Small candidate set for translational pattern search

Ziyun Huang, Qilong Feng, Jianxin Wang, Jinhui Xu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we study the following pattern search problem: Given a pair of point sets A and B in fixed dimensional space Rd, with |B| = n, |A| = m and n ≥ m, the pattern search problem is to find the translations T 's of A such that each of the identified translations induces a matching between T (A) and a subset B0 of B with cost no more than some given threshold, where the cost is defined as the minimum bipartite matching cost of T (A) and B0. We present a novel algorithm to produce a small set of candidate translations for the pattern search problem. For any B0 ⊆ B with |B0| = |A|, there exists at least one translation T in the candidate set such that the minimum bipartite matching cost between T (A) and B0 is no larger than (1 + ε) times the minimum bipartite matching cost between A and B0 under any translation (i.e., the optimal translational matching cost). We also show that there exists an alternative solution to this problem, which constructs a candidate set of size O(n log2 n) in O(n log2 n) time with high probability of success. As a by-product of our construction, we obtain a weak ε-net for hypercube ranges, which significantly improves the construction time and the size of the candidate set. Our technique can be applied to a number of applications, including the translational pattern matching problem.

Original languageEnglish (US)
Title of host publication30th International Symposium on Algorithms and Computation, ISAAC 2019
EditorsPinyan Lu, Guochuan Zhang
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771306
DOIs
Publication statusPublished - Dec 2019
Event30th International Symposium on Algorithms and Computation, ISAAC 2019 - Shanghai, China
Duration: Dec 8 2019Dec 11 2019

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume149
ISSN (Print)1868-8969

Conference

Conference30th International Symposium on Algorithms and Computation, ISAAC 2019
CountryChina
CityShanghai
Period12/8/1912/11/19

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All Science Journal Classification (ASJC) codes

  • Software

Cite this

Huang, Z., Feng, Q., Wang, J., & Xu, J. (2019). Small candidate set for translational pattern search. In P. Lu, & G. Zhang (Eds.), 30th International Symposium on Algorithms and Computation, ISAAC 2019 [26] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 149). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ISAAC.2019.26