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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| Vydáno v: | IEEE ... International Conference on Data Mining workshops s. 777 - 786 |
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IEEE
01.11.2022
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| ISSN: | 2375-9259 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Voorintholt, Kees Monemzadeh, Morteza Bateni, MohammadHossein |
| Author_xml | – sequence: 1 givenname: MohammadHossein surname: Bateni fullname: Bateni, MohammadHossein email: bateni@google.com organization: Google Research, NYC,New York,USA – sequence: 2 givenname: Morteza surname: Monemzadeh fullname: Monemzadeh, Morteza email: m.monemizadeh@tue.nl organization: TU Eindhoven,Eindhoven,The Netherlands – sequence: 3 givenname: Kees surname: Voorintholt fullname: Voorintholt, Kees email: kees.voorintholt@live.nl organization: NAVARA,Eindhoven,The Netherlands |
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| SubjectTerms | 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 |
| Title | Efficient Distributed Algorithms for Minimum Spanning Tree in Dense Graphs |
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