B. S. Chlebus, K. Diks, T. Hagerup, and T. Radzig. New simulations between CRCW PRAMs. In Fundamentals of Computation Theory, pages 95--105. Springer, August 1989. 21  Home/Search   Document Not in Database   Summary   Related Articles   Check

....partition algorithm log n= log log n times (each subsequent application on the marked elements from the previous application) Then if there is more than a single processor remaining in a group, each of the remaining processors will be assigned 2 processors. Now we can use a technique from [10] to choose one of the remaining (marked) processors for each cell as follows. Let k = 2 . Assign each marked processor to a cell in an n element array according to its processor number. Form a k ary tree T over this array. Assign the k processors of a marked processor P to the k leaves in T ....

B. S. Chlebus, K. Diks, T. Hagerup, and T. Radzik. New simulations between CRCW PRAMs. In Proc. 7th Intl. Conf. on Fundamentals of Comp. Theory, volume 380, pages 95--104. Springer Lecture Notes in Computer Science, 1989.

.... can also be performed in time (a) O(t) using O(p 2 ) weak CRCW processors [41] b) O(t log log p) using O(p) arbitrary winner processors [10] c) O(t log p) using O(p log p) probabilistic arbitrary winner processors [59] and (d) O(t log p (k log(log p) k) using kn common mode processors [11]. As special cases of (d) common mode CRCWs can take time O(t log p log log p) with O(p) processors [20] or time O(t) with O(p log p) processors [10] These results can be improved if we know the pattern of concurrent memory access. In particular, many uses of strong concurrent write reduce ....

B.S. Chlebus, K. Diks, T. Hagerup, and T. Radzik, New Simulations between CRCW PRAMs. Manuscript.

....we mean that there exists a constant c, c 1, such that the probability of success of our algorithm is at least (1 Gamma n Gammac ) for an input of size n. The randomised algorithms run on Tolerant Common CRCW PRAMs. We shall adopt the definitions of these models, as given by Chlebus et al. [7] Throughout the rest of the paper, we shall assume that all the elements are distinct. This does not result in any loss of generality in the analysis or implementation of our algorithms. We shall use superscripted or subscripted upper case letters to denote arrays and the corresponding lower case ....

Chlebus B.S., Diks K., Hagerup T., and Radzik T., New Simulations between CRCW PRAMs, in Proc 7th Int'l Conf. on Fundamentals of Computation Theory, Springer lecture notes in computer science, vol 380, pp 95-104.

.... called CRCW PRAM (concurrent read, concurrent write PRAM) There are several possibilities to solve write conflicts: The COMMON model requires all values written simultaneously into some memory cell to be equal, whereas in the PRIORITYmodel always the lowest numbered processor wins (see [KR90] and [CDHR89] for these and other submodels of CRCW PRAMs) In CREW PRAMs each memory cell must receive a new value from at most one processor at each time step, while simultaneous read accesses are still allowed. Finally there are EREW PRAMs that forbid both simultaneous read and write access. In addition to ....

B. S. Chlebus, K. Diks, T. Hagerup, and T. Radzig. New simulations between CRCW PRAMs. In Fundamentals of Computation Theory, pages 95--105. Springer, August 1989. 21

....reads from and concurrents writes into the communication windows. On the other hand the specific rule how to resolve write conflicts is not of major importance, because several authors have shown efficient simulations among parallel machines with different write conflict resolutions [5] [6], 10] 11] 13] 14] These simulations are described for PRAMs, but can be transfered to DMMs using Lemma 2.1. 4 For example the TOLERANT rule suffices: If several processors want to write to the same communication window then its contents remains unchanged. This can be done without ....

B. S. Chlebus, K. Diks, T. Hagerup, and T. Radzik. New simulations between CRCW PRAMs. In MFCS '89, pages 95--104, 1989.

....of batching or pipelining the load balancing, and so an algorithm which would take Theta(f (n) time with a constanttime load balancing operation still might be made to take o(f(n) log n) time. That is beyond the scope of the paper. Load balancing procedures have been used in Chlebus et al. [12] to perform simulations of strong CRCW PRAM models on weaker CRCW PRAM models, in MacKenzie and Stout [37] for Padded Sorting, finding Nearest Neighbors, and constructing the Voronoi Diagram, in Gil and Matias [20] to perform Parallel Hashing, in Hagerup [27] to perform Integer Chain Sorting, and ....

B. S. Chlebus, K. Diks, T. Hagerup, and T. Radzik, New simulations between CRCW PRAMs, in Proc. 7th Intl. Conf. on Fundamentals of Comp. Theory, vol. 380, Springer Lecture Notes in Computer Science, 1989, pp. 95--104.

....into the same shared memory location. The main sub models of crcw pram in descending order of power are: the Priority ( 29] in which the lowest numbered processor succeeds; the Arbitrary ( 42] in which one of the processors succeeds, and it is not known in advance which one; the Collision ([9]) in which if different values are attempted to be written, a special collision symbol is written in the cell; the Collision ( 15] in which a special collision symbol is written in the cell; the Tolerant ( 32] in which the contents of that cell do not change; and finally, the less standard ....

B. S. Chlebus, K. Diks, T. Hagerup, and T. Radzik. New simulations between CRCW PRAMs. In Proc. 7th Int. Conference on Fundamentals of Computation Theory, Springer LNCS 380, pages 95--104, 1989.

....into the same shared memory location. The main sub models of crcw pram in descending order of power are: the Priority ( 29] in which the lowest numbered processor succeeds; the Arbitrary ( 42] in which one of the processors succeeds, and it is not known in advance which one; the Collision ([9]) in which if different values are attempted to be written, a special collision symbol is written in the cell; the Collision ( 15] in which a special collision symbol is written in the cell; the Tolerant ( 32] in which the contents of that cell do not change; and finally, the less standard ....

