Related papers: Data structures for computing unique palindromes i…
Repeat finding in strings has important applications in subfields such as computational biology. Surprisingly, all prior work on repeat finding did not consider the constraint on the locality of repeats. In this paper, we propose and study…
A palindrome is a string that reads the same as its reverse, such as "aibohphobia" (fear of palindromes). Given an integer $d>0$, a $d$-near-palindrome is a string of Hamming distance at most $d$ from its reverse. We study the natural…
Let $\mathcal{D}$ be a collection of $D$ documents, which are strings over an alphabet of size $\sigma$, of total length $n$. We describe a data structure that uses linear space and and reports $k$ most relevant documents that contain a…
Given an array of distinct integers $A[1\ldots n]$, the Range Minimum Query (RMQ) problem requires us to construct a data structure from $A$, supporting the RMQ query: given an interval $[a,b]\subseteq[1,n]$, return the index of the minimum…
The text-to-pattern Hamming distances problem asks to compute the Hamming distances between a given pattern of length $m$ and all length-$m$ substrings of a given text of length $n\ge m$. We focus on the $k$-mismatch version of the problem,…
We devise a data structure that can answer shortest path queries for two query points in a polygonal domain $P$ on $n$ vertices. For any $\varepsilon > 0$, the space complexity of the data structure is $O(n^{10+\varepsilon })$ and queries…
Motivated by mass-spectrometry protein sequencing, we consider a simply-stated problem of reconstructing a string from the multiset of its substring compositions. We show that all strings of length 7, one less than a prime, or one less than…
Bille and G{\o}rtz (2011) recently introduced the problem of substring range counting, for which we are asked to store compactly a string $S$ of $n$ characters with integer labels in ([0, u]), such that later, given an interval ([a, b]) and…
In the Shortest Superstring problem we are given a set of strings $S=\{s_1, \ldots, s_n\}$ and integer $\ell$ and the question is to decide whether there is a superstring $s$ of length at most $\ell$ containing all strings of $S$ as…
Given a string $S$ of length $N$ on a fixed alphabet of $\sigma$ symbols, a grammar compressor produces a context-free grammar $G$ of size $n$ that generates $S$ and only $S$. In this paper we describe data structures to support the…
We consider several types of internal queries, that is, questions about fragments of a given text $T$ specified in constant space by their locations in $T$. Our main result is an optimal data structure for Internal Pattern Matching (IPM)…
Given an $n$-vertex planar embedded digraph $G$ with non-negative edge weights and a face $f$ of $G$, Klein presented a data structure with $O(n\log n)$ space and preprocessing time which can answer any query $(u,v)$ for the shortest path…
Makespan scheduling on identical machines is one of the most basic and fundamental packing problems studied in the discrete optimization literature. It asks for an assignment of $n$ jobs to a set of $m$ identical machines that minimizes the…
The Binary Jumbled String Matching problem is defined as: Given a string $s$ over $\{a,b\}$ of length $n$ and a query $(x,y)$, with $x,y$ non-negative integers, decide whether $s$ has a substring $t$ with exactly $x$ $a$'s and $y$ $b$'s.…
Analyzing patterns in data streams generated by network traffic, sensor networks, or satellite feeds is a challenge for systems in which the available storage is limited. In addition, real data is noisy, which makes designing data stream…
We consider the \textsf{Unit Interval Selection} problem in the one-pass random order streaming model. Here, an algorithm is presented a sequence of $n$ unit-length intervals on the line that arrive in uniform random order, and the…
Squares (fragments of the form $xx$, for some string $x$) are arguably the most natural type of repetition in strings. The basic algorithmic question concerning squares is to check if a given string of length $n$ is square-free, that is,…
We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that…
We present the first $\mathrm{o}(n)$-space polynomial-time algorithm for computing the length of a longest common subsequence. Given two strings of length $n$, the algorithm runs in $\mathrm{O}(n^{3})$ time with $\mathrm{O}\left(\frac{n…
Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…