Probing a Set of Trajectories to Maximize Captured Information

Authors Sándor P. Fekete , Alexander Hill , Dominik Krupke , Tyler Mayer, Joseph S. B. Mitchell , Ojas Parekh, Cynthia A. Phillips

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Author Details

Sándor P. Fekete
  • Department of Computer Science, TU Braunschweig, Germany
Alexander Hill
  • Department of Computer Science, TU Braunschweig, Germany
Dominik Krupke
  • Department of Computer Science, TU Braunschweig, Germany
Tyler Mayer
  • Decision Management Systems, Charles River Analytics Inc., Boston, MA, USA
Joseph S. B. Mitchell
  • Department of Applied Mathematics and Statistics, Stony Brook University, NY, USA
Ojas Parekh
  • Sandia National Laboratories, Albuquerque, NM, USA
Cynthia A. Phillips
  • Sandia National Laboratories, Albuquerque, NM, USA


Work by Tyler Mayer was mostly carried out while at Stony Brook University. Joe Mitchell and Tyler Mayer were partially supported by the National Science Foundation (CCF-1526406) and a grant from the US-Israel Binational Science Foundation (BSF project 2016116). Joe Mitchell was also partially supported by the DARPA Lagrange program. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525.

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Sándor P. Fekete, Alexander Hill, Dominik Krupke, Tyler Mayer, Joseph S. B. Mitchell, Ojas Parekh, and Cynthia A. Phillips. Probing a Set of Trajectories to Maximize Captured Information. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Algorithm engineering
  • optimization
  • complexity
  • approximation
  • trajectories


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