eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
32:1
32:9
10.4230/LIPIcs.ISAAC.2020.32
article
Geometric Pattern Matching Reduces to k-SUM
Aronov, Boris
1
https://orcid.org/0000-0003-3110-4702
Cardinal, Jean
2
https://orcid.org/0000-0002-2312-0967
Department of Computer Science and Engineering, Tandon School of Engineering, New York University, Brooklyn, NY ,USA
Université libre de Bruxelles (ULB), Belgium
We prove that some exact geometric pattern matching problems reduce in linear time to o k-SUM when the pattern has a fixed size k. This holds in the real RAM model for searching for a similar copy of a set of k ≥ 3 points within a set of n points in the plane, and for searching for an affine image of a set of k ≥ d+2 points within a set of n points in d-space.
As corollaries, we obtain improved real RAM algorithms and decision trees for the two problems. In particular, they can be solved by algebraic decision trees of near-linear height.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol181-isaac2020/LIPIcs.ISAAC.2020.32/LIPIcs.ISAAC.2020.32.pdf
Geometric pattern matching
k-SUM problem
Linear decision trees