Geometric Pattern Matching Reduces to k-SUM

03/26/2020
by   Boris Aronov, et al.
0

We prove that some exact geometric pattern matching problems reduce in linear time to 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/05/2023

Inapproximability of sufficient reasons for decision trees

In this note, we establish the hardness of approximation of the problem ...
research
08/01/2018

Geometric Fingerprint Recognition via Oriented Point-Set Pattern Matching

Motivated by the problem of fingerprint matching, we present geometric a...
research
11/20/2019

Geometric Planar Networks on Bichromatic Points

We study four classical graph problems – Hamiltonian path, Traveling sal...
research
11/05/2021

Hopcroft's Problem, Log-Star Shaving, 2D Fractional Cascading, and Decision Trees

We revisit Hopcroft's problem and related fundamental problems about geo...
research
11/30/2006

Lossless fitness inheritance in genetic algorithms for decision trees

When genetic algorithms are used to evolve decision trees, key tree qual...
research
09/15/2021

Subquadratic Algorithms for Some 3Sum-Hard Geometric Problems in the Algebraic Decision Tree Model

We present subquadratic algorithms in the algebraic decision-tree model ...
research
08/11/2022

Diamonds are Forever in the Blockchain: Geometric Polyhedral Point-Set Pattern Matching

Motivated by blockchain technology for supply-chain tracing of ethically...

Please sign up or login with your details

Forgot password? Click here to reset