@inproceedings{8e0a6ec5ad4448b784cb9417ba8fb456,
title = "Searching 2D-Strings for Matching Frames",
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 {\~O}(n2.5) time (assuming n ≥ m). The second algorithm finds a (1 − ε)-approximate solution in {\~O}(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 {\~O}(nm) time. Some technical elements and structural properties used in these algorithms can be of independent interest.",
keywords = "2D string, LCP, matching frame, multidimensional range query",
author = "Itai Boneh and Dvir Fried and Shay Golan and Matan Kraus and Adrian Micl{\u a}u{\c s} and Arseny Shur",
note = "Publisher Copyright: {\textcopyright} Itai Boneh, Dvir Fried, Shay Golan, Matan Kraus, Adrian Micl{\u a}u{\c s}, and Arseny Shur.; 35th Annual Symposium on Combinatorial Pattern Matching, CPM 2024 ; Conference date: 25-06-2024 Through 27-06-2024",
year = "2024",
month = jun,
doi = "10.4230/LIPIcs.CPM.2024.10",
language = "אנגלית",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Shunsuke Inenaga and Puglisi, \{Simon J.\}",
booktitle = "35th Annual Symposium on Combinatorial Pattern Matching, CPM 2024",
address = "גרמניה",
}