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Retrieval of scattered information by EREW, CREW, and CRCW PRAMs. (English) Zbl 0838.68052
Summary: The \(k\)-compaction problem arises when \(k\) out of \(n\) cells in an array are on-empty and the contents of these cells must be moved to the first \(k\)-locations in the array. Parallel algorithms for \(k\)-compaction have obvious applications in processor allocation and load balancing; \(k\)-compaction is also an important subroutine in many recently developed parallel algorithms. We show that any EREW PRAM that solves the \(k\)-compaction problem requires \(\Omega(\sqrt{\log n})\) time, even if the number of processors is arbitrarily large and \(k= 2\). On the CREW PRAM, we show that every \(n\)-processor algorithm for \(k\)-compaction problem requires \(\Omega(\log\log n)\) time, even if \(k= 2\). Finally, we show that \(O(\log k)\) time can be achieved on the ROBUST PRAM, a very weak CRCW PRAM model.

MSC:
68W15 Distributed algorithms
68Q25 Analysis of algorithms and problem complexity
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[1] H. Bast and T. Hagerup, Fast and Reliable Parallel Hashing. InProc. 3rd Ann. ACM Symp. Parallel Algorithms and Architectures, 1991, 50–61.
[2] P. Beame,Lower Bounds in Parallel Machine Computation. Ph.D. thesis, University of Toronto, 1986.
[3] P. Beame, M. Kik, andM. Kutyłowski, Information Broadcasting by Exclusive Read PRAMs.Parallel Processing Letters 4.1&2 (1994), 159–169. · doi:10.1142/S012962649400017X
[4] C. Berge,Graphs and Hypergraphs. North-Holland, Amsterdam, 1976.
[5] R. Cole, Parallel Merge Sort.SIAM J. Comput. 17 (1988), 770–785. · Zbl 0651.68077 · doi:10.1137/0217049
[6] S. Cook, C. Dwork, andR. Reischuk, Upper and Lower Time Bounds for Parallel Random Access Machines Without Simultaneous Writes.SIAM J. Comput. 15 (1986), 87–97. · Zbl 0591.68049 · doi:10.1137/0215006
[7] M. Dietzfelbinger, M. Kutyłowski, andR. Reischuk, Exact Time Bounds for Computing Boolean Functions on PRAMs Without Simultaneous Writes.J. Comput. System Sci. 48 (1994), pp. 231–254. · Zbl 0822.68049 · doi:10.1016/S0022-0000(05)80003-0
[8] F. E. Fich, R. Impagliazzo, B. Kapron, V. King, andM. Kutyłowski, Limits on the Power of Parallel Random Access Machines with Weak Forms of Write Conflict Resolution. InProc. 10th Ann. Symp. Theoret. Aspects Comput. Sci., Lecture Notes in Computer Science665, Springer-Verlag, Berlin, 1993, 386–397. · Zbl 0842.68033
[9] F. E. Fich, P. Ragde, andA. Wigderson, Relations Between Concurrent-Write Models of Parallel Computation.SIAM J. Comput. 17 (1988), 606–627. · Zbl 0652.68065 · doi:10.1137/0217037
[10] J. Gil and Y. Matias, Fast Hashing on a PRAM-Designing by Expectation. InProc. 2nd Ann. ACM Symp. Discrete Algorithms, 1991, 271–280. · Zbl 0800.68457
[11] J. Gil, Y. Matias, and U. Vishkin, Towards a Theory of Nearly Constant Parallel Time Algorithms. InProc. 32nd Ann. IEEE Symp. Found. Comput. Sci., 1991, 698–710.
[12] J. Gil and L. Rudolph, Counting and Packing in Parallel. InProc. 1986 Int. Conf. Parallel Processing, IEEE Comput. Soc. Press, 1986, 1000–1002.
[13] M. Goodrich, Using Approximation Algorithms to Design Parallel Algorithms that may Ignore Processor Allocation. InProc. 32nd Ann. IEEE Symp. Found. Comput. Sci., 1991, 711–722.
[14] T. Hagerup. Personal communication.
[15] T. Hagerup, Fast and Optimal Simulations between CRCW PRAMs. InProc. 9th Symp. Theoret. Aspects Comput. Sci., Lecture Notes in Computer Science577, Springer-Verlag, Berlin, 1992, 45–56.
[16] T. Hagerup, The Log-Star Revolution. InProc. 9th Symp. Theoret. Aspects Comput. Sci., Lecture Notes in Computer Science578, Springer-Verlag, Berlin, 1992, 259–278.
[17] T. Hagerup andM. Nowak, Parallel Retrieval of Scattered Information. InProc. 16th Int. Colloq. Automata Languages and Programming, Lecture Notes in Computer Science372, Springer-Verlag, Berlin, 1989, 439–450.
[18] T. Hagerup and T. Radzik, Every ROBUST CRCW PRAM can Efficiently Simulate a PRIORITY PRAM. InProc. 2nd ACM Symp. Parallel Algorithms and Architectures, 1990, 125–135.
[19] M. Kutyłowski, Time Complexity of Boolean Functions on CREW PRAMs.SIAM J. Comput. 20 (1991), 824–833. · Zbl 0732.68053 · doi:10.1137/0220051
[20] P. D. MacKenzie, Lower Bounds for Randomized Exclusive Write PRAMs InProc. 7th Ann. ACM Symp. Parallel Algorithms and Architectures, 1995, pp 254–263.
[21] Y. Matias andU. Vishkin, On Parallel Hashing and Integer Sorting.J. Algorithms 12 (1991), 573–606. · Zbl 0767.68051 · doi:10.1016/0196-6774(91)90034-V
[22] J. B. Rosser andL. Schoenfeld, Approximate Formulas for Some Functions of Prime Numbers.Illinois J. Math. 6 (1962), 64–94. · Zbl 0122.05001
[23] P. Ragde, The Parallel Simplicity of Compaction and Chaining.J. Algorithms 14 (1993), 371–380. · Zbl 0793.68072 · doi:10.1006/jagm.1993.1019
[24] L. Rudolph and W. Steiger, Subset Selection in Parallel. InProc. 1985 Int. Conf. Parallel Processing, IEEE Comput. Soc. Press, 1985, 11–14.
[25] M. Snir, On Parallel Searching.SIAM J. Comput. 14 (1985), 688–708. · Zbl 0607.68047 · doi:10.1137/0214051
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