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In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
Identifying clusters of similar objects in data plays a significant role in a wide range of applications. As a model problem for clustering, we consider the densest k-disjoint-clique problem, whose goal is to identify the collection of k…
Astroparticle experiments such as IceCube or MAGIC require a deconvolution of their measured data with respect to the response function of the detector to provide the distributions of interest, e.g. energy spectra. In this paper,…
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…
Vertex cover is one of the classical NP-complete problems in theoretical computer science. A vertex cover of a graph is a subset of vertices such that for each edge at least one of the two endpoints is contained in the subset. When studied…
In this paper we consider clustering problems in which each point is endowed with a color. The goal is to cluster the points to minimize the classical clustering cost but with the additional constraint that no color is over-represented in…
This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages…
The 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…
Following the success of convolution on non-Euclidean space, the corresponding pooling approaches have also been validated on various tasks regarding graphs. However, because of the fixed compression quota and stepwise pooling design, these…
Spectral clustering and its extensions usually consist of two steps: (1) constructing a graph and computing the relaxed solution; (2) discretizing relaxed solutions. Although the former has been extensively investigated, the discretization…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
The assembly of molecular networks into structures such as random tilings and glasses has recently been demonstrated for a number of two-dimensional systems. These structures are dynamically-arrested on experimental timescales so the…
In this article, we discuss the numerical solution of diffusion equations on random surfaces within the isogeometric framework. We describe in detail, how diffusion problems on random surfaces can be modelled and how quantities of interest…
Motivated by a geometric problem, we introduce a new non-convex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. A relaxed formulation is identified…
We study the structure of the solution space and behavior of local search methods on random 3-SAT problems close to the SAT/UNSAT transition. Using the overlap measure of similarity between different solutions found on the same problem…
The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy…
Document clustering is an unsupervised approach in which a large collection of documents (corpus) is subdivided into smaller, meaningful, identifiable, and verifiable sub-groups (clusters). Meaningful representation of documents and…
Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…
Sampling-based decoding underlies complex reasoning in large language models (LLMs), where decoding strategies critically shape model behavior. Temperature- and truncation-based methods reshape the next-token distribution through global…
We present a new algorithm for determining the satisfiability of conjunctions of non-linear polynomial constraints over the reals, which can be used as a theory solver for satisfiability modulo theory (SMT) solving for non-linear real…