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Faster and Simpler Distributed Algorithms for Testing and Correcting Graph Properties in the CONGEST-Model

Even, G., Levi, R., & Medina, M. (2017). Faster and Simpler Distributed Algorithms for Testing and Correcting Graph Properties in the CONGEST-Model. Retrieved from http://arxiv.org/abs/1705.04898.

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Latex : {Faster and Simpler Distributed Algorithms for Testing and Correcting Graph Properties in the CONGEST-Model}

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Creators:
Even, Guy1, Author
Levi, Reut2, Author
Medina, Moti2, Author
Affiliations:
1External Organizations, ou_persistent22
2Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019

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Free keywords: Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC,Computer Science, Data Structures and Algorithms, cs.DS
Abstract: In this paper we present distributed testing algorithms of graph properties in the CONGEST-model [Censor-Hillel et al. 2016]. We present one-sided error testing algorithms in the general graph model. We first describe a general procedure for converting $\epsilon$-testers with a number of rounds $f(D)$, where $D$ denotes the diameter of the graph, to $O((\log n)/\epsilon)+f((\log n)/\epsilon)$ rounds, where $n$ is the number of processors of the network. We then apply this procedure to obtain an optimal tester, in terms of $n$, for testing bipartiteness, whose round complexity is $O(\epsilon^{-1}\log n)$, which improves over the $poly(\epsilon^{-1} \log n)$-round algorithm by Censor-Hillel et al. (DISC 2016). Moreover, for cycle-freeness, we obtain a \emph{corrector} of the graph that locally corrects the graph so that the corrected graph is acyclic. Note that, unlike a tester, a corrector needs to mend the graph in many places in the case that the graph is far from having the property. In the second part of the paper we design algorithms for testing whether the network is $H$-free for any connected $H$ of size up to four with round complexity of $O(\epsilon^{-1})$. This improves over the $O(\epsilon^{-2})$-round algorithms for testing triangle freeness by Censor-Hillel et al. (DISC 2016) and for testing excluded graphs of size $4$ by Fraigniaud et al. (DISC 2016). In the last part we generalize the global tester by Iwama and Yoshida (ITCS 2014) of testing $k$-path freeness to testing the exclusion of any tree of order $k$. We then show how to simulate this algorithm in the CONGEST-model in $O(k^{k^2+1}\cdot\epsilon^{-k})$ rounds.

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Language(s): eng - English
Dates: 2017-05-132017
Publication Status: Published online
Pages: 14 p.
Publishing info: -
Rev. Method: -
Identifiers: arXiv: 1705.04898
URI: http://arxiv.org/abs/1705.04898
BibTex Citekey: DBLP:journals/corr/EvenLM17
Degree: -

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