Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Computers and Operations Research
Algorithms for the quickest path problem and the enumeration of quickest paths
Computers and Operations Research
Approximation schemes for the restricted shortest path problem
Mathematics of Operations Research
Finding the k quickest simple paths in a network
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Extend the quickest path problem to the system reliability evaluation for a stochastic-flow network
Computers and Operations Research
Reliability problem on all pairs quickest paths
ICCS'03 Proceedings of the 2003 international conference on Computational science
System reliability for quickest path problems under time threshold and budget
Computers & Mathematics with Applications
A simple efficient approximation scheme for the restricted shortest path problem
Operations Research Letters
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In a dynamic network, the quickest path problem asks for a path minimizing the time needed to send a given amount of flow from source to sink along this path. In practical settings, for example in evacuation or transportation planning, the reliability of network arcs depends on the specific scenario of interest. In this circumstance, the question of finding a quickest path among all those having at least a desired path reliability arises. In this article, this reliable quickest path problem is solved by transforming it to the restricted quickest path problem. In the latter, each arc is associated a nonnegative cost value and the goal is to find a quickest path among those not exceeding a predefined budget with respect to the overall (additive) cost value. For both, the restricted and reliable quickest path problem, pseudopolynomial exact algorithms and fully polynomial-time approximation schemes are proposed.