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)


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 \(\mathsf {RVRP}\).


Sentinel Node Optimum Path Distance Interval Edge Cost Orienteering Problem 
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© 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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