Related papers: Nearly Optimal Internal Dictionary Matching
The order preserving pattern matching (OPPM) problem is, given a pattern string $p$ and a text string $t$, find all substrings of $t$ which have the same relative orders as $p$. In this paper, we consider two variants of the OPPM problem…
In this work, we present a literature review for full-text and keyword indexes as well as our contributions (which are mostly practice-oriented). The first contribution is the FM-bloated index, which is a modification of the well-known…
Binary jumbled pattern matching asks to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of length $i$ and has exactly $j$ 1-bits. This problem naturally generalizes to…
Finding dense subgraphs is a fundamental problem with applications to community detection, clustering, and data mining. Our work focuses on finding approximate densest subgraphs in directed graphs in computational models for processing…
An elastic-degenerate (ED) string is a sequence of $n$ sets of strings of total length $N$, which was recently proposed to model a set of similar sequences. The ED string matching (EDSM) problem is to find all occurrences of a pattern of…
We establish nearly optimal upper and lower bounds for approximating decision tree splits in data streams. For regression with labels in the range $\{0,1,\ldots,M\}$, we give a one-pass algorithm using $\tilde{O}(M^2/\epsilon)$ space that…
The circular dictionary matching problem is an extension of the classical dictionary matching problem where every string in the dictionary is interpreted as a circular string: after reading the last character of a string, we can move back…
In a graph $G$ with a source $s$, we design a distance oracle that can answer the following query: Query$(s,t,e)$ -- find the length of shortest path from a fixed source $s$ to any destination vertex $t$ while avoiding any edge $e$. We…
The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently…
In this paper, we consider a generalized longest common subsequence problem with multiple substring inclusive constraints. For the two input sequences $X$ and $Y$ of lengths $n$ and $m$, and a set of $d$ constraints $P=\{P_1,\cdots,P_d\}$…
In this paper we define a new problem, motivated by computational biology, $LCSk$ aiming at finding the maximal number of $k$ length $substrings$, matching in both input strings while preserving their order of appearance. The traditional…
This paper studies parallel algorithms for the longest increasing subsequence (LIS) problem. Let $n$ be the input size and $k$ be the LIS length of the input. Sequentially, LIS is a simple problem that can be solved using dynamic…
A fundamental problem arising in many applications in Web science and social network analysis is, given an arbitrary approximation factor $c>1$, to output a set $S$ of nodes that with high probability contains all nodes of PageRank at least…
We consider the problem of finding \textit{semi-matching} in bipartite graphs which is also extensively studied under various names in the scheduling literature. We give faster algorithms for both weighted and unweighted case. For the…
In the $k$-Edit Circular Pattern Matching ($k$-Edit CPM) problem, we are given a length-$n$ text $T$, a length-$m$ pattern $P$, and a positive integer threshold $k$, and we are to report all starting positions of the substrings of $T$ that…
We study dynamic algorithms for the longest increasing subsequence (\textsf{LIS}) problem. A dynamic \textsf{LIS} algorithm maintains a sequence subject to operations of the following form arriving one by one: (i) insert an element, (ii)…
The circuit-level implementation of a quantum string-matching algorithm, which matches a search string (pattern) of length $M$ inside a longer text of length $N$, has already been demonstrated in the literature to outperform its classical…
We consider the problem of querying a string (or, a database) of length $N$ bits to determine all the locations where a substring (query) of length $M$ appears either exactly or is within a Hamming distance of $K$ from the query. We assume…
Given a string $T$ of length $n$ over an alphabet $\Sigma\subset \{1,2,\ldots,n^{O(1)}\}$ of size $\sigma$, we are to preprocess $T$ so that given a range $[i,j]$, we can return a representation of a shortest string over $\Sigma$ that is…
Fully indexable dictionaries (FID) store sets of integer keys while supporting rank/select queries. They serve as basic building blocks in many succinct data structures. Despite the great importance of FIDs, no known FID is succinct with…