Related papers: Longest Common Extension of a Dynamic String in Pa…
Longest common subsequence ($\mathsf{LCS}$) is a classic and central problem in combinatorial optimization. While $\mathsf{LCS}$ admits a quadratic time solution, recent evidence suggests that solving the problem may be impossible in truly…
Dynamic sequences with varying lengths have been widely used in the training of Transformer-based large language models (LLMs). However, current training frameworks adopt a pre-defined static parallel strategy for these sequences, causing…
A repetition free Longest Common Subsequence (LCS) of two sequences x and y is an LCS of x and y where each symbol may appear at most once. Let R denote the length of a repetition free LCS of two sequences of n symbols each one chosen…
The similarity between a pair of time series, i.e., sequences of indexed values in time order, is often estimated by the dynamic time warping (DTW) distance, instead of any in the well-studied family of measures including the longest common…
In this paper we consider the problem of computing the longest common abelian factor (LCAF) between two given strings. We present a simple $O(\sigma~ n^2)$ time algorithm, where $n$ is the length of the strings and $\sigma$ is the alphabet…
We present a parallel algorithm (EREW PRAM algorithm) for linked lists contraction. We show that when we contract a linked list from size $n$ to size $n/c$ for a suitable constant $c$ we can pack the linked list into an array of size $n/d$…
The 2-LCPS problem, first introduced by Chowdhury et al. [Fundam. Inform., 129(4):329-340, 2014], asks one to compute (the length of) a longest palindromic common subsequence between two given strings $A$ and $B$. We show that the 2-LCPS…
We prove that longest common prefix (LCP) information can be stored in much less space than previously known. More precisely, we show that in the presence of the text and the suffix array, o(n) additional bits are sufficient to answer…
We consider the classic problem of computing the Longest Common Subsequence (LCS) of two strings of length $n$. While a simple quadratic algorithm has been known for the problem for more than 40 years, no faster algorithm has been found…
When augmented with the longest common prefix (LCP) array and some other structures, the suffix array can solve many string processing problems in optimal time and space. A compressed representation of the LCP array is also one of the main…
Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. In the last two…
Approximating the length of the longest increasing sequence (LIS) of an array is a well-studied problem. We study this problem in the data stream model, where the algorithm is allowed to make a single left-to-right pass through the array…
The problem of aligning two strings A,B in order to determine their similarity is fundamental in the field of pattern matching. An important concept in this domain is the "all scores matrix" that encodes the local alignment comparison of…
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…
For a text given in advance, the substring minimal suffix queries ask to determine the lexicographically minimal non-empty suffix of a substring specified by the location of its occurrence in the text. We develop a data structure answering…
Covers are a kind of quasiperiodicity in strings. A string $C$ is a cover of another string $T$ if any position of $T$ is inside some occurrence of $C$ in $T$. The shortest and longest cover arrays of $T$ have the lengths of the shortest…
In many applications, it is necessary to determine the string similarity. Edit distance[WF74] approach is a classic method to determine Field Similarity. A well known dynamic programming algorithm [GUS97] is used to calculate edit distance…
We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology…
Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in $O(n \log n)$ time and space. Our goal in this paper is to reduce the space consumption while…
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…