Related papers: Restricted Common Superstring and Restricted Commo…
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 show that the following problem is NP-complete: Given an alphabet $\Sigma$ and two strings over $\Sigma$, the question is whether there exists a permutation of $\Sigma$ which is a subsequence of both of the given strings.
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 consider subsequences with gap constraints, i.e., length-k subsequences p that can be embedded into a string w such that the induced gaps (i.e., the factors of w between the positions to which p is mapped to) satisfy given gap…
The subset sum problem is one of the simplest and most fundamental NP-hard problems in combinatorial optimization. We consider two extensions of this problem: The subset sum problem with digraph constraint (SSG) and subset sum problem with…
Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the…
Let us call a sequence of numbers heapable if they can be sequentially inserted to form a binary tree with the heap property, where each insertion subsequent to the first occurs at a leaf of the tree, i.e. below a previously placed number.…
The most fundamental problem considered in algorithms for text processing is pattern matching: given a pattern $p$ of length $m$ and a text $t$ of length $n$, does $p$ occur in $t$? Multiple versions of this basic question have been…
The classic Resource Constrained Shortest Path (RCSP) problem aims to find a cost optimal path between a pair of nodes in a network such that the resources used in the path are within a given limit. Having been studied for over a decade,…
Motivated by applications in polymer-based data storage, we study the problem of reconstructing a string from part of its composition multiset. We give a full description of the structure of the strings that cannot be uniquely reconstructed…
Given a pattern string $P$ of length $n$ and a query string $T$ of length $m$, where the characters of $P$ and $T$ are drawn from an alphabet of size $\Delta$, the {\em exact string matching} problem consists of finding all occurrences of…
The problem of string reconstruction based on its substrings spectrum has received significant attention recently due to its applicability to DNA data storage and sequencing. In contrast to previous works, we consider in this paper a setup…
We address the satisfiability problem for string constraints that combine relational constraints represented by transducers, word equations, and string length constraints. This problem is undecidable in general. Therefore, we propose a new…
We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…
We study chance constrained optimization problems $\min_x f(x)$ s.t. $P(\left\{ \theta: g(x,\theta)\le 0 \right\})\ge 1-\epsilon$ where $\epsilon\in (0,1)$ is the violation probability, when the distribution $P$ is not known to the decision…
This note provides very simple, efficient algorithms for computing the number of distinct longest common subsequences of two input strings and for computing the number of LCS embeddings.
One of the most critical problems in the field of string algorithms is the longest common subsequence problem (LCS). The problem is NP-hard for an arbitrary number of strings but can be solved in polynomial time for a fixed number of…
Strings form a fundamental data type in computer systems. String searching has been extensively studied since the inception of computer science. Increasingly many applications have to deal with imprecise strings or strings with fuzzy…
This paper reformulates the problem of finding a longest common increasing subsequence of the two given input sequences in a very succinct way. An extremely simple linear space algorithm based on the new formula can find a longest common…
We consider the problem of efficiently designing sets (codes) of equal-length DNA strings (words) that satisfy certain combinatorial constraints. This problem has numerous motivations including DNA computing and DNA self-assembly. Previous…