Related papers: Global preferential consistency for the topologica…
Many real-world problems require making sequences of decisions where the outcomes of each decision are probabilistic and uncertain, and the availability of different actions is constrained by the outcomes of previous actions. There is a…
Computing a Euclidean minimum spanning tree of a set of points is a seminal problem in computational geometry and geometric graph theory. We combine it with another classical problem in graph drawing, namely computing a monotone geometric…
In this work, we state a general conjecture on the solvability of optimization problems via algorithms with linear convergence guarantees. We make a first step towards examining its correctness by fully characterizing the problems that are…
The network reconfiguration problem seeks to find a rooted tree $T$ such that the energy of the (unique) feasible electrical flow over $T$ is minimized. The tree requirement on the support of the flow is motivated by operational constraints…
This paper considers a general data-fitting problem over a networked system, in which many computing nodes are connected by an undirected graph. This kind of problem can find many real-world applications and has been studied extensively in…
We are concerned with a new type of supermartingale decomposition in the Max-Plus algebra, which essentially consists in expressing any supermartingale of class $(\mathcal{D})$ as a conditional expectation of some running supremum process.…
Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…
This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable…
In this lecture we will consider the minimum weight spanning tree (MST) problem, i.e., one of the simplest and most vital combinatorial optimization problems. We will discuss a particular greedy algorithm that allows to compute a MST for…
One of the key research interests in the area of Constraint Satisfaction Problem (CSP) is to identify tractable classes of constraints and develop efficient solutions for them. In this paper, we introduce generalized staircase (GS)…
The problem of relevant and diverse subset selection has a wide range of applications, including recommender systems and retrieval-augmented generation (RAG). For example, in recommender systems, one is interested in selecting relevant…
Tasks in multi-task learning often correlate, conflict, or even compete with each other. As a result, a single solution that is optimal for all tasks rarely exists. Recent papers introduced the concept of Pareto optimality to this field and…
Providing an analytical solution for the problem of finding Fastest Distributed Consensus (FDC) is one of the challenging problems in the field of sensor networks. Here in this work we present analytical solution for the problem of fastest…
We study approaches for the exact solution of the \NP--hard minimum spanning tree problem under conflict constraints. Given a graph $G(V,E)$ and a set $C \subset E \times E$ of conflicting edge pairs, the problem consists of finding a…
In this work, we propose a new method for ordering nets during the process of layer assignment in global routing problems. The global routing problems that we focus on in this work are based on routing problems that occur in the design of…
We address the problem of configuring a power distribution network with reliability and resilience objectives by satisfying the demands of the consumers and saturating each production source as little as possible. We consider power…
The classical linear ordering problem seeks a single ranking representing a given preference matrix. While suitable for homogeneous populations, it fails when observed preferences arise from several latent groups with distinct ranking…
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
Solving optimization tasks based on functions and losses with a topological flavor is a very active, growing field of research in data science and Topological Data Analysis, with applications in non-convex optimization, statistics and…
A cut of a graph can be represented in many different ways. Here we propose to represent a cut through a ``relation tree'', which is a spanning tree with signed edges. We show that this picture helps to classify the main greedy heuristics…