Related papers: Online algorithms for finding distinct substrings …
Packing several characters into one computer word is a simple and natural way to compress the representation of a string and to speed up its processing. Exploiting this idea, we propose an index for a packed string, based on a {\em sparse…
In this paper, we present and study the \emph{Hamming distance oracle problem}. In this problem, the task is to preprocess two strings $S$ and $T$ of lengths $n$ and $m$, respectively, to obtain a data-structure that is able to answer…
For a partial word $w$ the longest common compatible prefix of two positions $i,j$, denoted $lccp(i,j)$, is the largest $k$ such that $w[i,i+k-1]\uparrow w[j,j+k-1]$, where $\uparrow$ is the compatibility relation of partial words (it is…
We revisit various string indexing problems with range reporting features, namely, position-restricted substring searching, indexing substrings with gaps, and indexing substrings with intervals. We obtain the following main results.…
A predecessor (successor) search finds the largest element $x^-$ smaller than the input string $x$ (the smallest element $x^+$ larger than or equal to $x$, respectively) out of a given set $S$; in this paper, we consider the static case…
In this paper we describe a data structure that supports pattern matching queries on a dynamically arriving text over an alphabet ofconstant size. Each new symbol can be prepended to $T$ in O(1) worst-case time. At any moment, we can report…
In this paper, we consider the ``Shortest Superstring Problem''(SSP) or the ``Shortest Common Superstring Problem''(SCS). The problem is as follows. For a positive integer $n$, a sequence of n strings $S=(s^1,\dots,s^n)$ is given. We should…
Determining whether an unordered collection of overlapping substrings (called shingles) can be uniquely decoded into a consistent string is a problem that lies within the foundation of a broad assortment of disciplines ranging from…
We present parallel algorithms for exact and approximate pattern matching with suffix arrays, using a CREW-PRAM with $p$ processors. Given a static text of length $n$, we first show how to compute the suffix array interval of a given…
Longest common extension queries (often called longest common prefix queries) constitute a fundamental building block in multiple string algorithms, for example computing runs and approximate pattern matching. We show that a sequence of $q$…
The string indexing problem is a fundamental computational problem with numerous applications, including information retrieval and bioinformatics. It aims to efficiently solve the pattern matching problem: given a text T of length n for…
We show how to build several data structures of central importance to string processing, taking as input the Burrows-Wheeler transform (BWT) and using small extra working space. Let $n$ be the text length and $\sigma$ be the alphabet size.…
Finding an Approximate Longest Common Substring (ALCS) within a given set $S=\{s_1,s_2,\ldots,s_m\}$ of $m \ge 2$ strings is a key problem in computational biology, such as identifying related mutations across multiple genetic sequences. We…
Let $P$ be a set of $m$ points in ${\mathbb R}^2$, let $\Sigma$ be a set of $n$ semi-algebraic sets of constant complexity in ${\mathbb R}^2$, let $(S,+)$ be a semigroup, and let $w: P \rightarrow S$ be a weight function on the points of…
A substring $u$ of a string $T$ is called a minimal unique substring (MUS) of $T$ if $u$ occurs exactly once in $T$ and any proper substring of $u$ occurs at least twice in $T$. A string $w$ is called a minimal absent word (MAW) of $T$ if…
The size of the \textit{smallest suffixient set} of positions of a string recently emerged as a new measure of string \textit{repetitiveness} -- a measure reflecting how much of repetitive content the string contains. We study how to…
We consider a variation of the spectral sparsification problem where we are required to keep a subgraph of the original graph. Formally, given a union of two weighted graphs $G$ and $W$ and an integer $k$, we are asked to find a $k$-edge…
We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm,…
We initiate the study of sub-linear sketching and streaming techniques for estimating the output size of common dictionary compressors such as Lempel-Ziv '77, the run-length Burrows-Wheeler transform, and grammar compression. To this end,…
We consider the longest common subsequence (LCS) problem with the restriction that the common subsequence is required to consist of at least $k$ length substrings. First, we show an $O(mn)$ time algorithm for the problem which gives a…