Holger Bast and Torben Hagerup. Fast and reliable parallel hashing. In 3rd Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA '91), pages 50--61. ACM Press, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....acceptable. We shall avoid it using a perfect hash function. Definition 5.3: A perfect hash function for a set X of l integers is an injective function h : X f1; sg, where s = O(l) that can be stored in O(l) space and evaluated in constant time by a single processor. Bast and Hagerup [5] showed that a perfect hash function for a given set of l integers can be constructed optimally in O( time using O(n= processors for any log n. Resources (space and processors) To each vertex u 2 V , we allocate an auxiliary array A u of size equal to its neighorhood n u . Two ....

H. Bast and T. Hagerup. Fast and reliable parallel hashing. In Proceedings of 3rd Annual ACM Symposium on Parallel Algorithms and Architecture (SPAA), pages 50--61, 1991.

....simulation can easily be modified to guarantee constant contention. Time processor optimal simulations on CRCW DMMs can be achieved with expected delay O(log log n log n) These simulations are very difficult, in particular the simulation of the write steps uses parallel perfect hashing (compare [2] or [17] A survey of shared memory simulations on DMMs (including the results of this paper) is presented in [19] All expected delays mentioned above are very reliable: always, the delay is within a constant factor of its expectation with high probability, i.e. with probability 1 Gamma n ....

.... memory modules M h 1 (x i ) M h 3 (x i ) Access Schedule 2: Each Q i , 1 i n, performs the following steps: y and s[1: 3] are local to Q i ; s[r] indicates whether M hr (x i ) has been accessed successfully ) y : x i ; for r : 1; 2; 3 do s[r] 0; r : 1; while s[1] s[2] s[3] 2 do begin if s[r] 0 then access(hr (y) s[r] r : r 1) mod 3 end. All processors perform the call access( in the tth execution of the loop exactly at the same time. A round consists of three consecutive executions of the loop body, for r = 1; 2; 3. The c collision rule ....

[Article contains additional citation context not shown here]

H. Bast and T. Hagerup. Fast and reliable parallel hashing. In Proc. of the 3rd Ann. ACM Symp. on Parallel Algorithms and Architectures, pp. 50--61, 1991.

....them into an array of size k such that all records with equal key form a consecutive block, can be performed in time O(k=p log n) using p PUs of a CRCW PRAM whp. Proof. First nd a perfect hash function h : V 1: ck for an appropriate constant c. Using the algorithm of Bast and Hagerup [2] this can be done in time O(k=p log n) and even faster) whp. Subsequently, we apply a fast, work ecient sorting algorithm for small integer keys such as the one by Rajasekaran and Reif [13] to sort by the hash values. Once the set of requests Req is grouped by receiving nodes w, we can use ....

H. Bast and T. Hagerup. Fast and reliable parallel hashing. In 3rd Symposium on Parallel Algorithms and Architectures, pages 50-61, 1991.

.... on the properties of a particular p n universal class of hash functions which combines the constructions given in [8] and [21] The structure of these hash functions enables us to analyze the delay in our simulation using a powerful martingale tail estimate that was derived independently in [2] and [18] 2 Computation Models A PRAM consists of processors P 1 ; Pm and a shared memory with cells U = p] The processors work synchronously and have random access to the shared memory cells, each of which can store an integer. We consider EREW PRAMs where concurrent access to the ....

....is presented in section 7. The process 2 in section 6 models the shrinking and growing of the set of unsatisfied requests stored in SM. We show that this set will always be of linear size, with high probability. For implementing SM we use a fast perfect hash table, based on results from [17] and [2], described in section 4. This guarantees that time O(log (n) is sufficient to insert the new write requests into SM, with high probability, and that a parallel read in SM can be done in constant time. Thus, with respect to one hash function, a write step can be simulated in time O(log ....

[Article contains additional citation context not shown here]

H. Bast and T. Hagerup. Fast and reliable parallel hashing. In Proc. of the 3rd Ann. ACM Symp. on Parallel Algorithms and Architectures, pages 50--61, 1991.

.... time algorithm presented in [14] An O(log 3 n log log 3 n) expected time 8 algorithm was given in [20] its time complexity was later shown to actually be O(log 3 n) with high probability [15] A similar improvement (from O(log 3 n log log 3 n) to O(log 3 n) was also given by [6]. A realtime parallel dynamic hashing algorithm was given by [15] the algorithm supports a batch of n membership query or delete instructions in constant time, and a batch of n insert instructions in O(log 3 n) time with high probability, using an optimal number of processors. Applications As ....

H. Bast and T. Hagerup. Fast and reliable parallel hashing. In SPAA '91, pages 50--61, July 1991.

.... problem is to compute in parallel a hash function h : U 7 [1: cn] such that (i) h is injective on the set induced by the multiset X; and (ii) given a sequence Y = y 1 ; y 2 ; yn , each h(y i ) i = 1; n, separately, can be computed in constant time, using a single processor [18, 9, 17, 3, 11, 16]. The main result, of reducing the general simulation problem to various integer sorting problems, is given in the next section. Concrete simulation results are derived in Section 3 by using known integer sorting algorithms. 2 Reductions to Integer Sorting In this section we give efficient ....

H. Bast and T. Hagerup. Fast and reliable parallel hashing. In 3rd ACM Symp. on Parallel Algorithms and Architectures, pages 50--61, July 1991.

