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Searching 2D-Strings for Matching Frames

Authors Itai Boneh , Dvir Fried , Shay Golan , Matan Kraus , Adrian Miclăuş , Arseny Shur

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Author Details

Itai Boneh
  • Reichman University, Herzliya, Israel
  • University of Haifa, Israel
Dvir Fried
  • Bar Ilan University, Ramat Gan, Israel
Shay Golan
  • Reichman University, Herzliya, Israel
  • University of Haifa, Israel
Matan Kraus
  • Bar Ilan University, Ramat Gan, Israel
Adrian Miclăuş
  • Faculty of Mathematics and Computer Science, University of Bucharest, Romania
Arseny Shur
  • Bar Ilan University, Ramat Gan, Israel

Funding

  • Boneh, Itai: supported by Israel Science Foundation grant 810/21.
  • Fried, Dvir: supported by ISF grant no. 1926/19, by a BSF grant 2018364, and by an ERC grant MPM under the EU’s Horizon 2020 Research and Innovation Programme (grant no. 683064).
  • Golan, Shay: supported by Israel Science Foundation grant 810/21.
  • Kraus, Matan: supported by the ISF grant no. 1926/19, by the BSF grant 2018364, and by the ERC grant MPM under the EU’s Horizon 2020 Research and Innovation Programme (grant no. 683064).
  • Miclăuş, Adrian: supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS - UEFISCDI, project number PN-III-P1-1.1-TE-2021-0253, within PNCDI III.
  • Shur, Arseny: supported by the ERC grant MPM under the EU’s Horizon 2020 Research and Innovation Programme (grant no. 683064) and by the State of Israel through the Center for Absorption in Science of the Ministry of Aliyah and Immigration.

Cite AsGet BibTex

Itai Boneh, Dvir Fried, Shay Golan, Matan Kraus, Adrian Miclăuş, and Arseny Shur. Searching 2D-Strings for Matching Frames. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CPM.2024.10

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(n^{2.5}) time (assuming n ≥ m). The second algorithm finds a (1-ε)-approximate solution in Õ((nm)/ε⁴) 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • 2D string
  • matching frame
  • LCP
  • multidimensional range query

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