On paths with the shortest average arc length in weighted graphs

On Paths with the Shortest Average Arc Length in Weighted Graphs

Wimer, S., I. Koren and I. Cederbaum, On paths with the shortest average arc length in weighted graphs, Discrete Applied Mathematics 45 (1993) 169-179. The problem of finding the path having the smallest average arc length in an acyclic digraph with a single source and a single sink is considered in this paper. This problem arises in VLSI block placement procedures when spreading the building b...

Approximate shortest paths in weighted graphs

We present an approximation algorithm for the all pairs shortest paths (APSP) problem in weighed graphs. Our algorithm solves the APSP problem for weighted directed graphs, with real (positive or negative) weights, up to an additive error of . For any pair of vertices u, v, the algorithm finds a path whose length is at most δ(u, v) + . The algorithm is randomized and runs in Õ(n) < O(n) time, w...

Shortest paths in fuzzy weighted graphs

The task of finding shortest paths in weighted graphs is one of the archetypical problems encountered in the domain of combinatorial optimization and has been studied intensively over the past five decades. More recently, fuzzy weighted graphs, along with generalizations of algorithms for finding optimal paths within them, have emerged as an adequate modeling tool for prohibitively complex and/...

Shortest Path Problem with Gamma Probability Distribution Arc Length

We propose a dynamic program to find the shortest path in a network having gamma probability distributions as arc lengths. Two operators of sum and comparison need to be adapted for the proposed dynamic program. Convolution approach is used to sum two gamma probability distributions being employed in the dynamic program.

Single Source Shortest Paths on Weighted Co-Interval Graphs