Abstract
This work bridges the gap between distributed and centralised models of computing in the context of sublinear-time graph algorithms. A priori, typical centralised models of computing (e.g., parallel decision trees or centralised local algorithms) seem to be much more powerful than distributed message-passing algorithms: centralised algorithms can directly probe any part of the input, while in distributed algorithms nodes can only communicate with their immediate neighbours. We show that for a large class of graph problems, this extra freedom does not help centralised algorithms at all: efficient stateless deterministic centralised local algorithms can be simulated with efficient distributed message-passing algorithms. In particular, this enables us to transfer existing lower bound results from distributed algorithms to centralised local algorithms.
Keywords
- Graph Problems
- Parallel Decision Tree
- Message-passing Algorithm
- Centralised Local Algorithms
- Stateless Algorithm
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The full version of this paper can be found in http://arxiv.org/abs/1512.05411.
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Notes
- 1.
We note that in [16] the algorithm for approximated maximum matching takes the advantage of remote probes. However, since in this algorithm there is an underlying assumption that the input graph is connected, our simulation result cannot be applied in order to eliminate the remote probes.
- 2.
One can also consider a randomised \(\mathsf {ParallelDecTree}\) model in which every tree has access to an independent source of randomness. We note that the randomised stateless \(\mathsf {CentLOCAL}\) model is stronger than this model since the algorithm has access to the same random seed throughout its entire execution.
- 3.
The construction stated in Theorem 5 computes \(\pi (v)\) for some v in time \(\mathsf {poly}(\log n, k, \log (1/\epsilon ))\). This construction does not describe a time efficient way to access \(\pi ^{-1}\). As time complexity is not the focus of this paper, we implement the inverse access in a straightforward manner.
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Göös, M., Hirvonen, J., Levi, R., Medina, M., Suomela, J. (2016). Non-local Probes Do Not Help with Many Graph Problems. In: Gavoille, C., Ilcinkas, D. (eds) Distributed Computing. DISC 2016. Lecture Notes in Computer Science(), vol 9888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53426-7_15
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