Related papers: A Minimum Doubly Resolving Set and Strong Resolvin…
Chemical graph theory is commonly used to analyse and comprehend chemical structures and networks, as well as their features. The resolvability parameters for graph $G$= $(V,E)$ are a relatively new advanced field in which the complete…
In this paper, we consider the minimal doubly resolving set problem in Hamming graphs, hypercubes and folded hypercubes. We prove that the minimal doubly resolving set problem in hypercubes is equivalent to the coin weighing problem. Then…
Crystal Structure Prediction (csp) is one of the central and most challenging problems in materials science and computational chemistry. In csp, the goal is to find a configuration of ions in 3D space that yields the lowest potential…
We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…
This paper considers coresets for the robust $k$-medians problem with $m$ outliers, and new constructions in various metric spaces are obtained. Specifically, for metric spaces with a bounded VC or doubling dimension $d$, the coreset size…
An ordered set $S$ of vertices of a graph $G$ is a resolving set for $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The metric dimension of G is the minimum cardinality of a resolving set. In…
A resolving set for a graph $G$ is a set of vertices $Q = \{q_1, ..., q_k\}$ such that, for all $p\in V(G)$ the $k$-tuple $(d(p, q_1), ..., d(p, q_k ))$ uniquely determines $p$, where $d(p, q_i)$ is considered as the minimum length of a…
In this paper we study some cube packing problems. In particular we are interested in compact subsets of $\mathbb{R}^n,n\geq 2$, which contain boundaries of cubes with all side lengths in $(0,1)$. We show here that such sets must have lower…
We introduce and study Minimum Cut Representability, a framework to solve optimization and feasibility problems over stable matchings by representing them as minimum s-t cut problems on digraphs over rotations. We provide necessary and…
In this paper, we present an ultra lightweight system that can effectively recognize different circuit components in an image with very limited training data. Along with the system, we also release the data set we created for the task. A…
This paper addresses problems on the robust structural design of complex networks. More precisely, we address the problem of deploying the minimum number of dedicated sensors, i.e., those measuring a single state variable, that ensure the…
The widely used crystal structures for both heptazine-based and triazine-based two-dimensional (2D) graphitic carbon nitride (g-C$_3$N$_4$) are the flat P-6m2 configurations. However, the experimentally synthesized 2D g-C$_3$N$_4$ possess…
Strong blocking sets and their counterparts, minimal codes, attracted lots of attention in the last years. Combining the concatenating construction of codes with a geometric insight into the minimality condition, we explicitly provide…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
What is the minimal information that a robot must retain to achieve its task? To design economical robots, the literature dealing with reduction of combinatorial filters approaches this problem algorithmically. As lossless state compression…
Crystal structures are indispensable across various domains, from batteries to solar cells, and extensive research has been dedicated to predicting their properties based on their atomic configurations. However, prevailing Crystal Structure…
A novel canonical duality theory (CDT) is presented for solving general bilevel mixed integer nonlinear optimization governed by linear and quadratic knapsack problems. It shows that the challenging knapsack problems can be solved…
This paper aims at investigating the contractibility of the solution sets for set optimization problems by utilizing strictly quasi cone-convexlikeness, which is an assumption weaker than strictly cone-convexity, strictly…
We consider cylindrical algebraic decompositions (CADs) as a tool for representing semi-algebraic subsets of $\mathbb{R}^n$. In this framework, a CAD $\mathscr{C}$ is adapted to a given set $S$ if $S$ is a union of cells of $\mathscr{C}$.…
In sphere of research of discrete optimization algorithms efficiency the important place occupies a method of polynomial reducibility of some problems to others with use of special purpose components. In this paper a novel method of compact…