TY - GEN
T1 - Probing a Set of Trajectories to Maximize Captured Information
AU - Fekete, Saoóndor P.
AU - Hill, Alexander
AU - Krupke, Dominik
AU - Mayer, Tyler
AU - Mitchell, Joseph S.B.
AU - Parekh, Ojas
AU - Phillips, Cynthia A.
N1 - Publisher Copyright:
© 2020 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - 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. 2012 ACM Subject Classification Theory of computation ! Design and analysis of algorithms.
AB - 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. 2012 ACM Subject Classification Theory of computation ! Design and analysis of algorithms.
KW - Algorithm engineering
KW - Approximation
KW - Complexity
KW - Optimization
KW - Trajectories
UR - https://www.scopus.com/pages/publications/85088166178
U2 - 10.4230/LIPIcs.SEA.2020.5
DO - 10.4230/LIPIcs.SEA.2020.5
M3 - Conference contribution
AN - SCOPUS:85088166178
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 18th International Symposium on Experimental Algorithms, SEA 2020
A2 - Faro, Simone
A2 - Cantone, Domenico
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 18th International Symposium on Experimental Algorithms, SEA 2020
Y2 - 16 June 2020 through 18 June 2020
ER -