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The longest common substring problem consists in finding a longest string that appears as a (contiguous) substring of two input strings. We consider the dynamic variant of this problem, in which we are to maintain two dynamic strings $S$…
Compression is beneficial because it helps detract resource usage. It reduces data storage space as well as transmission traffic and improves web pages loading. Run-length coding (RLC) is a lossless data compression algorithm. Data are…
A string matching -- and more generally, sequence matching -- algorithm is presented that has a linear worst-case computing time bound, a low worst-case bound on the number of comparisons (2n), and sublinear average-case behavior that is…
In this paper, we propose a novel method, aggregation cross-entropy (ACE), for sequence recognition from a brand new perspective. The ACE loss function exhibits competitive performance to CTC and the attention mechanism, with much quicker…
We investigate the longest common substring problem for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the…
Let $X_1, X_2, ..., X_s$ and $Y_1, Y_2, ..., Y_t$ be strings over an alphabet $\Sigma$, where $s$ and $t$ are positive integers. The longest common subsequence and substring problem for multiple strings $X_1, X_2, ..., X_s$ and $Y_1, Y_2,…
The Longest Common Subsequence (LCS) problem is a very important problem in math- ematics, which has a broad application in scheduling problems, physics and bioinformatics. It is known that the given two random sequences of infinite…
Approximate spectral clustering (ASC) was developed to overcome heavy computational demands of spectral clustering (SC). It maintains SC ability in predicting non-convex clusters. Since it involves a preprocessing step, ASC defines new…
Compressed indexing is a powerful technique that enables efficient querying over data stored in compressed form, significantly reducing memory usage and often accelerating computation. While extensive progress has been made for…
We present novel randomized approximation schemes for the Edit Distance (ED) problem and the Longest Common Subsequence (LCS) problem that, for any constant $\epsilon>0$, compute a $(1+\epsilon)$-approximation for ED and a…
Computing string or sequence alignments is a classical method of comparing strings and has applications in many areas of computing, such as signal processing and bioinformatics. Semi-local string alignment is a recent generalisation of this…
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…
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…
Recent techniques such as retrieval-augmented generation or chain-of-thought reasoning have led to longer contexts and increased inference costs. Context compression techniques can reduce these costs, but the most effective approaches…
Given a string $T$ of length $n$, a substring $u = T[i..j]$ of $T$ is called a shortest unique substring (SUS) for an interval $[s,t]$ if (a) $u$ occurs exactly once in $T$, (b) $u$ contains the interval $[s,t]$ (i.e. $i \leq s \leq t \leq…
One-bit compressed sensing (1bCS) addresses the recovery of sparse signals from highly quantized measurements, retaining only the sign of each linear measurement. In the support recovery setting, the goal is to identify $\text{supp}(x)$,…
This study investigates whether reoptimization can help in solving the closest substring problem. We are dealing with the following reoptimization scenario. Suppose, we have an optimal l-length closest substring of a given set of sequences…
We revisit the exact shortest unique substring (SUS) finding problem, and propose its approximate version where mismatches are allowed, due to its applications in subfields such as computational biology. We design a generic in-place…
In the first part of the paper, we present an (1+\mu)-approximation algorithm to the minimum-spanning tree of points in a planar arrangement of lines, where the metric is the number of crossings between the spanning tree and the lines. The…
Remote sensing (RS) involves the acquisition of data about objects or areas from a distance, primarily to monitor environmental changes, manage resources, and support planning and disaster response. A significant challenge in RS…