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Spectral clustering is a powerful unsupervised machine learning algorithm for clustering data with non convex or nested structures. With roots in graph theory, it uses the spectral properties of the Laplacian matrix to project the data in a…
This paper considers the problem of distributed optimization over time-varying graphs. For the case of undirected graphs, we introduce a distributed algorithm, referred to as DIGing, based on a combination of a distributed inexact gradient…
We present a collection of new results on problems related to 3SUM, including: 1. The first truly subquadratic algorithm for $\ \ \ \ \ $ 1a. computing the (min,+) convolution for monotone increasing sequences with integer values bounded by…
This paper is about conceptual modeling of aggregates in software engineering. An aggregate is a cluster of domain objects that can be treated as a single unit. In UML, an aggregation is a type of association in which objects are configured…
Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…
A distributed algorithm is described for finding a common fixed point of a family of $m>1$ nonlinear maps $M_i : \mathbb{R}^n \rightarrow \mathbb{R}^n$ assuming that each map is a paracontraction and that such a common fixed point exists.…
Answer Set Programming (ASP) is a well-known problem-solving formalism in computational logic. Nowadays, ASP is used in many real world scenarios thanks to ASP solvers. Standard evaluation of ASP programs suffers from an intrinsic…
An existing approach for dealing with massive data sets is to stream over the input in few passes and perform computations with sublinear resources. This method does not work for truly massive data where even making a single pass over the…
This paper focuses on the discrimination capacity of aggregation functions: these are the permutation invariant functions used by graph neural networks to combine the features of nodes. Realizing that the most powerful aggregation functions…
We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum $\sum_{i=1}^{m}f_i(z)$ of functions over in a network. We provide complexity bounds for four different…
Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the…
Overplotting of data points is a common problem when visualizing large datasets in a scatterplot, particularly when mapping nominal dimensions to one of the scatterplot axes. Transparency, aggregation, and jittering have previously been…
Ordinal Embedding places n objects into R^d based on comparisons such as "a is closer to b than c." Current optimization-based approaches suffer from scalability problems and an abundance of low quality local optima. We instead consider a…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…
Rank aggregation seeks a representative permutation for a collection of rankings and plays a central role in areas such as social choice, information retrieval, and computational biology. Two fundamental aggregation tasks are the center and…
Over the past decade, there has been increasing interest in distributed/parallel algorithms for processing large-scale graphs. By now, we have quite fast algorithms -- usually sublogarithmic-time and often $poly(\log\log n)$-time, or even…
A dominating set $S$ of graph $G$ is called an $r$-grouped dominating set if $S$ can be partitioned into $S_1,S_2,\ldots,S_k$ such that the size of each unit $S_i$ is $r$ and the subgraph of $G$ induced by $S_i$ is connected. The concept of…
Approximating Subset Sum is a classic and fundamental problem in computer science and mathematical optimization. The state-of-the-art approximation scheme for Subset Sum computes a $(1-\varepsilon)$-approximation in time…