Related papers: On combinatorial optimization for dominating sets …
We use Sidon sets to present an elementary method to study some combinatorial problems in finite fields, such as sum product estimates, solubility of some equations and distribution of sequences in small intervals. We obtain classic and…
Given a dominating set, how much smaller a dominating set can we find through elementary operations? Here, we proceed by iterative vertex addition and removal while maintaining the property that the set forms a dominating set of bounded…
The article contains a preliminary glance at balanced clustering problems. Basic balanced structures and combinatorial balanced problems are briefly described. A special attention is targeted to various balance/unbalance indices (including…
A minimum dominating set for a digraph (directed graph) is a smallest set of vertices such that each vertex either belongs to this set or has at least one parent vertex in this set. We solve this hard combinatorial optimization problem…
This paper investigates a combinatorial optimization problem motived from a secure power network design application in [D\'{a}n and Sandberg 2010]. Two equivalent graph optimization formulations are derived. One of the formulations is a…
Minimum connected dominating set problem is an NP-hard combinatorial optimization problem in graph theory. Finding connected dominating set is of high interest in various domains such as wireless sensor networks, optical networks, and…
This is a survey of old and new problems and results in additive number theory.
How to observe the state of a network from a limited number of measurements has become an important issue in complex networks, engineering, communication, epidemiology, etc. Under some scenarios, it is neither unfeasible nor unnecessary to…
In this paper, we extend a previously presented Grover-based heuristic to tackle general combinatorial optimization problems with linear constraints. We further describe the introduced method as a framework that enables performance…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
The twenty-first century is a data-driven era where human activities and behavior, physical phenomena, scientific discoveries, technology advancements, and almost everything that happens in the world resulting in massive generation,…
In robust combinatorial optimization, we would like to find a solution that performs well under all realizations of an uncertainty set of possible parameter values. How we model this uncertainty set has a decisive influence on the…
Generalized entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…
In this paper, we study a number of well-known combinatorial optimization problems that fit in the following paradigm: the input is a collection of (potentially inconsistent) local relationships between the elements of a ground set (e.g.,…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
We survey recent results on combinatorial optimization problems in which the objective function is the entropy of a discrete distribution. These include the minimum entropy set cover, minimum entropy orientation, and minimum entropy…
This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…
The application of combinatorial optimization problems to solving the problems of planning processes for industries based on a fund of reconfigurable production resources is considered. The results of their solution by mixed integer…