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|}.
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Akutsu, T. (2004). Algorithms for Point Set Matching with k-Differences. In: Chwa, KY., Munro, J.I.J. (eds) Computing and Combinatorics. COCOON 2004. Lecture Notes in Computer Science, vol 3106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27798-9_28
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DOI: https://doi.org/10.1007/978-3-540-27798-9_28
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