M. Snir. On parallel searching. In Proc. SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pages 242--253, Ottawa, Canada, 1982. 20  Home/Search   Document Not in Database   Summary   Related Articles   Check

....bounds holds for any number of processors or memory cells. It should be noted that any function can be computed on any PRAM in O(log n) time if the number of processors is not bounded so the separation is tight. A natural question is whether read concurrency provides true additional power. Snir [Sni85] proves that given inputs y and a sorted list x 1 x 2 : x n , finding the minimum i such that x i y requires Omega Gamma p log n) time on a EREW PRAM, but can be done in O(1) time on a CREW PRAM. This lower bound uses Ramsey theory, and holds only if the domain of the x i s is huge. ....

M. Snir. On parallel searching. SIAM J. Comput., 14:688--708, 1985. 17

....in which it halts, the state transition function q and the value to be written function v of M are identity functions, i.e. q t i = q(q t Gamma1 i ; v t Gamma1 j ) q t Gamma1 i ; v t Gamma1 j ) and v(q t i ) q t i . This definition is essentially the same as that given by Snir [Sn] for EREW PRAM s. It is clear that for a maximal information PRAM, it is always the case that P (M; i; t) is a refinement of P (M; i; t Gamma 1) We can convert any abstract PRAM into a maximal information PRAM by allowing the processors to remember and write more detail but keeping the same ....

....a function which is not defined on a full domain. The Cook, Dwork and Reischuk lower bound does not depend on the function in question being defined on a full domain, but, if some inputs do not have to be considered, it is easier to construct functions for which the bound in [CDR] is small. Snir [Sn] looked at the following problem: given an integer key y and a sorted list of n distinct integers x 1 Delta Delta Delta x n , determine if y appears in the list of x s. Using a Ramsey theoretic argument he was able to obtain a tight Theta( p log n) bound on the time an EREW PRAM requires ....

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Snir, M. On Parallel Searching, SIAM J. Computing, vol. 14(3), 1985, pp. 688708.

....no fast simulation of the concurrent read operation on EREW 4 PRAMs is possible [3] which makes it necessary to design efficient EREW algorithms by completely different techniques than CREW algorithms. There are some results elaborating on what EREW PRAMs can do less efficiently than CREW PRAMs [3, 14, 30], but still a deep understanding of the EREW PRAM model is missing. We will construct a feasible algorithm for the EREW PRAM that computes PARITY n in approximately 0:86 log n steps (Theorem 3.1) This is the second example after the algorithm for OR n of an EREW algorithm with time ....

M. Snir, On parallel searching, SIAM J. Comput. 14 (1985), 688--708.

....cells of the shared memory are unbounded. In view of such a hardware power, the analysis is directed to the bounds on the number of data movements between processors and memory. The seminal contributions in this line of research are due to Cook, Dwork and Reischuk [1] for CREW PRAMs, and to Snir [8] for EREW PRAMs. Virtually all subsequent works are deeply influenced by these papers, or at least mention their results as basic ones (e.g. see Parberry [7] Jaja [5] Karp and Ramachandran [6] After some variations and improvements, a fundamental advancement over the results This work has ....

M. Snir. On parallel searching. SIAM J. Comp. 14 (1985) 688-708. 9

....circuit families. PRAMs were introduced by Fortune and Wyllie [FW78] as a parallel analogon of random access machines. APRAM consists of infinitely many RAMs that have access to a shared global memory and work synchronously. Many variants of this model have been considered in literature (see e.g. [SV84, Gol82, Sni82]) The main difference between these models is the restriction of simultaneous read and write accesses to global memory cells. 2 According to Snir a PRAM that allows both simultaneous read and write access to a memory cell is called CRCW PRAM (concurrent read, concurrent write PRAM) There are ....

....local memory cell of each processor, which contains the input length n. The first p(n) processors are started simultaneously at the beginning of their programs, where p(n) is some polynomial. The definition we use is not critical. Though there are many PRAM definitions that differ in details (e.g. [FW78, Sch80, Gol82, Sni82, Vis83, FRW84, EG88]) the accepted classes of languages are the same for resource bounds considered in this paper. 3 Subsequently we describe some of the instructions of a PRAM. Herein, L i stands for a local memory cell and G a for a global memory cell. L i : const Assignment of a constant to local memory cell ....

