Related papers: Longest Square Subsequence Problem Revisited

A fundamental problem in shape matching and geometric similarity is computing the maximum area overlap between two polygons under translation. For general simple polygons, the best-known algorithm runs in $O((nm)^2 \log(nm))$ time [Mount,…

The Shortest Common Superstring problem (SCS) consists, for a set of strings S = {s_1,...,s_n}, in finding a minimum length string that contains all s_i, 1<= i <= n, as substrings. While a 2+11/30 approximation ratio algorithm has recently…

Real-world data often comes in compressed form. Analyzing compressed data directly (without decompressing it) can save space and time by orders of magnitude. In this work, we focus on fundamental sequence comparison problems and try to…

The convolution between a text string $S$ of length $N$ and a pattern string $P$ of length $m$ can be computed in $O(N \log m)$ time by FFT. It is known that various types of approximate string matching problems are reducible to…

Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence…

Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the…

Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with…

We present an algorithm for computing the Lyndon factorization of a string that is given in grammar compressed form, namely, a Straight Line Program (SLP). The algorithm runs in $O(n^4 + mn^3h)$ time and $O(n^2)$ space, where $m$ is the…

Separable nonlinear least squares (SNLS)problem is a special class of nonlinear least squares (NLS)problems, whose objective function is a mixture of linear and nonlinear functions. It has many applications in many different areas,…

Given a string $S$ of $n$ symbols, a longest common extension query $\mathsf{LCE}(i,j)$ asks for the length of the longest common prefix of the $i$th and $j$th suffixes of $S$. LCE queries have several important applications in string…

Palindromes are strings that read the same forward and backward. The computation of palindromic structures within strings is a fundamental problem in string algorithms, being motivated by potential applications in formal language theory and…

We study approximation algorithms for the following three string measures that are widely used in practice: edit distance (ED), longest common subsequence (LCS), and longest increasing sequence (LIS). All three problems can be solved…

Let $P$ be a simple polygon of $n$ vertices. We consider two-point $L_1$ shortest path queries in $P$. We build a data structure of $O(n)$ size in $O(n)$ time such that given any two query points $s$ and $t$, the length of an $L_1$ shortest…

Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…

The longest common extension problem is to preprocess a given string of length $n$ into a data structure that uses $S(n)$ bits on top of the input and answers in $T(n)$ time the queries $\mathit{LCE}(i,j)$ computing the length of the…

A longest common extension (LCE) query on a string computes the length of the longest common suffix or prefix at two given positions. A dynamic LCE algorithm maintains a data structure that allows efficient LCE queries on a string that can…

Given a sequence of n numbers, the Maximum Consecutive Subsums Problem (MCSP) asks for the maximum consecutive sum of lengths l for each l = 1,...,n. No algorithm is known for this problem which is significantly better than the naive…

We study algorithms for solving three problems on strings. The first one is the Most Frequently String Search Problem. The problem is the following. Assume that we have a sequence of $n$ strings of length $k$. The problem is finding the…

The palindromic tree (a.k.a. eertree) for a string $S$ of length $n$ is a tree-like data structure that represents the set of all distinct palindromic substrings of $S$, using $O(n)$ space [Rubinchik and Shur, 2018]. It is known that, when…

Geometric data structures have been extensively studied in the regime where the dimension is much smaller than the number of input points. But in many scenarios in Machine Learning, the dimension can be much higher than the number of points…