Shortest paths with a cost constraint: a probabilistic analysis

TL;DR

This paper analyzes the shortest path problem in complete graphs with random edge lengths and costs, focusing on the asymptotic behavior of the minimum path length under a cost constraint.

Contribution

It provides a probabilistic analysis of the constrained shortest path problem, deriving the asymptotic minimum length as a function of the cost-budget.

Findings

Asymptotic value of minimum path length derived

Probabilistic model for edge lengths and costs used

Results applicable to large complete graphs

Abstract

We consider a constrained version of the shortest path problem on the complete graphs whose edges have independent random lengths and costs. We establish the asymptotic value of the minimum length as a function of the cost-budget within a wide range.