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.
The full version of this paper can be found in http://arxiv.org/abs/1512.05411.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 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.
References
Alon, N.: On constant time approximation of parameters of bounded degree graphs. In: Goldreich, O. (ed.) Property Testing. LNCS, vol. 6390, pp. 234–239. Springer, Heidelberg (2010)
Alon, N., Lovett, S.: Almost \(k\)-Wise vs. \(k\)-wise independent permutations, and uniformity for general group actions. Theor. Comput. 9(15), 559–577 (2013)
Alon, N., Rubinfeld, R., Vardi, S., Xie, N.: Space-efficient local computation algorithms. In: Proceedings of SODA, pp. 1132–1139. SIAM (2012)
Campagna, A., Guo, A., Rubinfeld, R.: Local reconstructors and tolerant testers for connectivity and diameter. In: Raghavendra, P., Raskhodnikova, S., Jansen, K., Rolim, J.D.P. (eds.) RANDOM 2013 and APPROX 2013. LNCS, vol. 8096, pp. 411–424. Springer, Heidelberg (2013)
Czygrinow, A., Hańćkowiak, M., Wawrzyniak, W.: Fast distributed approximations in planar graphs. In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 78–92. Springer, Heidelberg (2008)
Even, G., Medina, M., Ron, D.: Best of Two Local Models: Local Centralized and Local Distributed Algorithms (2014). arXiv:1402.3796
Even, G., Medina, M., Ron, D.: Deterministic stateless centralized local algorithms for bounded degree graphs. In: Schulz, A.S., Wagner, D. (eds.) ESA 2014. LNCS, vol. 8737, pp. 394–405. Springer, Heidelberg (2014)
Even, G., Medina, M., Ron, D.: Distributed maximum matching in bounded degree graphs. In: Proceedings of ICDCN, pp. 1–19. ACM (2014)
Feige, U., Mansour, Y., Schapire, R.E.: Learning and Inference in the Presence of Corrupted Inputs. In: Proceedings of the 28th Conference on Learning Theory, vol. 40, pp. 637–657. J. Mach. Learn. Res. (2015)
Fich, F.E., Ramachandran, V.: Lower bounds for parallel computation on linked structures. In: Proceedings of SPAA, pp. 109–116. ACM Press (1990)
Kaplan, E., Naor, M., Reingold, O.: Derandomized constructions of k-wise (almost) independent permutations. Algorithmica 55(1), 113–133 (2009)
Kuhn, F., Moscibroda, T., Wattenhofer, R.: What cannot be computed locally! In: Proceedings of PODC, pp. 300–309. ACM Press (2004)
Lenzen, C., Wattenhofer, R.: Leveraging Linial’s locality limit. In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 394–407. Springer, Heidelberg (2008)
Levi, R., Moshkovitz, G., Ron, D., Rubinfeld, R., Shapira, A.: Constructing near spanning trees with few local inspections. Random Struct. Algorithms (2016)
Levi, R., Ron, D., Rubinfeld, R.: Local algorithms for sparse spanning graphs. In: Proceedings of APPROX/RANDOM, pp. 826–842. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2014)
Levi, R., Rubinfeld, R., Yodpinyanee, A.: Local computation algorithms for graphs of non-constant degrees. In: Proceedings of SPAA, pp. 59–61. ACM Press (2015)
Linial, N.: Locality in distributed graph algorithms. SIAM J. Comput. 21(1), 193–201 (1992)
Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann Publishers, San Francisco (1996)
Mansour, Y., Rubinstein, A., Vardi, S., Xie, N.: Converting online algorithms to local computation algorithms. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part I. LNCS, vol. 7391, pp. 653–664. Springer, Heidelberg (2012)
Mansour, Y., Vardi, S.: A local computation approximation scheme to maximum matching. In: Raghavendra, P., Raskhodnikova, S., Jansen, K., Rolim, J.D.P. (eds.) RANDOM 2013 and APPROX 2013. LNCS, vol. 8096, pp. 260–273. Springer, Heidelberg (2013)
Naor, M., Stockmeyer, L.: What can be computed locally? SIAM J. Comput. 24(6), 1259–1277 (1995)
Parnas, M., Ron, D.: Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms. Theor. Comput. Sci. 381(1–3), 183–196 (2007)
Peleg, D.: Distributed Computing: A Locality-sensitive Approach. SIAM Monographs on Discrete Mathematics and Applications. Society for Industrial and Applied Mathematics, Philadelphia (2000)
Reingold, O., Vardi, S.: New Techniques and Tighter Bounds for Local Computation Algorithms (2014). arXiv:1404.5398
Rubinfeld, R., Tamir, G., Vardi, S., Xie, N.: Fast local computation algorithms. In: Proceedings of the ICS (2011)
Suomela, J.: Survey of local algorithms. ACM Comput. Surv. 45(2), 24:1–24:40 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-662-53426-7_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-53425-0
Online ISBN: 978-3-662-53426-7
eBook Packages: Computer ScienceComputer Science (R0)