in the presence of polyhedral obstacles between two points in Euclidean 3-space stems from the general problem of obtaining optimal coliision free paths in robot systems. For the special case when paths are constrained to the surfaces of 3-dimensional objects, simple planar unfoldings are used to obtain the shortest path. For the general case wben paths...

In data analysis, there is a strong demand for graph metrics that differ from the classical shortest path and resistance distances. Recently, several new classes of graph metrics have been proposed. This paper presents some of them featuring the cutpoint additive distances. These include the path distances, the reliability distance, the walk distances, and the logarithmic forest distances among...

This note attempts to summarize the best of the currently existing theoretical results on the single-source shortest paths problem for graphs with non-negative edge weights. The main purpose of this note is to make available the statements of all of these results, as well as the building blocks they use, together in one document. We also note some new theoretical implications of a recent result...

The original idea in developing Pd [?] was to make a real-time computer music performance environment like Max, but somehow to include also a facility for making computer music scores with user-specifiable graphical representations. This idea has important precedents in Animal [?] and SSSP [?]. An even earlier class of precedents lies in the rich variety of paper scores for electronic music bef...

This paper proposes two models of adding relations to a linking pin type organization structure where every pair of siblings in a complete Kary tree of height H is adjacent: (i) a model of adding an edge between two nodes with the same depth N and (ii) a model of adding edges between every pair of nodes with the same depth N . For each of the two models, an optimal depth N∗ is obtained by maxim...