Small Candidate Set for Translational Pattern Search

Authors Ziyun Huang, Qilong Feng, Jianxin Wang, Jinhui Xu

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Ziyun Huang
  • Department of Computer Science and Software Engineering, Penn State Erie, The Behrend College, Erie, PA, USA
Qilong Feng
  • School of Computer Science and Engineering, Central South University, P.R. China
Jianxin Wang
  • School of Computer Science and Engineering, Central South University, P.R. China
Jinhui Xu
  • Department of Computer Science and Engineering, State University of New York at Buffalo, USA

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Ziyun Huang, Qilong Feng, Jianxin Wang, and Jinhui Xu. Small Candidate Set for Translational Pattern Search. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


In this paper, we study the following pattern search problem: Given a pair of point sets A and B in fixed dimensional space R^d, 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 B' 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 B'. We present a novel algorithm to produce a small set of candidate translations for the pattern search problem. For any B' subseteq B with |B'| = |A|, there exists at least one translation T in the candidate set such that the minimum bipartite matching cost between T(A) and B' is no larger than (1+epsilon) times the minimum bipartite matching cost between A and B' 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 log^2 n) in O(n log^2 n) time with high probability of success. As a by-product of our construction, we obtain a weak epsilon-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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
  • Theory of computation
  • Bipartite matching
  • Alignment
  • Discretization
  • Approximate algorithm


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