### Abstract

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^{0} 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^{0}. We present a novel algorithm to produce a small set of candidate translations for the pattern search problem. For any B^{0} ⊆ B with |B^{0}| = |A|, there exists at least one translation T in the candidate set such that the minimum bipartite matching cost between T (A) and B^{0} is no larger than (1 + ε) times the minimum bipartite matching cost between A and B^{0} 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 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 language | English (US) |
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Title of host publication | 30th International Symposium on Algorithms and Computation, ISAAC 2019 |

Editors | Pinyan Lu, Guochuan Zhang |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959771306 |

DOIs | |

Publication status | Published - Dec 2019 |

Event | 30th International Symposium on Algorithms and Computation, ISAAC 2019 - Shanghai, China Duration: Dec 8 2019 → Dec 11 2019 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 149 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 30th International Symposium on Algorithms and Computation, ISAAC 2019 |
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Country | China |

City | Shanghai |

Period | 12/8/19 → 12/11/19 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software

### Cite this

*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