离散数学
This manuscript describes the notions of blocker and interdiction applied to well-known optimization problems. The main interest of these two concepts is the capability to analyze the existence of a combinatorial structure after some…
The network-based study of financial systems has received considerable attention in recent years but has seldom explicitly incorporated the dynamic aspects of such systems. We consider this problem setting from the temporal point of view…
The growing need for sustainable logistics solutions has led to the evolution of vehicle routing problems (VRPs) into more complex variants that address modern challenges. Among these, the Two-Echelon Electric Vehicle Routing Problem…
In this work, we extend the concept of Robinson spaces to asymmetric dissimilarities, enhancing their applicability in representing and analyzing complex data. Within this generalized framework, we introduce two different problems that…
Scarf's algorithm--a pivoting procedure that finds a dominating extreme point in a down-monotone polytope--can be used to show the existence of a fractional stable matching in hypergraphs. The problem of finding a fractional stable matching…
Seventy years on, Moessner's theorem and Moessner's process -- i.e., the additive computation of integral powers -- continue to fascinate. They have given rise to a variety of elegant proofs, to an implementation in hardware, to…
The broadcast model is widely used to describe the process of information dissemination from a single node to all nodes within an interconnected network. In this model, a graph represents the network, where vertices correspond to nodes and…
Motivated by applications to monotonicity testing, Lehman and Ron (JCTA, 2001) proved the existence of a collection of vertex disjoint paths between comparable sub-level sets in the directed hypercube. The main technical contribution of…
Closeness is an important measure of network centrality. In this article we will calculate the closeness of graphs, created by using operations on graphs. We will prove a formula for the closeness of shadow graphs. We will calculate the…
Multi-objective unconstrained combinatorial optimization problems (MUCO) are in general hard to solve, i.e., the corresponding decision problem is NP-hard and the outcome set is intractable. In this paper we explore special cases of MUCO…
An integer linear system (ILS) is a linear system with integer constraints. The solution graph of an ILS is defined as an undirected graph defined on the set of feasible solutions to the ILS. A pair of feasible solutions is connected by an…
In Concentrated Solar Power (CSP) plants based on Parabolic Trough Collectors (PTC), the Sun is tracked at discrete time intervals, with each interval representing a movement of the collector system. The act of moving heavy mechanical…
The sum of the absolute values of the Fourier coefficients of a function $f:\mathbb{F}_2^n \to \mathbb{R}$ is called the spectral norm of $f$. Green and Sanders' quantitative version of Cohen's idempotent theorem states that if the spectral…
We study the lift-and-project rank of the stable set polytopes of graphs with respect to the Lov\'{a}sz--Schrijver SDP operator $\text{LS}_+$, with a particular focus on finding and characterizing the smallest graphs with a given…
Immersion minor is an important variant of graph minor, defined through an injective mapping from vertices in a smaller graph $H$ to vertices in a larger graph $G$ where adjacent elements of the former are connected in the latter by…
Dillon-like Boolean functions are known, in the literature, to be those trace polynomial functions from $\mathbb{F}_{2^{2n}}$ to $\mathbb{F}_{2}$, with all the exponents being multiples of $2^n-1$ often called Dillon-like exponents. This…
Emerging applications such as autonomous driving pose the challenge of efficient cost-driven offloading in edge-cloud environments. This involves assigning tasks to edge and cloud servers for separate execution, with the goal of minimizing…
Constructing a suitable schedule for sports competitions is a crucial issue in sports scheduling. The round-robin tournament is a competition adopted in many professional sports. For most round-robin tournaments, it is considered…
Complex systems frequently exhibit multi-way, rather than pairwise, interactions. These group interactions cannot be faithfully modeled as collections of pairwise interactions using graphs and instead require hypergraphs. However, methods…
We introduce and analyze a natural game formulated as follows. In this one-person game, the player is given a random permutation $A=(a_1,\dots, a_n)$ of a multiset $M$ of $n$ reals that sum up to $0$, where each of the $n!$ permutation…