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Compact, Provably-Good LPs for Orienteering and Regret-Bounded Vehicle Routing

  • Zachary Friggstad
  • Chaitanya SwamyEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10328)

Abstract

We develop polynomial-size LP-relaxations for orienteering and the regret-bounded vehicle routing problem (\(\mathsf {RVRP}\)) and devise suitable LP-rounding algorithms that lead to various new insights and approximation results for these problems. In orienteering, the goal is to find a maximum-reward r-rooted path, possibly ending at a specified node, of length at most some given budget B. In \(\mathsf {RVRP}\), the goal is to find the minimum number of r-rooted paths of regret at most a given bound R that cover all nodes, where the regret of an r-v path is its length − \(c_{rv}\). For rooted orienteering, we introduce a natural bidirected LP-relaxation and obtain a simple 3-approximation algorithm via LP-rounding. This is the first LP-based guarantee for this problem. We also show that point-to-point (\(\mathsf {P2P}\)) orienteering can be reduced to a regret-version of rooted orienteering at the expense of a factor-2 loss in approximation. For \(\mathsf {RVRP}\), we propose two compact LPs that lead to significant improvements, in both approximation ratio and running time, over the approach in [10]. One is a natural modification of the LP for rooted orienteering; the other is an unconventional formulation motivated by certain structural properties of an \(\mathsf {RVRP}\)-solution, which leads to a 15-approximation for \(\mathsf {RVRP}\).

Keywords

Sentinel Node Optimum Path Distance Interval Edge Cost Orienteering Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computing ScienceUniversity of AlbertaEdmontonCanada
  2. 2.Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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