Related papers: Distributed Quantum Advantage for Local Problems
Efficient computation of graph diffusion equations (GDEs), such as Personalized PageRank, Katz centrality, and the Heat kernel, is crucial for clustering, training neural networks, and many other graph-related problems. Standard iterative…
We consider graph coloring and related problems in the distributed message-passing model. {Locally-iterative algorithms} are especially important in this setting. These are algorithms in which each vertex decides about its next color only…
Local SGD is a popular optimization method in distributed learning, often outperforming other algorithms in practice, including mini-batch SGD. Despite this success, theoretically proving the dominance of local SGD in settings with…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
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…
(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…
We provide a new constant factor approximation algorithm for the (connected) distance-$r$ dominating set problem on graph classes of bounded expansion. Classes of bounded expansion include many familiar classes of sparse graphs such as…
We investigate the distributed complexity of maximal matching and maximal independent set (MIS) in hypergraphs in the LOCAL model. A maximal matching of a hypergraph $H=(V_H,E_H)$ is a maximal disjoint set $M\subseteq E_H$ of hyperedges and…
Optimization problems become fundamentally challenging as the number of variables increases. Because the volume of the search space grows exponentially, classical algorithms frequently fail to locate the global minimum of non-convex…
Distributed graph algorithms that separately optimize for either the number of rounds used or the total number of messages sent have been studied extensively. However, algorithms simultaneously efficient with respect to both measures have…
The congested clique model is a message-passing model of distributed computation where the underlying communication network is the complete graph of $n$ nodes. In this paper we consider the situation where the joint input to the nodes is an…
The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a…
Common definitions of the "standard" LOCAL model tend to be sloppy and even self-contradictory on one point: do the nodes update their state using an arbitrary function or a computable function? So far, this distinction has been safe to…
A natural operational paradigm for distributed quantum and classical information processing involves local operations coordinated by multiple rounds of public communication. In this paper we consider the minimum number of communication…
Distributed optimization for resource allocation problems is investigated and a sub-optimal continuous-time algorithm is proposed. Our algorithm has lower order dynamics than others to reduce burdens of computation and communication, and is…
This paper gives the first separation of quantum and classical pure (i.e., non-cryptographic) computing abilities with no restriction on the amount of available computing resources, by considering the exact solvability of a celebrated…
Vizing showed that it suffices to color the edges of a simple graph using $\Delta + 1$ colors, where $\Delta$ is the maximum degree of the graph. However, up to this date, no efficient distributed edge-coloring algorithms are known for…
We propose a Greedy strategy to solve the problem of Graph Cut, called GGC. It starts from the state where each data sample is regarded as a cluster and dynamically merges the two clusters which reduces the value of the global objective…
We give deterministic distributed $(1+\epsilon)$-approximation algorithms for Minimum Vertex Coloring and Maximum Independent Set on chordal graphs in the LOCAL model. Our coloring algorithm runs in $O(\frac{1}{\epsilon} \log n)$ rounds,…
Local thresholding algorithms were first presented more than a decade ago and have since been applied to a variety of data mining tasks in peer-to-peer systems, wireless sensor networks, and in grid systems. One critical assumption made by…