License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SEA.2020.5
URN: urn:nbn:de:0030-drops-120796
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12079/
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Fekete, Sándor P. ; Hill, Alexander ; Krupke, Dominik ; Mayer, Tyler ; Mitchell, Joseph S. B. ; Parekh, Ojas ; Phillips, Cynthia A.

Probing a Set of Trajectories to Maximize Captured Information

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LIPIcs-SEA-2020-5.pdf (3 MB)

Abstract

We study a trajectory analysis problem we call the Trajectory Capture Problem (TCP), in which, for a given input set T of trajectories in the plane, and an integer k≥ 2, we seek to compute a set of k points ("portals") to maximize the total weight of all subtrajectories of T between pairs of portals. This problem naturally arises in trajectory analysis and summarization.
We show that the TCP is NP-hard (even in very special cases) and give some first approximation results. Our main focus is on attacking the TCP with practical algorithm-engineering approaches, including integer linear programming (to solve instances to provable optimality) and local search methods. We study the integrality gap arising from such approaches. We analyze our methods on different classes of data, including benchmark instances that we generate. Our goal is to understand the best performing heuristics, based on both solution time and solution quality. We demonstrate that we are able to compute provably optimal solutions for real-world instances.

BibTeX - Entry

@InProceedings{fekete_et_al:LIPIcs:2020:12079,
  author =	{S{\'a}ndor P. Fekete and Alexander Hill and Dominik Krupke and Tyler Mayer and Joseph S. B. Mitchell and Ojas Parekh and Cynthia A. Phillips},
  title =	{{Probing a Set of Trajectories to Maximize Captured Information}},
  booktitle =	{18th International Symposium on Experimental Algorithms (SEA 2020)},
  pages =	{5:1--5:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-148-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{160},
  editor =	{Simone Faro and Domenico Cantone},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12079},
  URN =		{urn:nbn:de:0030-drops-120796},
  doi =		{10.4230/LIPIcs.SEA.2020.5},
  annote =	{Keywords: Algorithm engineering, optimization, complexity, approximation, trajectories}
}

Keywords: Algorithm engineering, optimization, complexity, approximation, trajectories
Collection: 18th International Symposium on Experimental Algorithms (SEA 2020)
Issue Date: 2020
Date of publication: 12.06.2020
Supplementary Material: The code and data of the experimental evaluation is available at https://github.com/ahillbs/trajectory_capturing.

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