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New algorithm for finding longest increasing subsequence is discussed. This algorithm is based on the ideas of idempotent mathematics and uses Max-Plus idempotent semiring. Problem of finding longest increasing sub- sequence is reformulated…
Machine scheduling problems involving conflict jobs can be seen as a constrained version of the classical scheduling problem, in which some jobs are conflict in the sense that they cannot be proceeded simultaneously on different machines.…
For a finite binary string $x$ its logical depth $d$ for significance $b$ is the shortest running time of a program for $x$ of length $K(x)+b$. There is another definition of logical depth. We give a new proof that the two versions are…
A set of n segments in the plane may form a Euclidean TSP tour, a tree, or a matching, among others. Optimal TSP tours as well as minimum spanning trees and perfect matchings have no crossing segments, but several heuristics and…
Suppose we want to seek the longest common subsequences (LCSs) of two strings as informative patterns that explain the relationship between the strings. The dynamic programming algorithm gives us a table from which all LCSs can be extracted…
The expected length of longest common subsequences is a problem that has been in the literature for at least twenty five years. Determining the limiting constants \gamma_k appears to be quite difficult, and the current best bounds leave…
Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.
We address the text-to-text generation problem of sentence-level paraphrasing -- a phenomenon distinct from and more difficult than word- or phrase-level paraphrasing. Our approach applies multiple-sequence alignment to sentences gathered…
Algorithms to find optimal alignments among strings, or to find a parsimonious summary of a collection of strings, are well studied in a variety of contexts, addressing a wide range of interesting applications. In this paper, we consider…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
At CPM 2017, Castelli et al. define and study a new variant of the Longest Common Subsequence Problem, termed the Longest Filled Common Subsequence Problem (LFCS). For the LFCS problem, the input consists of two strings $A$ and $B$ and a…
We study several variations of line segment covering problem with axis-parallel unit squares in $I\!\!R^2$. A set $S$ of $n$ line segments is given. The objective is to find the minimum number of axis-parallel unit squares which cover at…
We study the problem of cutting a length-$n$ string of positive real numbers into $k$ pieces so that every piece has sum at least $b$. The problem can also be phrased as transforming such a string into a new one by merging adjacent numbers.…
Consider an inhomogeneous Poisson process and let $D$ be the first of its epochs which is followed by a gap of size $\ell>0$. We establish a criterion for $D<\infty$ a.s., as well as for $D$ being long-tailed and short-tailed, and obtain…
A longest repeat query on a string, motivated by its applications in many subfields including computational biology, asks for the longest repetitive substring(s) covering a particular string position (point query). In this paper, we extend…
We consider the problem of finding a subgraph of a given graph which minimizes the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already when all functions are the same, we show that it…
This article aims to explain the Nested Benders algorithm for the solution of large-scale stochastic programming problems in a way that is intelligible to someone coming to it for the first time. In doing so it gives an explanation of…
We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
The forcing number of a graph with a perfect matching $M$ is the minimum number of edges in $M$ whose endpoints need to be deleted, such that the remaining graph only has a single perfect matching. This number is of great interest in…