NDLI: Approximation algorithms for regret-bounded vehicle routing and applications to distance-constrained vehicle routing

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Approximation algorithms for regret-bounded vehicle routing and applications to distance-constrained vehicle routing

Content Provider	ACM Digital Library
Author	Swamy, Chaitanya Friggstad, Zachary
Abstract	We consider vehicle-routing problems (VRPs) that incorporate the notion of regret of a client, which is a measure of the waiting time of a client relative to its shortest-path distance from the depot. Formally, we consider both the additive and multiplicative versions of, what we call, the regret-bounded vehicle routing problem (RVRP). In these problems, we are given an undirected complete graph G = ({r} ∪ V,E) on n nodes with a distinguished root (depot) node r, edge costs $\{c_{uv}\}$ that form a metric, and a regret bound R. Given a path P rooted at r and a node v ∈ P, let $c_{P}(v)$ be the distance from r to v along P. The goal is to find the fewest number of paths rooted at r that cover all the nodes so that for every node v covered by (say) path P: (i) its additive regret $c_{P}(v)$ -- $c_{rv},$ with respect to P is at most R in additive-RVRP; or (ii) its multiplicative regret, $c_{P}(v)/c_{rv},$ with respect to P is at most R in multiplicative-RVRP. Our main result is the first constant-factor approximation algorithm for additive-RVRP. This is a substantial improvement over the previous-best O(log n)-approximation. Additive-RVRP turns out be a rather central vehicle-routing problem, whose study reveals insights into a variety of other regret-related problems as well as the classical distance-constrained VRP (DVRP), enabling us to obtain guarantees for these various problems by leveraging our algorithm for additive-RVRP and the underlying techniques. We obtain approximation ratios of [EQUATION] for multiplicative-RVRP, and [EQUATION] for DVRP with distance bound D via reductions to additive-RVRP; the latter improves upon the previous-best approximation for DVRP. A noteworthy aspect of our results is that they are obtained by devising rounding techniques for a natural configuration-style LP. This furthers our understanding of LP-relaxations for VRPs and enriches the toolkit of techniques that have been utilized for configuration LPs.
Starting Page	744
Ending Page	753
Page Count	10
File Format	PDF MP4
ISBN	9781450327107
DOI	10.1145/2591796.2591840
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2014-05-31
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Lp rounding Distance-constrained vehicle routing Vehicle routing Approximation algorithms Configuration lps
Content Type	Audio Text
Resource Type	Article

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