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Title: On a Two-Dimensional Search Problem
Authors: Kolev, Emil
Landgev, Ivan
Keywords: Two-Dimensional Search Problem
Issue Date: 1995
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 21, No 3, (1995), 219p-230p
Abstract: In this article we explore the so-called two-dimensional tree− search problem. We prove that for integers m of the form m = (2^(st) − 1)/(2^s − 1) the rectangles A(m, n) are all tight, no matter what n is. On the other hand, we prove that there exist infinitely many integers m for which there is an infinite number of n’s such that A(m, n) is loose. Furthermore, we determine the smallest loose rectangle as well as the smallest loose square (A(181, 181)). It is still undecided whether there exist infinitely many loose squares.
ISSN: 1310-6600
Appears in Collections:Volume 21 Number 3

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