Abstract
We study the problem of list ranking in the parallel external memory (PEM) model. We observe an interesting dual nature for the hardness of the problem due to limited information exchange among the processors about the structure of the list, on the one hand, and its close relationship to the problem of permuting data, which is known to be hard for the external memory models, on the other hand.
By carefully defining the power of the computational model, we prove a permuting lower bound in the PEM model. Furthermore, we present a stronger Ω(log2 N) lower bound for a special variant of the problem and for a specific range of the model parameters, which takes us a step closer toward proving a non-trivial lower bound for the list ranking problem in the bulk-synchronous parallel (BSP) and MapReduce models. Finally, we also present an algorithm that is tight for a larger range of parameters of the model than in prior work.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Wyllie, J.: The Complexity of Parallel Computation. PhD thesis, Cornell University (1979)
Anderson, R.J., Miller, G.L.: Deterministic parallel list ranking. In: Reif, J.H. (ed.) AWOC 1988. LNCS, vol. 319, pp. 81–90. Springer, Heidelberg (1988)
Aggarwal, A., Vitter, J.S.: The input/output complexity of sorting and related problems. Commun. ACM 31(9), 1116–1127 (1988)
Chiang, Y.J., Goodrich, M., Grove, E., Tamassia, R., Vengroff, D.E., Vitter, J.S.: External-memory graph algorithms. In: Proceedings of SODA 1995, pp. 139–149 (1995)
Valiant, L.G.: A bridging model for parallel computation. Commun. ACM 33(8), 103–111 (1990)
Dean, J., Ghemawat, S.: Mapreduce: Simplified data processing on large clusters. Commun. ACM 51(1), 107–113 (2008)
Karloff, H.J., Suri, S., Vassilvitskii, S.: A model of computation for mapreduce. In: Charikar, M. (ed.) SODA, pp. 938–948. SIAM (2010)
Goodrich, M.: Communication-efficient parallel sorting. SIAM J. Comput. 29(2), 416–432 (1999)
Goodrich, M., Sitchinava, N., Zhang, Q.: Sorting, searching, and simulation in the mapreduce framework. In: Asano, T., Nakano, S.-I., Okamoto, Y., Watanabe, O. (eds.) ISAAC 2011. LNCS, vol. 7074, pp. 374–383. Springer, Heidelberg (2011)
Arge, L., Goodrich, M., Nelson, M., Sitchinava, N.: Fundamental parallel algorithms for private-cache chip multiprocessors. In: SPAA 2008, pp. 197–206 (2008)
Greiner, G.: Sparse Matrix Computations and their I/O Complexity. Dissertation, Technische Universität München, München (2012)
Karp, R.M., Ramachandran, V.: Handbook of theoretical computer science, pp. 869–941 (1990)
Vishkin, U.: Randomized speed-ups in parallel computation. In: STOC, pp. 230–239 (1984)
Arge, L., Goodrich, M., Sitchinava, N.: Parallel external memory graph algorithms. In: IPDPS, pp. 1–11. IEEE (2010)
Jacob, R., Lieber, T., Sitchinava, N.: On the complexity of list ranking in the parallel external memory model. CoRR abs/1406.3279 (2014)
Yao, A.C.C.: Probabilistic computations: Toward a unified measure of complexity (extended abstract). In: FOCS, pp. 222–227. IEEE Computer Society (1977)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jacob, R., Lieber, T., Sitchinava, N. (2014). On the Complexity of List Ranking in the Parallel External Memory Model. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44465-8_33
Download citation
DOI: https://doi.org/10.1007/978-3-662-44465-8_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44464-1
Online ISBN: 978-3-662-44465-8
eBook Packages: Computer ScienceComputer Science (R0)