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...

Let PG(s, t) denote a shortest path between two nodes s and t in an undirected graph G with nonnegative edge weights. A detour at a node u ∈ PG(s, t) = (s, . . . , u, v, . . . , t) is defined as a shortest path PG−e(u, t) from u to t which does not make use of (u, v). In this paper, we focus on the problem of finding an edge e = (u, v) ∈ PG(s, t) whose removal produces a detour at node u such t...

The shortest path problem is common in many different fields (transportation systems, mechanical systems, etc). Most of the telecommunication industry protocols such as PNNI, OSPF and IISP use Dijkstra’s algorithm or Bellman-Ford’s algorithm to solve the shortest path problem. Today, the majority of the shortest path computations are performed in software, which is inefficient for real-time app...