M. Snir. On parallel searching. In Proc. SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pages 242--253, Ottawa, Canada, 1982.

....cells of the shared memory are unbounded. In view of such a hardware power, the analysis is directed to the bounds on the number of data movements between processors and memory. The seminal contributions in this line of research are due to Cook, Dwork and Reischuk [1] for CREW PRAMs, and to Snir [9] for EREW PRAMs. Virtually all subsequent works are deeply in uenced by these papers, or at least mention their results as basic ones (e.g. see Parberry [7] Jaja [5] Karp and Ramachandran [6] After some variations and improvements, a fundamental advancement over the results This work has ....

M. Snir. On parallel searching. SIAM J. Comp. 14 (1985) 688-708. 9

....how hard it is to find the chromatic number (recursive chromatic number) of a graph in terms of the number of queries to F K p (F # ### p ) that are required. Some of the results obtained in Sections 3 and 5 have analogs in this new setting. In particular, when using K, p 1) ary search [26, 34] is optimal for finding the chromatic number of a 2 graph. If other oracles can be used then (p 1) ary search is not optimal. In Section 9 we examine using parallel queries and an auxiliary (weaker) oracle. Section 10 contains a summary of our results and some open questions. Other work on ....

....Lemma 7.13. 27 8 Parallel Queries In this section we look at machines that can ask p (a fixed constant) queries to a set simultaneously. This notion is formalized by considering queries to the function F X p (where X is some oracle) Binary search can be replaced by (p 1) ary search [26, 34] in many of our theorems, but this is not always optimal. The constant p is fixed throughout this section. The following lemma will be useful in establishing a lower bound on the number of queries to F K p that are needed to find the chromatic number of a recursive graph. Lemma 8.1 If A is a ....

M. Snir. On parallel searching. SIAM J. Comput., 14(3):688--708, Aug. 1985.

....bounds holds for any number of processors or memory cells. It should be noted that any function can be computed on any PRAM in O(logn) time if the number of processors is not bounded so the lower bound is tight. A natural question is whether read concurrency provides true additional power. Snir [Sni85] proves that given inputs y and a sorted list x 1 x 2 : xn , finding the minimum i such that x i y requires Omega Gamma p log n) time on a EREW PRAM, but can be done in O(1) time on a CREW PRAM. This lower bound uses Ramsey theory, and holds only if the domain of the x i s is huge. ....

M. Snir. On parallel searching. SIAM J. Comput., 14:688--708, 1985.

....all the processors have access to all the memory cells, situations in which a number of processors access the same cell simultaneously may arise. This feature is often useful in the design of parallel algorithms; if it is supported, the model is dubbed concurrent read concurrentwrite, or CRCW PRAM [38]. The implementation of concurrent access is considered difficult, however, so algorithm designers tend to make an effort not to use simultaneous access to the same cell (e.g. 40, 9] The model in which all cells are shared but not accessed simultaneously is called exclusive read ....

.... of concurrent access is considered difficult, however, so algorithm designers tend to make an effort not to use simultaneous access to the same cell (e.g. 40, 9] The model in which all cells are shared but not accessed simultaneously is called exclusive read exclusive write, or EREW PRAM [38]. The implementation of large scale shared memory parallel computers has been an elusive goal. While small scale systems can be built using a bus [4] or crossbar switch [42] the only approach suitable for large scale machines seems to be multistage interconnection networks [18, 32, 33] The main ....

M. Snir, "On parallel searching ". SIAM J. Comput. 14(3), pp. 688--708, Aug 1985.

....more limited attention despite the fact that the EREW restriction is arguably more practical. For example, the simulations of PRAMs by networks due to Ranade [10] has additional complications to handle concurrent memory access and these are at least as bad for reading as for writing. Snir [11] showed a time separation of Omega Gamma p log n) between CREW and EREW PRAMs for the problem of searching a sorted list and this has been extended to a problem with full domain [7] A major drawback of these results is that they use multi variate Ramsey theory and thus require huge input ....

