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Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…
A large body of work has investigated the properties of graph neural networks and identified several limitations, particularly pertaining to their expressive power. Their inability to count certain patterns (e.g., cycles) in a graph lies at…
We propose here a number of approaches to implement constraint propagation for arithmetic constraints on integer intervals. To this end we introduce integer interval arithmetic. Each approach is explained using appropriate proof rules that…
Commutativity has the same inherent limitations as compatibility. Then, it is worth conceiving simple concurrency control techniques. We propose a restricted form of commutativity which increases parallelism without incurring a higher…
Exponentiating the hypergeometric series gives a recursion relation for integer sequences which are generalizations of conventional Bell numbers. The corresponding associated Stirling numbers of the second kind are also generated and…
We introduce several new constructions of finite posets with the number of linear extensions given by generalized continued fractions. We apply our results to the problem of the minimum number of elements needed for a poset with a given…
Given a primitive collection of vectors in the integer lattice, we count the number of ways it can be extended to a basis by vectors with sup-norm bounded by $T$, producing an asymptotic estimate as $T \to \infty$. This problem can be…
The study of minimal complements in a group or a semigroup was initiated by Nathanson. The notion of minimal complements and being a minimal complement leads to the notion of co-minimal pairs which was considered in a prior work of the…
Recent advances in computer architecture and networking opened the opportunity for parallelizing the clustering algorithms. This divide-and-conquer strategy often results in better results to centralized clustering with a much-improved time…
Integer iteration rules such as n |-> {a n + b, c n +d} are studied as minimal examples of the general process of multicomputation. Despite the simplicity of such rules, their multiway graphs can be complex, exhibiting, for example,…
Mixed-integer mathematical programs are among the most commonly used models for a wide set of problems in Operations Research and related fields. However, there is still very little known about what can be expressed by small mixed-integer…
We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also consider a random interval partial order on $n$ elements,…
The unprecedented performance achieved by deep convolutional neural networks for image classification is linked primarily to their ability of capturing rich structural features at various layers within networks. Here we design a series of…
We conduct a systematic study of asynchronous models of distributed computing consisting of identical finite-state devices that cooperate in a network to decide if the network satisfies a given graph-theoretical property. Models discussed…
The encoding representation of the genetic algorithm can boost or hinder its performance albeit the care one can devote to operator design. Unfortunately, a representation-theory foundation that helps to find the suitable encoding for any…
The work in this article is concerned with two different types of families of finite sets: separating families and splitting families (they are also called "systems"). These families have applications in combinatorial search, coding theory,…
We investigate the computational complexity of minimizing the source side-effect in order to remove a given number of tuples from the output of a conjunctive query. This is a variant of the well-studied {\em deletion propagation} problem,…
Diophantine tuples are of ancient and modern interest, with a huge literature. In this paper we study Diophantine graphs, i.e., finite graphs whose vertices are distinct positive integers, and two vertices are linked by an edge if and only…
There are enormous amount of examples of Computation in nature, exemplified across multiple species in biology. One crucial aim for these computations across all life forms their ability to learn and thereby increase the chance of their…
In this paper we study the algebra of graph invariants, focusing mainly on the invariants of simple graphs. All other invariants, such as sorted eigenvalues, degree sequences and canonical permutations, belong to this algebra. In fact,…