Abstract
We study a natural type of repetitions in 2-dimensional strings. Such a repetition, called a matching frame, is a rectangular substring of size at least 2 × 2 with equal marginal rows and equal marginal columns. Matching frames first appeared in literature in the context of Wang tiles. We present two algorithms finding a matching frame with the maximum perimeter in a given n×m input string. The first algorithm solves the problem exactly in Õ(n2.5) time (assuming n ≥ m). The second algorithm finds a (1 − ε)-approximate solution in Õ(nmε4 ) time, which is near linear in the size of the input for constant ε. In particular, by setting ε = O(1) the second algorithm decides the existence of a matching frame in a given string in Õ(nm) time. Some technical elements and structural properties used in these algorithms can be of independent interest.
Original language | English |
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Title of host publication | 35th Annual Symposium on Combinatorial Pattern Matching, CPM 2024 |
Editors | Shunsuke Inenaga, Simon J. Puglisi |
Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
ISBN (Electronic) | 9783959773263 |
DOIs | |
State | Published - Jun 2024 |
Event | 35th Annual Symposium on Combinatorial Pattern Matching, CPM 2024 - Fukuoka, Japan Duration: 25 Jun 2024 → 27 Jun 2024 |
Publication series
Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 296 |
ISSN (Print) | 1868-8969 |
Conference
Conference | 35th Annual Symposium on Combinatorial Pattern Matching, CPM 2024 |
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Country/Territory | Japan |
City | Fukuoka |
Period | 25/06/24 → 27/06/24 |
Bibliographical note
Publisher Copyright:© Itai Boneh, Dvir Fried, Shay Golan, Matan Kraus, Adrian Miclăuş, and Arseny Shur.
Keywords
- 2D string
- LCP
- matching frame
- multidimensional range query