DeepAI AI Chat
Log In Sign Up

How fast can you update your MST? (Dynamic algorithms for cluster computing)

by   Seth Gilbert, et al.
National University of Singapore

Imagine a large graph that is being processed by a cluster of computers, e.g., described by the k-machine model or the Massively Parallel Computation Model. The graph, however, is not static; instead it is receiving a constant stream of updates. How fast can the cluster process the stream of updates? The fundamental question we want to ask in this paper is whether we can update the graph fast enough to keep up with the stream. We focus specifically on the problem of maintaining a minimum spanning tree (MST), and we give an algorithm for the k-machine model that can process O(k) graph updates per O(1) rounds with high probability. (And these results carry over to the Massively Parallel Computation (MPC) model.) We also show a lower bound, i.e., it is impossible to process k^1+ϵ updates in O(1) rounds. Thus we provide a nearly tight answer to the question of how fast a cluster can respond to a stream of graph modifications while maintaining an MST.


page 1

page 2

page 3

page 4


Dynamic Graph Algorithms with Batch Updates in the Massively Parallel Computation Model

We study dynamic graph algorithms in the Massively Parallel Computation ...

Parallel Batch-Dynamic Graphs: Algorithms and Lower Bounds

In this paper we study the problem of dynamically maintaining graph prop...

Near-Optimal Massively Parallel Graph Connectivity

Identifying the connected components of a graph, apart from being a fund...

k-Center Clustering with Outliers in the MPC and Streaming Model

Given a point set P ⊆ X of size n in a metric space (X,dist) of doubling...

Massively Parallel Algorithms for High-Dimensional Euclidean Minimum Spanning Tree

We study the classic Euclidean Minimum Spanning Tree (MST) problem in th...

Massively Parallel Computation and Sublinear-Time Algorithms for Embedded Planar Graphs

While algorithms for planar graphs have received a lot of attention, few...

Analysis of Solitaire

The Solitaire cipher was designed by Bruce Schneier as a plot point in t...