TY - GEN

T1 - Small candidate set for translational pattern search

AU - Huang, Ziyun

AU - Feng, Qilong

AU - Wang, Jianxin

AU - Xu, Jinhui

N1 - Funding Information:
The research of the first and last authors was supported in part by NSF through grant CCF-1716400. The research of the last author was also supported by NSF through grant IIS-1910492. The research of the second and third authors was supported in part by NSFC through grants 61872450, 61828205, and 61672536.
Funding Information:
Funding The research of the first and last authors was supported in part by NSF through grant CCF-1716400. The research of the last author was also supported by NSF through grant IIS-1910492. The research of the second and third authors was supported in part by NSFC through grants 61872450, 61828205, and 61672536.

PY - 2019/12

Y1 - 2019/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85076373477&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85076373477&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ISAAC.2019.26

DO - 10.4230/LIPIcs.ISAAC.2019.26

M3 - Conference contribution

AN - SCOPUS:85076373477

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 30th International Symposium on Algorithms and Computation, ISAAC 2019

A2 - Lu, Pinyan

A2 - Zhang, Guochuan

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 30th International Symposium on Algorithms and Computation, ISAAC 2019

Y2 - 8 December 2019 through 11 December 2019

ER -