Probing a Set of Trajectories to Maximize Captured Information

Sándor P. Fekete, Alexander Hill, Dominik Krupke, Tyler Mayer, Joseph S. B. Mitchell, Ojas Parekh, Cynthia A. Phillips, Domenico Cantone, Simone Faro
2020 Symposium on Experimental and Efficient Algorithms  
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
more » ... ttacking 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.
doi:10.4230/lipics.sea.2020.5 dblp:conf/wea/FeketeHKMMPP20 fatcat:bw4jzh4bwzawlp5tpiiur44cwq