M. Snir, On parallel searching, SIAM J. Comput. 14(4) (1985) 688--708. 9

....realistic ones: Fortune and Wyllie defined that any number of processors is allowed to simultaneously read from a single global memory cell, but only one processor may write into each memory cell at each step. To distinguish this model from other ones, Snir called this type of PRAM a CREW PRAM [Sni82] (concurrent read, exclusive write parallel random access machine) We can also consider PRAMs in which any number of processors is allowed to write simultaneously into a single memory cell. This type is called CRCW PRAM (concurrent read, concurrent write parallel random access machine) ....

....space and there is also a characterization in terms of auxiliary pushdown automata [DR86, Sud78] It is only natural to apply these three different methods to solve write conflicts also to read conflicts. Since the owner write concept is fairly new, this only led to EREW PRAMs by now (see e.g. [LPV81, Sni82]) but it seems useful to consider EROW and finally OROW PRAMs, too. An OROW PRAM can be seen as a PRAM without global memory, but provided with communication channels between some pairs of processors. Certainly, OROW PRAMs are the most realistic model mentioned by now. In this paper we will ....

[Article contains additional citation context not shown here]

M. Snir. On parallel searching. In Proc. SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pages 242--253, Ottawa, Canada, 1982.

....an Accept instruction. In a PRAM, several processors may attempt to access the same memory cell at the same time. A PRAM may allow concurrent read and concurrent write (CRCW) operations, concurrent read and exclusive write (CREW) operations, or exclusiveread and exclusive write (EREW) operations [2, 22, 25]. In a CRCW PRAM, some mechanism is necessary to resolve the simultaneous write conflicts [2, 8, 21] Fich et al. 5] studied the relationships between CRCW PRAMs with di#erent conflict resolution mechanisms. In what follows, we restrict our attention to CREW PRAMs. Unless otherwise stated, our ....

M. Snir, On parallel searching, SIAM J. Comput., 14 (1985), pp. 688--708.

....theoretic arguments to force the algorithms to behave in a structured manner on some subset of the inputs. Then, it is argued that this subset of inputs (3,4) is rich enough that this structured behaviour cannot find a quick solution. Examples of lower bounds that use this method can be found in [27, 23, 2, 3]. However, applying Ramsey theoretic arguments necessitates assuming an unrealistically large domain size, often an iterated exponential in the size of the problem. These lower bounds become invalid when considering smaller domains. Thus, a major thrust of parallel complexity is to prove lower ....

M. Snir, "On Parallel Searching", SIAM J. of Computing, vol. 14, no. 2, 1985, 688--708.

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M. Snir. On parallel searching. In Proc. SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pages 242--253, Ottawa, Canada, 1982. 20

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M. Snir. On parallel searching. In Proc. SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pages 242--253, Ottawa, Canada, 1982.

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M. Snir. On parallel searching. In Proc. SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pages 242--253, Ottawa, Canada, 1982.

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Snir, M. On parallel searching. SIAM J. Comput. 14, 3(Aug. 1985), pp. 688-708.

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. M. Snir. On parallel searching. SIAM J. Comput. 14, 3(Aug. 1985), pp. 688-708.

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M. Snir. On parallel searching. SIAM J. Comput., 14, 3(Aug. 1985), pp. 688708. 26

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. M. Snir. On parallel searching. SIAM J. Comput., Vol. 14, No. 3, 688-708(Aug., 1985).

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Snir, M. On parallel searching. SIAM J. Comput. 14, 3(Aug. 1985), 688-708.

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. M. Snir. On parallel searching. SIAM J. Comput. Vol. 14, No. 3, Aug. 1985, pp. 688-708.

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. M. Snir. On parallel searching, SIAM J. Comput., Vol. 14, No. 3, 688-708(Aug. 1985).

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M. Snir, "On parallel searching," SIAM J. Comput., vol. 14, no. 3, pp. 688-708, Aug. 1985.

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. M. Snir. On parallel searching, SIAM J. Comput., Vol. 14, No. 3, 688-708(Aug., 1985).

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