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Fast Computation of Shortest Smooth Paths and Uniformly Bounded Stretch with Lazy RPHAST

Author Tim Zeitz



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Tim Zeitz
  • Karlsruhe Institute of Technology, Germany

Acknowledgements

I want to thank my colleagues for from the scalable algorithms group Christopher Weyand, Marcus Wilhelm and Thomas Bläsius for pointing out a crucial fact on subpath-optimality at our group workshop. Further, I want to thank my colleague Jonas Sauer for many helpful discussions on algorithmic ideas and proofreading of early drafts of this paper. I also want to thank the anonymous reviewers for their helpful comments. Finally, I would like to thank Jakob Bussas who did a proof-of-concept implementation of the ideas presented here for his bachelor’s thesis.

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Tim Zeitz. Fast Computation of Shortest Smooth Paths and Uniformly Bounded Stretch with Lazy RPHAST. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 3:1-3:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.SEA.2022.3

Abstract

We study the shortest smooth path problem (SSPP), which is motivated by traffic-aware routing in road networks. The goal is to compute the fastest route according to the current traffic situation while avoiding undesired detours, such as briefly using a parking area to bypass a jammed highway. Detours are prevented by limiting the uniformly bounded stretch (UBS) with respect to a second weight function which disregards the traffic situation. The UBS is a path quality metric which measures the maximum relative length of detours on a path. In this paper, we settle the complexity of the SSPP and show that it is strongly NP-complete. We then present practical algorithms to solve the problem on continental-sized road networks both heuristically and exactly. A crucial building block of these algorithms is the UBS evaluation. We propose a novel algorithm to compute the UBS with only a few shortest path computations on typical paths. All our algorithms utilize Lazy RPHAST, a recently proposed technique to incrementally compute distances from many vertices towards a common target. An extensive evaluation shows that our algorithms outperform competing SSPP algorithms by up to two orders of magnitude and that our new UBS algorithm is the first to consistently compute exact UBS values in a matter of milliseconds.

Subject Classification

ACM Subject Classification
  • Theory of computation → Shortest paths
  • Mathematics of computing → Graph algorithms
  • Applied computing → Transportation
Keywords
  • realistic road networks
  • route planning
  • shortest paths
  • traffic-aware routing
  • live traffic
  • uniformly bounded stretch

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