B. S. Chlebus, K. Diks, T. Hagerup, and T. Radzik. New simulations between CRCW PRAMs. In Proc. 7th Int. Conference on Fundamentals of Computation Theory, Springer LNCS 380, pages 95--104, 1989.

....For each sub ocpc we wish to make lg 2 (n 0 ) copies of the relevant sub problem, all of which will reside in its processors 1; n 0 =2. We will use an approximate compaction tool to divide the problem into sub problems and to make copies of the problem. For similar tools see [5, 15, 25, 26]. Given ffl an n ocpc in which at most s senders each have one message to send, ffl a set of fis receivers which is known to all of the senders, the (s; fi) approximate compaction problem is to deliver all of the messages to the set of receivers in such a way that each receiver receives at ....

B.S. Chlebus, K. Diks, T. Hagerup, and T. Radzik, New Simulations between CRCW PRAMs, Proc. Foundations of Computation Theory 7 , Lecture Notes in Computer Science 380 (Springer-Verlag 1989) 95--104.

....For each sub ocpc we wish to make lg 2 (n 0 ) copies of the relevant sub problem, all of which will reside in its processors 1; n 0 =2. We will use an approximate compaction tool to divide the problem into sub problems and to make copies of the problem. For similar tools see [5, 15, 25, 26]. Given ffl an n ocpc in which at most s senders each have one message to send, ffl a set of fis receivers which is known to all of the senders, the (s; fi) approximate compaction problem is to deliver all of the messages to the set of receivers in such a way that each receiver receives at most ....

B.S. Chlebus, K. Diks, T. Hagerup, and T. Radzik, New Simulations between CRCW PRAMs, Proc. Foundations of Computation Theory 7 , Lecture Notes in Computer Science 380 (Springer-Verlag 1989) 95--104.

....p log n= log log n times (each subsequent application on the marked elements from the previous application) Then if there is more than a single processor remaining in a group, each of the remaining processors will be assigned 2 p log n= log log n processors. Now we can use a technique from [10] to choose one of the remaining (marked) processors for each cell as follows. Let k = 2 p log n= log log n . Assign each marked processor to a cell in an n element array according to its processor number. Form a k ary tree T over this array. Assign the k processors of a marked processor P to ....

B. S. Chlebus, K. Diks, T. Hagerup, and T. Radzik. New simulations between CRCW PRAMs. In Proc. 7th Intl. Conf. on Fundamentals of Comp. Theory, volume 380, pages 95--104. Springer Lecture Notes in Computer Science, 1989.

....subsequent application on the marked processors from the previous application. Then if there is more than a single processor remaining in a group, each of the remaining processors will be assigned 2 p log n= log log n processors. In the second phase of our simulation, we use a technique from [16] to choose one of the remaining (marked) processors for each cell as follows. Let k = 2 p log n= log log n . Assign each marked processor to a cell in an n element array according to its processor number. Form a k ary tree T over this array. For each marked processor P do the following: ....

B. S. Chlebus, K. Diks, T. Hagerup, and T. Radzik. New simulations between CRCW PRAMs. In Proc. 7th Intl. Conf. on Fundamentals of Comp. Theory, volume 380, pages 95--104. Springer Lecture Notes in Computer Science, 1989.

....Each remaining message is copied log p times and the processors are re allocated so that log p processors can work together to send each message to its target group. The approximate compaction technique and the copying technique were first used in PRAM algorithms such as those described in [CDHR 89] and in [GM 91] and [MV 91] In this work we require a smaller failure probability for approximate compaction than previous authors because our target groups are only polylogarithmic in size and we need to bound the probability of failure in any group. At the end of the third procedure the ....

....an alternate implementation which runs in Theta(h log log p) communication steps and succeeds with probability at least 1 Gamma p Gammaff . The constant in the running time depends upon ff . We will use the following tool in the implementation of our algorithm. For similar tools see [CDHR 89, GM 91, and MV 91] Definition 1. The (s; fi; Delta) approximate compaction problem is defined as follows. y The case in which k does not divide p presents no real difficulty. In this case the target groups should be defined in such a way that all but one of the groups has size k and the ....

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B. S. Chlebus, K. Diks, T. Hagerup, and T. Radzik, New Simulations between CRCW PRAMs, Proc. Foundations of Computation Theory 7 , Lecture Notes in Computer Science 380 (Springer-Verlag 1989) 95--104.

....to write to a memory cell, then there are two cases: if all the values of the processors are equal then this common value gets written, otherewise the collision symbol is written to the cell. The algorithms of section 3 and 4 are designed for Collision, and of section 4 for Collision . See [5] for more on the relative power of these variants of the CRCW PRAM. We use the following notations. The simulated ideal PRAM is denoted by C I , and the simulating faulty memory PRAM by C F . Two main parameters of a simulation algorithm are the size of memory and the number of processors. The ....

B.S. Chlebus, K. Diks, T. Hagerup, and T. Radzik, New Simulations between CRCW PRAMs, Proc. 7th International Conference on Fundamentals of Computation Theory (1989), 95-104, Springer LNCS 380.

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B. S. Chlebus, K. Diks, T. Hagerup, and T. Radzig. New simulations between CRCW PRAMs. In Fundamentals of Computation Theory, pages 95--105. Springer, August 1989. 21

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. B. S. Chlebus, K. Diks, T. Hagerup, T. Radzik. New simulations between CRCW PRAMs. LNCS 380, 95-104.

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