The All-Colors Shortest Path (ACSP) is a recently introduced NP-Hard optimization problem, in which color assigned to each vertex of an edge weighted graph, and the aim find shortest path spanning all colors. solution can be not simple, that it possible visit multiple times same vertices if convenient choice. starting constrained or (ACSP-UE). We propose reduction heuristic based on transformat...

The path length of a tree, that is the sum of the lengths of all root-leaf paths, is an important measure of eeciency of the tree. The fringe of a tree is the diierence between the lengths of the longest path and the shortest path in the tree. The minimal and the maximal path length of trees with N leaves and given fringe have been well studied. In this paper, we initiate the study of the expec...

Given a communication network or a road network one of the most natural algorithmic question is how to determine the shortest path from one point to another. In this paper we deal with one of the most fundamental problems of Graph Theory, the All Pairs Shortest Path (APSP) problem. We study three algorithms namely The FloydWarshall algorithm, APSP via Matrix Multiplication and the Johnson’s alg...