Chapter

Computing and Combinatorics

Volume 3106 of the series Lecture Notes in Computer Science pp 249-258

Algorithms for Point Set Matching with k-Differences

  • Tatsuya AkutsuAffiliated withBioinformatics Center, Institute for Chemical Research, Kyoto University

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Abstract

The largest common point set problem (LCP) is, given two point set P and Q in d-dimensional Euclidean space, to find a subset of P with the maximum cardinality that is congruent to some subset of Q. We consider a special case of LCP in which the size of the largest common point set is at least (|P|+|Q|–k)/2. We develop efficient algorithms for this special case of LCP and a related problem. In particular, we present an O(k 3 n 1.34 + kn 2 log n) time algorithm for LCP in two dimensions, which is much better for small k than an existing O(n 3.2 log n) time algorithm, where n =  max {|P|,|Q|}.