离散数学

The third annual International Applied Category Theory Conference (ACT2020) was planned to take place at MIT in Cambridge, Massachusetts USA. However, the global COVID-19 pandemic made the prospect of holding a large in-person meeting…

A set of nonnegative matrices is called primitive if there exists a product of these matrices that is entrywise positive. Motivated by recent results relating synchronizing automata and primitive sets, we study the length of the shortest…

In this work we consider two two-criteria optimization problems: given an input graph, the goal is to find its interval (or chordal) supergraph that minimizes the number of edges and its clique number simultaneously. For the interval…

We study several problems of clearing subgraphs by mobile agents in digraphs. The agents can move only along directed walks of a digraph and, depending on the variant, their initial positions may be pre-specified. In general, for a given…

We study the shared processor scheduling problem with a single shared processor where a unit time saving (weight) obtained by processing a job on the shared processor depends on the job. A polynomial-time optimization algorithm has been…

We consider the following distributed pursuit-evasion problem. A team of mobile agents called searchers starts at an arbitrary node of an unknown $n$-node network. Their goal is to execute a search strategy that guarantees capturing a fast…

The main aim of decision support systems is to find solutions that satisfy user requirements. Often, this leads to predictability of those solutions, in the sense that having the input data and the model, an adversary or enemy can predict…

This paper introduces a problem in which the state of a system needs to be determined through costly tests of its components by a limited number of testing units and before a given deadline. We also consider a closely related search problem…

Unusually large prize pools in lotteries like Mega Millions and Powerball attract additional bettors, which increases the likelihood that multiple winners will have to share the pool. Thus, the expected value of a lottery ticket decreases…

The NC versus P-hard classification of the prediction problem for sandpiles on the two dimensional grid with von Neumann neighborhood is a famous open problem. In this paper we make two kinds of progresses, by studying its freezing variant.…

We study the problem of approximating the value of the matching polynomial on graphs with edge parameter $\gamma$, where $\gamma$ takes arbitrary values in the complex plane. When $\gamma$ is a positive real, Jerrum and Sinclair showed that…

Dempster-Shafer Theory (DST) generalizes Bayesian probability theory, offering useful additional information, but suffers from a much higher computational burden. A lot of work has been done to reduce the time complexity of information…

A majority of real life networks are weighted and sparse. The present article aims at characterization of weighted networks based on sparsity, as a measure of inherent diversity, of different network parameters. It utilizes sparsity index…

We present a new aperiodic tileset containing 11 Wang tiles on 4 colors, and we show that this tileset is minimal, in the sense that no Wang set with either fewer than 11 tiles or fewer than 4 colors is aperiodic. This gives a definitive…

A matrix is incomplete when some of its entries are missing. A Robinson incomplete symmetric matrix is an incomplete symmetric matrix whose non-missing entries do not decrease along rows and columns when moving toward the diagonal. A…

We consider the problem of devising algorithms to count exactly the number of independent sets of a graph G . We show that there is a polynomial time algorithm for this problem when G is restricted to the class of strongly orderable graphs,…

We introduce a variant of the well-studied sum choice number of graphs, which we call the interactive sum choice number. In this variant, we request colours to be added to the vertices' colour-lists one at a time, and so we are able to make…

This paper provides a short and transparent solution for the covering cost of white-grey trees which play a crucial role in the algorithm of Bergeron {\it et al.}\ to compute the rearrangement distance between two multichromosomal genomes…

Risk classification plays an important role in many regulations and standards. However, a general method that provides an optimal classification has not been proposed yet. Also, the criteria of optimality are not defined in these…

This paper aims to establish the theoretical foundation for shift inclusion in mathematical morphology. In this paper, we prove that the morphological opening and closing concerning structuring elements of shift inclusion property would…