相关论文: Relaxed Voronoi: a Simple Framework for Terminal-C…

Voronoi diagrams appear in many areas in science and technology and have numerous applications. They have been the subject of extensive investigation during the last decades. Roughly speaking, they are a certain decomposition of a given…

Community detection is a ubiquitous problem in applied network analysis, yet efficient techniques do not yet exist for all types of network data. Most techniques have been developed for undirected graphs, and very few exist that handle…

We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…

In the Euclidean Steiner Tree problem, we are given as input a set of points (called terminals) in the $\ell_2$-metric space and the goal is to find the minimum-cost tree connecting them. Additional points (called Steiner points) from the…

Minimization diagrams encompass a large class of diagrams of interest in the literature, such as generalized Voronoi diagrams. We develop an abstract perturbation theory and perform a sensitivity analysis for functions depending on sets…

This paper investigates the use of a sampling-based approach, the RRT*, to reconfigure a 2D set of connected tiles in complex environments, where multiple obstacles might be present. Since the target application is automated building of…

The Controlled Loosening-up (CLuP) mechanism that we recently introduced in \cite{Stojnicclupint19} is a generic concept that can be utilized to solve a large class of problems in polynomial time. Since it relies in its core on an iterative…

We study the problem of clustering $T$ trajectories of length $H$, each generated by one of K unknown ergodic Markov chains over a finite state space of size $S$. We derive an instance-dependent, high-probability lower bound on the…

In the Dominated Cluster Deletion problem, we are given an undirected graph $G$ and integers $k$ and $d$ and the question is to decide whether there exists a set of at most $k$ vertices whose removal results in a graph in which each…

Given a set of $n$ sites from $\mathbb{R}^d$, each having some positive weight factor, the Multiplicatively Weighted Voronoi Diagram is a subdivision of space that associates each cell to the site whose weighted Euclidean distance is…

Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…

Given a finite metric space $(X\cup Y, \mathbf{d})$ the $k$-median problem is to find a set of $k$ centers $C\subseteq Y$ that minimizes $\sum_{p\in X} \min_{c\in C} \mathbf{d}(p,c)$. In general metrics, the best polynomial time algorithm…

We propose a two-step algorithm for optimal controlled islanding that partitions a power grid into islands of limited volume while optimizing several criteria: high generator coherency inside islands, minimum power flow disruption due to…

Given a set $P$ of terminals in the plane and a partition of $P$ into $k$ subsets $P_1, ..., P_k$, a two-level rectilinear Steiner tree consists of a rectilinear Steiner tree $T_i$ connecting the terminals in each set $P_i$ ($i=1,...,k$)…

This paper continues our effort initiated in [9] to study Multicast Communication Networks, modeled as bilevel hierarchical clustering problems, by using mathematical optimization techniques. Given a finite number of nodes, we consider two…

We consider the problems ZERO EXTENSION and METRIC LABELLING under the paradigm of parameterized complexity. These are natural, well-studied problems with important applications, but have previously not received much attention from…

This paper presents Constrained Centroid Clustering (CCC), a method that extends classical centroid-based clustering by enforcing a constraint on the maximum distance between the cluster center and the farthest point in the cluster. Using a…

The Security-Constrained Unit Commitment (SCUC) problem presents formidable computational challenges due to its combinatorial complexity, large-scale network dimensions, and numerous security constraints. While conventional temporal…

Given a set of sites in a simple polygon, a geodesic Voronoi diagram of the sites partitions the polygon into regions based on distances to sites under the geodesic metric. We present algorithms for computing the geodesic nearest-point,…

The article addresses balanced clustering problems with an additional requirement as a tree-like structure over the obtained balanced clusters. This kind of clustering problems can be useful in some applications (e.g., network design,…