Related papers: Approximating solution structure of the Weighted S…
While alignment of texts on the sentential level is often seen as being too coarse, and word alignment as being too fine-grained, bi- or multilingual texts which are aligned on a level in-between are a useful resource for many purposes.…
In process mining, alignments quantify the degree of deviation between an observed event trace and a business process model and constitute the most important conformance checking technique. We study the algorithmic complexity of computing…
Consensus problems for strings and sequences appear in numerous application contexts, ranging from bioinformatics over data mining to machine learning. Closing some gaps in the literature, we show that several fundamental problems in this…
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…
String consensus problems aim at finding a string that minimizes some given distance with respect to an input set of strings. In particular, in the Closest string problem, we are given a set of strings of equal length and a radius $d$. The…
Alignments, i.e., position-wise comparisons of two or more strings or ordered lists are of utmost practical importance in computational biology and a host of other fields, including historical linguistics and emerging areas of research in…
It is well known that sparse approximation problem is \textsf{NP}-hard under general dictionaries. Several algorithms have been devised and analyzed in the past decade under various assumptions on the \emph{coherence} $\mu$ of the…
Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
We study a geometric representation problem, where we are given a set $\cal R$ of axis-aligned rectangles with fixed dimensions and a graph with vertex set $\cal R$. The task is to place the rectangles without overlap such that two…
We present a new efficient method for approximate search in electronic lexica. Given an input string (the pattern) and a similarity threshold, the algorithm retrieves all entries of the lexicon that are sufficiently similar to the pattern.…
We consider the problem of evaluation of the weight enumerator of a binary linear code. We show that the exact evaluation is hard for polynomial hierarchy. More exactly, if WE is an oracle answering the solution of the evaluation problem…
An NP-hard combinatorial optimization problem $\Pi$ is said to have an {\em approximation threshold} if there is some $t$ such that the optimal value of $\Pi$ can be approximated in polynomial time within a ratio of $t$, and it is NP-hard…
Semantic textual similarity is one of the open research challenges in the field of Natural Language Processing. Extensive research has been carried out in this field and near-perfect results are achieved by recent transformer-based models…
The hitting set problem is a well-known NP-hard optimization problem in which, given a set of elements and a collection of subsets, the goal is to find the smallest selection of elements, such that each subset contains at least one element…
In this paper we provide an approximation \`a la Ambrosio-Tortorelli of some classical minimization problems involving the length of an unknown one-dimensional set, with an additional connectedness constraint, in dimension two. We introduce…
We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis…
Large language models (LLMs) that fluently converse with humans are a reality - but do LLMs experience human-like processing difficulties? We systematically compare human and LLM sentence comprehension across seven challenging linguistic…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…
Text-to-pattern distance is a fundamental problem in string matching, where given a pattern of length $m$ and a text of length $n$, over an integer alphabet, we are asked to compute the distance between pattern and the text at every…