Searching 2D-Strings for Matching Frames
Itai Boneh, Dvir Fried, Shay Golan, Matan Kraus, Adrian Miclaus, and, Arseny Shur

TL;DR
This paper introduces algorithms for finding maximum perimeter matching frames in 2D strings, including an exact algorithm with $ ilde{O}(n^{2.5})$ complexity and a near-linear approximation, along with new structural insights.
Contribution
The paper presents the first algorithms for maximum perimeter matching frames in 2D strings, including an exact and a near-linear approximation method, with novel structural properties.
Findings
Exact algorithm with $ ilde{O}(n^{2.5})$ complexity
Near-linear $(1- ext{epsilon})$-approximation algorithm
Introduction of new structural properties of 2D strings
Abstract
We introduce the natural notion of a matching frame in a -dimensional string. A matching frame in a -dimensional string , is a rectangle such that the strings written on the horizontal sides of the rectangle are identical, and so are the strings written on the vertical sides of the rectangle. Formally, a matching frame in is a tuple such that and . In this paper, we present an algorithm for finding the maximum perimeter matching frame in a matrix in time (assuming . Additionally, for every constant we present a near-linear -approximation algorithm for the maximum perimeter of a matching frame. In the development of the aforementioned algorithms, we introduce inventive technical elements and uncover distinctive structural…
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