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We establish new results concerning projectors on max-plus spaces, as well as separating half-spaces, and derive an explicit formula for the distance in Hilbert's projective metric between a point and a half-space over the max-plus…

This paper is a survey on universal algorithms for solving the matrix Bellman equations over semirings and especially tropical and idempotent semirings. However, original algorithms are also presented. Some applications and software…

We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus…

Finding the longest common subsequence in $k$-length substrings (LCS$k$) is a recently proposed problem motivated by computational biology. This is a generalization of the well-known LCS problem in which matching symbols from two sequences…

It is well-known that the graph isomorphism problem can be posed as an equivalent problem of determining whether an auxiliary graph structure contains a clique of specific order. However, the algorithms that have been developed so far for…

Given a graph $G=(V,E)$, the longest induced path problem asks for a maximum cardinality node subset $W\subseteq V$ such that the graph induced by $W$ is a path. It is a long established problem with applications, e.g., in network analysis.…

A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoint matrix.

In this paper we introduce min-plus low rank matrix approximation. By using min and plus rather than plus and times as the basic operations in the matrix multiplication; min-plus low rank matrix approximation is able to detect…

We present MADAM, a parallel semidefinite based exact solver for Max-Cut, a problem of finding the cut with maximum weight in a given graph. The algorithm uses branch and bound paradigm that applies alternating direction method of…

In this paper, we study linear programming based approaches to the maximum matching problem in the semi-streaming model. The semi-streaming model has gained attention as a model for processing massive graphs as the importance of such graphs…

A multidimensional extremal problem in the idempotent algebra setting is considered which consists in minimizing a nonlinear functional defined on a finite-dimensional semimodule over an idempotent semifield. The problem integrates two…

An approach to schedule development in project management is developed within the framework of idempotent algebra. The approach offers a way to represent precedence relationships among activities in projects as linear vector equations in…

In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal…

Algorithms for embedding certain types of nilpotent subalgebras in maximal subalgebras of the same type are developed, using methods of real algebraic groups. These algorithms are applied to determine non-conjugate subalgebras of the…

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…

Frequent pattern mining is widely used to find ``important'' or ``interesting'' patterns in data. While it is not easy to mathematically define such patterns, maximal frequent patterns are promising candidates, as frequency is a natural…

Much effort has been directed at algorithms for obtaining the highest probability configuration in a probabilistic random field model known as the maximum a posteriori (MAP) inference problem. In many situations, one could benefit from…

Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of…

We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm,…