A border of a string is a non-empty prefix of the string that is also a suffix of the string, and a string is unbordered if it has no border other than itself. Loptev, Kucherov, and Starikovskaya [CPM'15] conjectu...
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A border of a string is a non-empty prefix of the string that is also a suffix of the string, and a string is unbordered if it has no border other than itself. Loptev, Kucherov, and Starikovskaya [CPM'15] conjectured the following: If we pick a string of length n from a fixed non-unary alphabet uniformly at random, then the expected maximum length of its unbordered factors is n - O(1). We confirm this conjecture by proving that the expected value is, in fact, n - O(sigma(-1)), where sigma is the size of the alphabet. This immediately implies that we can find such a maximal unbordered factor in linear time on average. However, we go further and show that the optimum average-case running time is in Omega(root n) boolean AND O(,/n log(sigma) n) due to analogous bounds by Czumaj and G asieniec [CPM'00] for the problem of computing the shortest period of a uniformly random string. (C) 2020 Elsevier B.V. All rights reserved.
Given a textstring x of length n, the Minimal Augmented Suffix Tree (T) over cap (x) of x is a digital-search index that returns, for any query string w and in a number of comparisons bounded by the length of w, the m...
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Given a textstring x of length n, the Minimal Augmented Suffix Tree (T) over cap (x) of x is a digital-search index that returns, for any query string w and in a number of comparisons bounded by the length of w, the maximum number of nonoverlapping occurrences of w in x. It is shown that, denoting the length of x by n, (T) over cap (x) can be built in time O(n log(2) n) and space O(n log n), off-line on a RAM.
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