Abstract
We give processor-allocation algorithms for grid architectures, where the objective is to select processors from a set of available processors to minimize the average number of communication hops.
The associated clustering problem is as follows: Given n points in \(\mathcal{R}^d\), find a size-k subset with minimum average pairwise L 1 distance. We present a natural approximation algorithm and show that it is a \(\frac{7}{4}\)-approximation for 2D grids. In d dimensions, the approximation guarantee is 2 - \(\frac{1}{2d}\), which is tight. We also give a polynomial-time approximation scheme (PTAS) for constant dimension d and report on experimental results.
Extended Abstract. A full version is available as [5].
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References
Ahmadinia, A., Bobda, C., Fekete, S., Teich, J., der Veen, J.: Optimal routing-conscious dynamic placement for reconfigurable computing. In: Becker, J., Platzner, M., Vernalde, S. (eds.) FPL 2004. LNCS, vol. 3203, pp. 847–851. Springer, Heidelberg (2004)
Bartal, Y., Charikar, M., Raz, D.: Approximating min-sum k-clustering in metric spaces. In: Proc. 33rd Symp. on Theory of Computation, pp. 11–20 (2001)
Baylor, S., Benveniste, C., Hsu, Y.: Performance evaluation of a massively paralel I/O subsystem. In: Jain, R., Werth, J., Browne, J. (eds.) Synthesizing Synchronous Systems by Static Scheduling in Space-Time. The Kluwer International Series in Engineering and Computer Science, ch. 13, vol. 362, pp. 293–311. Kluwer Academic Publishers, Dordrecht (1996)
Bender, C.M., Bender, M.A., Demaine, E.D., Fekete, S.P.: What is the optimal shape of a city? J. Physics A: Mathematical and General 37, 147–159 (2004)
Bender, M.A., Bunde, D.P., Demaine, E.D., Fekete, S.P., Leung, V.J., Meijer, H., Phillips, C.A.: Communication-aware processor allocation for supercomputers. Technical Report cs.DS/0407058, Computing Research Repository (2004), http://arxiv.org/abs/cs.DS/0407058
Bhattacharya, S., Tsai, W.-T.: Lookahead processor allocation in mesh connected massively parallel computers. In: Proc. 8th International Parallel Processing Symposium, pp. 868–875 (1994)
Brightwell, R., Fisk, L.A., Greenberg, D.S., Hudson, T., Levenhagen, M., Maccabe, A.B., Riesen, R.: Massively parallel computing using commodity components. Parallel Computing 26(2-3), 243–266 (2000)
Chang, C., Mohapatra, P.: Improving performance of mesh connected multicomputers by reducing fragmentation. Journal of Parallel and Distributed Computing 52(1), 40–68 (1998)
Chuang, P.-J., Tzeng, N.-F.: An efficient submesh allocation strategy for mesh computer systems. In: Proc. Int. Conf. Dist. Comp. Systems, pp. 256–263 (1991)
Feitelson, D.: The parallel workloads archive, http://www.cs.huji.ac.il/labs/parallel/workload/index.html
Fekete, S.P., Meijer, H.: Maximum dispersion and geometric maximum weight cliques. Algorithmica 38, 501–511 (2004)
Guttmann-Beck, N., Hassin, R.: Approximation algorithms for minimum sum p-clustering. Disc. Appl. Math. 89, 125–142 (1998)
Indyk, P.: A sublinear time approximation scheme for clustering in metric spaces. In: Proc. 40th Ann. IEEE Symp. Found. Comp. Sci (FOCS), pp. 154–159 (1999)
Karp, R.M., McKellar, A.C., Wong, C.K.: Near-optimal solutions to a 2-dimensional placement problem. SIAM Journal on Computing 4, 271–286 (1975)
Krueger, P., Lai, T.-H., Dixit-Radiya, V.: Job scheduling is more important than processor allocation for hypercube computers. IEEE Trans. on Parallel and Distributed Systems 5(5), 488–497 (1994)
Krumke, S., Marathe, M., Noltemeier, H., Radhakrishnan, V., Ravi, S., Rosenkrantz, D.: Compact location problems. Th. Comp. Sci. 181, 379–404 (1997)
Leung, V., Arkin, E., Bender, M., Bunde, D., Johnston, J., Lal, A., Mitchell, J., Phillips, C., Seiden, S.: Processor allocation on Cplant: achieving general processor locality using one-dimensional allocation strategies. In: Proc. 4th IEEE International Conference on Cluster Computing, pp. 296–304 (2002)
Li, K., Cheng, K.-H.: A two-dimensional buddy system for dynamic resource allocation in a partitionable mesh connected system. Journal of Parallel and Distributed Computing 12, 79–83 (1991)
Lo, V., Windisch, K., Liu, W., Nitzberg, B.: Non-contiguous processor allocation algorithms for mesh-connected multicomputers. IEEE Transactions on Parallel and Distributed Computing 8(7) (1997)
Mache, J., Lo, V.: Dispersal metrics for non-contiguous processor allocation. Technical Report CIS-TR-96-13, University of Oregon (1996)
Mache, J., Lo, V.: The effects of dispersal on message-passing contention in processor allocation strategies. In: Proc. Third Joint Conf. on Information Sciences, Sessions on Parallel and Distributed Processing, vol. 3, pp. 223–226 (1997)
Mache, J., Lo, V., Windisch, K.: Minimizing message-passing contention in fragmentation-free processor allocation. In: Proc. 10th Intern. Conf. Parallel and Distributed Computing Systems, pp. 120–124 (1997)
Moore, S., Ni, L.: The effects of network contention on processor allocation strategies. In: Proc. 10th Int. Par. Proc. Symp., pp. 268–274 (1996)
Sahni, S., Gonzalez, T.: p-complete approximation problems. JACM 23(3), 555–565 (1976)
Sandia National Laboratories. The Computational Plant Project, http://www.cs.sandia.gov/cplant
Subramani, V., Kettimuthu, R., Srinivasan, S., Johnson, J., Sadayappan, P.: Selective buddy allocation for scheduling parallel jobs on clusters. In: Proc. 4th IEEE International Conference on Cluster Computing (2002)
University of Oregon Resource Allocation Group. Procsimity. http://www.cs.uoregon.edu/research/DistributedComputing/ProcSimity.html
Windisch, K., Miller, J., Lo, V.: Procsimity: An experimental tool for processor allocation and scheduling in highly parallel systems. In: Proc. Fifth Symp. on the Frontiers of Massively Parallel Computation, pp. 414–421 (1995)
Zhu, Y.: Efficient processor allocation strategies for mesh-connected parallel computers. J. Parallel and Distributed Computing 16, 328–337 (1992)
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Bender, M.A. et al. (2005). Communication-Aware Processor Allocation for Supercomputers. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_16
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DOI: https://doi.org/10.1007/11534273_16
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