Chapter

SOFSEM 2007: Theory and Practice of Computer Science

Volume 4362 of the series Lecture Notes in Computer Science pp 212-223

Fast Approximate Point Set Matching for Information Retrieval

  • Raphaël CliffordAffiliated withUniversity of Bristol, Department of Computer Science, Woodland Road, Bristol, BS8 1UB
  • , Benjamin SachAffiliated withUniversity of Bristol, Department of Computer Science, Woodland Road, Bristol, BS8 1UB

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Abstract

We investigate randomised algorithms for subset matching with spatial point sets—given two sets of d-dimensional points: a data set T consisting of n points and a pattern P consisting of m points, find the largest match for a subset of the pattern in the data set. This problem is known to be 3-SUM hard and so unlikely to be solvable exactly in subquadratic time. We present an efficient bit-parallel O(nm) time algorithm and an O(nlogm) time solution based on correlation calculations using fast Fourier transforms. Both methods are shown experimentally to give answers within a few percent of the exact solution and provide a considerable practical speedup over existing deterministic algorithms.