Efficient Distributed Algorithms for Minimum Spanning Tree in Dense Graphs

In recent years, the Massively Parallel Computation (MPC) model capturing the MapReduce framework has become the de facto standard model for large-scale data analysis, given the ubiquity of efficient and affordable cloud implementations. In this model, an input of size m is initially distributed amo...

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Bibliographic Details
Published in:IEEE ... International Conference on Data Mining workshops pp. 777 - 786
Main Authors: Bateni, MohammadHossein, Monemzadeh, Morteza, Voorintholt, Kees
Format: Conference Proceeding
Language:English
Published: IEEE 01.11.2022
Subjects:
affinity clustering
Analytical models
Clustering algorithms
Computational efficiency
Computational modeling
Conferences
Data analysis
Data models
distributed setting
minimum spanning tree
number of rounds
work and space efficient algorithm
ISSN:2375-9259
Online Access:Get full text
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Summary:In recent years, the Massively Parallel Computation (MPC) model capturing the MapReduce framework has become the de facto standard model for large-scale data analysis, given the ubiquity of efficient and affordable cloud implementations. In this model, an input of size m is initially distributed among t machines, each with a local space of size s . Computation proceeds in synchronous rounds in which each machine performs arbitrary local computation on its data and then sends messages to other machines. In this paper, we study the Minimum Spanning Tree (MST) problem for dense graphs in the MPC model. We say a graph G(V,\ E) is relatively dense if m=\Theta(n^{1+c}) where n=\vert V\vert is the number of vertices, m=\vert E\vert is the number of edges in this graph, and 0 < c\leq 1 . We develop the first work- and space-efficient MPC algorithm that with high probability computes an MST of G using \lceil\log\frac{c}{\epsilon}\rceil+1 rounds of communication. As an MPC algorithm, our algorithm uses t=O(n^{c-\epsilon}) machines each one having local storage of size s=O(n^{1+\epsilon}) for any 0 < \epsilon\leq c . Indeed, not only is this algorithm very simple and easy to implement, it also simultaneously achieves optimal total work, per-machine space, and number of rounds.
ISSN:2375-9259
DOI:10.1109/ICDMW58026.2022.00106