Related papers: Indexed Dynamic Programming to boost Edit Distance…
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…
In this paper we introduce a dynamic programming algorithm to perform linear text segmentation by global minimization of a segmentation cost function which consists of: (a) within-segment word similarity and (b) prior information about…
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…
We consider the problem of maintaining a collection of strings while efficiently supporting splits and concatenations on them, as well as comparing two substrings, and computing the longest common prefix between two suffixes. This problem…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
We revisit a fundamental problem in string matching: given a pattern of length m and a text of length n, both over an alphabet of size $\sigma$, compute the Hamming distance between the pattern and the text at every location. Several…
The problem of computing the edit-distance between a string and a finite automaton arises in a variety of applications in computational biology, text processing, and speech recognition. This paper presents linear-space algorithms for…
In this paper, we describe a new type of match between a pattern and a text that aren't necessarily maximal in the query, but still contain useful matching information: locally maximal exact matches (LEMs). There are usually a large amount…
Integer programs with m constraints are solvable in pseudo-polynomial time in $\Delta$, the largest coefficient in a constraint, when m is a fixed constant. We give a new algorithm with a running time of $O(\sqrt{m}\Delta)^{2m} + O(nm)$,…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
The constrained LCS problem asks one to find a longest common subsequence of two input strings $A$ and $B$ with some constraints. The STR-IC-LCS problem is a variant of the constrained LCS problem, where the solution must include a given…
Finding the largest code with a given minimum distance is one of the most basic problems in coding theory. In this paper, we study the linear programming bound for codes in the Lee metric. We introduce refinements on the linear programming…
Suffix arrays and LCP arrays are one of the most fundamental data structures widely used for various kinds of string processing. We consider two problems for a read-only string of length $N$ over an integer alphabet $[1, \dots, \sigma]$ for…
Here we study the complexity of string problems as a function of the size of a program that generates input. We consider straight-line programs (SLP), since all algorithms on SLP-generated strings could be applied to processing…
The dynamic matrix inverse problem is to maintain the inverse of a matrix undergoing element and column updates. It is the main subroutine behind the best algorithms for many dynamic problems whose complexity is not yet well-understood,…
Recently we presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with $o(mn)$ total update time, where $m$ is the number of edges and $n$ is the…
We study approximation algorithms for variants of the \emph{median string} problem, which asks for a string that minimizes the sum of edit distances from a given set of $m$ strings of length $n$. Only the straightforward $2$-approximation…
Dynamic diversification---finding a set of data points with maximum diversity from a time-dependent sample pool---is an important task in recommender systems, web search, database search, and notification services, to avoid showing users…
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 propose two novel numerical schemes for approximate implementation of the dynamic programming~(DP) operation concerned with finite-horizon, optimal control of discrete-time systems with input-affine dynamics. The proposed algorithms…