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arXiv · 1711.00284

Improved Approximation Schemes for the Restricted Shortest Path Problem

David Holzmüller
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Abstract

The Restricted Shortest Path (RSP) problem, also known as the Delay-Constrained Least-Cost (DCLC) problem, is an NP-hard bicriteria optimization problem on graphs with $n$ vertices and $m$ edges. In a graph where each edge is assigned a cost and a delay, the goal is to find a min-cost path which does not exceed a delay bound. In this paper, we present improved approximation schemes for RSP on several graph classes. For planar graphs, undirected graphs with positive integer resource (= delay) values, and graphs with $m \in \Omega(n \log n)$, we obtain $(1 + \varepsilon)$-approximations in time $O(mn/\varepsilon)$. For general graphs and directed acyclic graphs, we match the results by Xue et al. (2008, [10]) and Ergun et al. (2002, [1]), respectively, but with arguably simpler algorithms.

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David Holzmüller. 2017-11-01. Improved Approximation Schemes for the Restricted Shortest Path Problem. https://arxiv.org/abs/1711.00284

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