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We propose new succinct representations of ordinal trees, which have been studied extensively. It is known that any $n$-node static tree can be represented in $2n + o(n)$ bits and a number of operations on the tree can be supported in…
We study the problem of recognizing regular languages in a variant of the streaming model of computation, called the sliding window model. In this model, we are given a size of the sliding window $n$ and a stream of symbols. At each time…
The palindromic fingerprint of a string $S[1\ldots n]$ is the set $PF(S) = \{(i,j)~|~ S[i\ldots j] \textit{ is a maximal }\\ \textit{palindrome substring of } S\}$. In this work, we consider the problem of string reconstruction from a…
We propose a new linear-size data structure which provides a fast access to all palindromic substrings of a string or a set of strings. This structure inherits some ideas from the construction of both the suffix trie and suffix tree. Using…
The Longest Common Substring (LCS) and Longest Palindromic Substring (LPS) are classical problems in computer science, representing fundamental challenges in string processing. Both problems can be solved in linear time using a classical…
We present an improved wavelet tree construction algorithm and discuss its applications to a number of rank/select problems for integer keys and strings. Given a string of length n over an alphabet of size $\sigma\leq n$, our method builds…
Let $S$ be a string of length $n$ over an alphabet $\Sigma$ and let $Q$ be a subset of $\Sigma$ of size $q \geq 2$. The 'co-occurrence problem' is to construct a compact data structure that supports the following query: given an integer $w$…
A string is said to be closed if its length is one, or if it has a non-empty factor that occurs both as a prefix and as a suffix of the string, but does not occur elsewhere. The notion of closed words was introduced by [Fici, WORDS 2011].…
In binary jumbled pattern matching we wish to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of size $i$ and has exactly $j$ 1-bits. The problem naturally generalizes to…
A palindrome is a string that reads the same forward and backward. A palindromic substring $P$ of a string $S$ is called a shortest unique palindromic substring ($\mathit{SUPS}$) for an interval $[x, y]$ in $S$, if $P$ occurs exactly once…
Palindromes are non-empty strings that read the same forward and backward. The problem of recognizing strings that can be represented as the concatenation of even-length palindromes, the concatenation of palindromes of length at least two,…
Suppose an oracle knows a string $S$ that is unknown to us and that we want to determine. The oracle can answer queries of the form "Is $s$ a substring of $S$?". In 1995, Skiena and Sundaram showed that, in the worst case, any algorithm…
We extend the multi-pass streaming model to sliding window problems, and address the problem of computing order statistics on fixed-size sliding windows, in the multi-pass streaming model as well as the closely related communication…
In grammar-based compression a string is represented by a context-free grammar, also called a straight-line program (SLP), that generates only that string. We refine a recent balancing result stating that one can transform an SLP of size…
Given a string $s$ of length $n$ over a general alphabet and an integer $k$, the problem is to decide whether $s$ is a concatenation of $k$ nonempty palindromes. Two previously known solutions for this problem work in time $O(kn)$ and…
We revisit two well-known algorithmic problems on strings: computing a shortest unique substring (SUS) and a shortest absent substring (SAS) of a string $S$ of length $n$. Both problems admit folklore $\mathcal{O}(n)$-time solutions using…
Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the…
Given two rooted, ordered, and labeled trees $P$ and $T$ the tree inclusion problem is to determine if $P$ can be obtained from $T$ by deleting nodes in $T$. This problem has recently been recognized as an important query primitive in XML…
In the classic longest common substring (LCS) problem, we are given two strings $S$ and $T$, each of length at most $n$, over an alphabet of size $\sigma$, and we are asked to find a longest string occurring as a fragment of both $S$ and…
We show that the problem of constructing tree-structured descriptions of data layouts that are optimal with respect to space or other criteria from given sequences of displacements, can be solved in polynomial time. The problem is relevant…