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Finding long and similar parts of trajectories

Published:04 November 2009Publication History

ABSTRACT

A natural time-dependent similarity measure for two trajectories is their average distance at corresponding times. We give algorithms for computing the most similar subtrajectories under this measure, assuming the two trajectories are given as two polygonal, possibly self-intersecting lines. When a minimum duration is specified for the subtrajectories, and they must start at exactly corresponding times in the input trajectories, we give a linear-time algorithm for computing the starting time and duration of the most similar subtrajectories. The algorithm is based on a result of independent interest: We present a linear-time algorithm to find, for a piece-wise monotone function, an interval of at least a given length that has minimum average value.

When the two subtrajectories can start at different times in the two input trajectories, it appears difficult to give an exact algorithm for the most similar subtrajectories problem, even if the duration of the desired two subtrajectories is fixed to some length. We show that the problem can be solved approximately, and with a performance guarantee. More precisely, we present (1 + ε)-approximation algorithms for computing the most similar subtrajectories of two input trajectories for the case where the duration is specified, and also for the case where only a minimum on the duration is specified.

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    • Published in

      cover image ACM Conferences
      GIS '09: Proceedings of the 17th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
      November 2009
      575 pages
      ISBN:9781605586496
      DOI:10.1145/1653771

      Copyright © 2009 ACM

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      Publication History

      • Published: 4 November 2009

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