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In this paper, we study decentralized empirical risk minimization problems, where the goal is to minimize a finite-sum of smooth and strongly-convex functions available over a network of nodes. In this Part I, we propose…
In scheduling and timetabling applications, the mutual-exclusion constraint stipulates that certain pairs of tasks that cannot be executed at the same time. This corresponds to the vertex colouring problem in graph theory, for which there…
Quantum optimization as a field has largely been restricted by the constraints of current quantum computing hardware, as limitations on size, performance, and fidelity mean most non-trivial problem instances won't fit on quantum devices.…
The goal of multi-task learning is to enable more efficient learning than single task learning by sharing model structures for a diverse set of tasks. A standard multi-task learning objective is to minimize the average loss across all…
Graph machine learning has been extensively studied in both academia and industry. However, in the literature, most existing graph machine learning models are designed to conduct training with data samples in a random order, which may…
Graph partitioning schedules parallel calculations like sparse matrix-vector multiply (SpMV). We consider contiguous partitions, where the $m$ rows (or columns) of a sparse matrix with $N$ nonzeros are split into $K$ parts without…
Graph planning gives rise to fundamental algorithmic questions such as shortest path, traveling salesman problem, etc. A classical problem in discrete planning is to consider a weighted graph and construct a path that maximizes the sum of…
Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…
In recent years, finding new satisfiability algorithms for various circuit classes has been a very active line of research. Despite considerable progress, we are still far away from a definite answer on which circuit classes allow fast…
In the classical facility location problem we consider a graph $G$ with fixed weights on the edges of $G$. The goal is then to find an optimal positioning for a set of facilities on the graph with respect to some objective function. We…
With the recent proliferation of large-scale learning problems,there have been a lot of interest on distributed machine learning algorithms, particularly those that are based on stochastic gradient descent (SGD) and its variants. However,…
Generalized from the concept of consensus, this paper considers a group of edge agreements, i.e. constraints defined for neighboring agents, in which each pair of neighboring agents is required to satisfy one edge agreement constraint. Edge…
The convergence of SGD based distributed training algorithms is tied to the data distribution across workers. Standard partitioning techniques try to achieve equal-sized partitions with per-class population distribution in proportion to the…
We study the problem of executing an application represented by a precedence task graph on a parallel machine composed of standard computing cores and accelerators. Contrary to most existing approaches, we distinguish the allocation and the…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…
Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used in machine learning over homogeneous graphs. In heterogeneous graphs such as knowledge graphs, however, sparsification has not been systematically…
The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. In this paper, we engineer the fastest known exact algorithm for the problem.…
We study how we can accelerate the spreading of information in temporal graphs via shifting operations; a problem that captures real-world applications varying from information flows to distribution schedules. In a temporal graph there is a…
An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…