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Given a pattern string $P$ of length $n$ and a query string $T$ of length $m$, where the characters of $P$ and $T$ are drawn from an alphabet of size $\Delta$, the {\em exact string matching} problem consists of finding all occurrences of…
Longest Increasing Subsequence (LIS) is a fundamental statistic of a sequence, and has been studied for decades. While the LIS of a sequence of length $n$ can be computed exactly in time $O(n\log n)$, the complexity of estimating the…
Given the vast reservoirs of data stored worldwide, efficient mining of data from a large information store has emerged as a great challenge. Many databases like that of intrusion detection systems, web-click records, player statistics,…
Given a set of pattern strings $\mathcal{P}=\{P_1, P_2,\ldots P_k\}$ and a text string $S$, the classic dictionary matching problem is to report all occurrences of each pattern in $S$. We study the dictionary problem in the compressed…
The net frequency (NF) of a string, of length $m$, in a text, of length $n$, is the number of occurrences of the string in the text with unique left and right extensions. Recently, Guo et al. [CPM 2024] showed that NF is combinatorially…
In this paper we revisit the classical regular expression matching problem, namely, given a regular expression $R$ and a string $Q$, decide if $Q$ matches one of the strings specified by $R$. Let $m$ and $n$ be the length of $R$ and $Q$,…
We study the problem of cutting a length-$n$ string of positive real numbers into $k$ pieces so that every piece has sum at least $b$. The problem can also be phrased as transforming such a string into a new one by merging adjacent numbers.…
A substring Q of a string S is called a shortest unique substring (SUS) for interval [s,t] in S, if Q occurs exactly once in S, this occurrence of Q contains interval [s,t], and every substring of S which contains interval [s,t] and is…
The maximal sum of a sequence "A" of "n" real numbers is the greatest sum of all elements of any strictly contiguous and possibly empty subsequence of "A", and it can be computed in "O(n)" time by means of Kadane's algorithm. Letting "A^(x…
We study the problem of estimating the size of a maximum matching in sublinear time. The problem has been studied extensively in the literature and various algorithms and lower bounds are known for it. Our result is a $0.5109$-approximation…
Palindromes are important objects in strings which have been extensively studied from combinatorial, algorithmic, and bioinformatics points of views. It is known that the length of the longest palindromic substrings (LPSs) of a given string…
The problem of finding a longest common subsequence of two main sequences with some constraint that must be a substring of the result (STR-IC-LCS) was formulated recently. It is a variant of the constrained longest common subsequence…
The Longest Common Subsequence (LCS) is the problem of finding a subsequence among a set of strings that has two properties of being common to all and is the longest. The LCS has applications in computational biology and text editing, among…
Given two random finite sequences from $[k]^n$ such that a prefix of the first sequence is a suffix of the second, we examine the length of their longest common subsequence. If $\ell$ is the length of the overlap, we prove that the expected…
The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…
We study an abstract optimization problem arising from biomolecular sequence analysis. For a sequence A of pairs (a_i,w_i) for i = 1,..,n and w_i>0, a segment A(i,j) is a consecutive subsequence of A starting with index i and ending with…
Encoding data structures store enough information to answer the queries they are meant to support but not enough to recover their underlying datasets. In this paper we give the first encoding data structure for the challenging problem of…
For a string $S$, a palindromic substring $S[i..j]$ is said to be a \emph{shortest unique palindromic substring} ($\mathit{SUPS}$) for an interval $[s, t]$ in $S$, if $S[i..j]$ occurs exactly once in $S$, the interval $[i, j]$ contains $[s,…
Longest Common Subsequence ($LCS$) deals with the problem of measuring similarity of two strings. While this problem has been analyzed for decades, the recent interest stems from a practical observation that considering single characters is…
We describe a RAM algorithm computing all runs (maximal repetitions) of a given string of length $n$ over a general ordered alphabet in $O(n\log^{\frac{2}3} n)$ time and linear space. Our algorithm outperforms all known solutions working in…