....CRCW on n= log n processor CRCW with O(log n) step overhead. For the sake of presentation, we will present first the simulation of EREW using n processors working in time O( log n) 2 ) Then we sketch how to achive optimal simulation by resorting to techniques of Bast and Hagerup [3]. Finally, we show how to use the algorithms to simulate CRCW PRAM. Let l = O( As in [7] the memory cells of the simulated PRAM are stored in O(m= log n) blocks of the memory of the simulated machine, in such a way that one blocks stores log n consecutive memory cells. To access a memory cell ....

....subsequent phases. Their search can be supported by the processors which already have finished their search. In other words, we need to make an allocation of successful processors to the ones which still have to perform searching. Such an allocation algorithm was proposed by Bast and Hagerup [3]. Their algorithm works in time O(log n) with probability 1 Gamma 2 GammajGj 1 4 . Since the size of G is O(log c n) thus for a proper constant c we achieve a high probability. Assume that after the allocation every searching processor gets O(h) additional helpers. The helpers try to ....

[Article contains additional citation context not shown here]

H. Bast, T. Hagerup, Fast and reliable parallel hashing, in Proceedings of the 3rd Annual ACM Symposium on Parallel Algorithms and Architectures (1991), pp. 50--61.

....geometry. An exciting development over the last few years has been the development of a large number of new deterministic [35, 36, 37] and randomised [96, 117, 266] parallel algorithms for important problems, which achieve nearly constant time on a CRCW PRAM. The problems include hashing [31, 94, 96, 97, 183, 184], dictionary (insert, delete, query operations) 96] integer sorting [38, 115, 183, 184, 218, 219] integer chain sorting [96, 115, 116] space allocation [96, 116] linear approximate compaction [96, 105, 183] estimation [96, 116] load balancing [93, 96, 116] leaders election [95, 96, 116, ....

H Bast and T Hagerup. Fast and reliable parallel hashing. In Proc. 3rd Annual ACM Symposium on Parallel Algorithms and Architectures, pages 50--61, 1991.

....require Omega Gammaeq n= lg lg n) time to be solved by a polynomial number of processors, as implied by the lower bound of Beame and Hastad [4] This lower bound holds even for randomized algorithms. More recent results have found other, more involved, ways to circumvent these barriers; cf. [38, 3, 26, 30]. We circumvent the obstacle of learning buckets sizes for the purpose of appropriate memory allocation by a technique of oblivious execution, sketched by Figure 1. 1. Partition the input set into buckets by a random polynomial of constant degree. 2. For t : 1 to O(lg lg n) do (a) Allocate M t ....

.... Matias, and Vishkin [26] gave a tighter failure probability analysis for the algorithm in [38] yielding O(lg n) time with high probability; a similar improvement (from O(lg n lg lg n) expected time to O(lg n) time with high probability) was described independently by Bast and Hagerup [3]. An O(lg n) time hashing algorithm is used as a building block in a parallel dictionary algorithm presented in [26] A parallel dictionary algorithm supports in parallel batches of operations insert , delete, and lookup. The oblivious execution technique has an important role in the ....

H. Bast and T. Hagerup. Fast and reliable parallel hashing. In 3rd ACM Symp. on Parallel Algorithms and Architectures, pages 50--61, July 1991.

....which require Omega Gammaeq n= lg lg n) time to be solved by polynomial number of processors, as implied by the lower bound of Beame and Hastad [4] This lower bound holds even for randomized algorithms. More recent results have found other, more involved, ways to circumvent these barriers; cf. [38, 3, 26, 30]. We circumvent the obstacle of learning buckets sizes for the purpose of appropriate memory allocation by a technique of oblivious execution, sketched by Figure 1. 1. Partition the input set into buckets by a random polynomial of constant degree. 2. For t : 1 to O(lg lg n) do (a) Allocate M t ....

.... Matias, and Vishkin [26] gave a tighter failure probability analysis for the algorithm in [38] yielding O(lg n) time with high probability; similar improvement (from O(lg n lg lg n) expected time to O(lg n) time with high probability) was described independently by Bast and Hagerup [3]. An O(lg n) time hashing algorithm is used as a building block in a parallel dictionary algorithm presented in [26] A parallel dictionary algorithm supports in parallel batches of operations insert , delete, and lookup. The oblivious execution technique has an important role in the ....

H. Bast and T. Hagerup. Fast and reliable parallel hashing. In 3rd ACM Symp. on Parallel Algorithms and Architectures, pages 50--61, July 1991.

....enough to prove the lemma for the n processor CRCW PRAM that uses only O(n) space. 1) Bast and Hagerup [3] show how to solve strong semisorting in O(log n) time with the desired probability on a CRCW PRAM, provided the input is from [n] For a general input, O(log n) time perfect hashing [2, 10] reduces the problem to the solution of Bast and Hagerup. See also [14, p. 275] 2) The all nearest one problem can be solved in O(ff(n) O(log n) time deterministically on a CRCW PRAM by an algorithm due to Ragde [26] and Berkman and Vishkin [4] 3) Approximate prefix sums can be solved ....

H. Bast and T. Hagerup, Fast and reliable parallel hashing, in Proceedings of the 3rd Annual ACM Symposium on Parallel Algorithms and Architectures, ACM Press, New York, NY, 1991, pp. 50--61.

....in case of three hash functions, in M h0 (x) We refer to the representants of x in the M h i (x) s as its copies. In some simulations we further assume that few, i.e. O(n) keys may be intermediately stored at further positions. This will be done by using a perfect hash table of size O(n) In [1] and [7] it is shown how to implement such a table on a CRCWPRAM using space O(n) in time not exceeding O(log (n) with high probability. Because of the space bound it also can be implemented on a CRCW DMM within the same time bound, as long as only O(n) keys have to be stored in it. 5.1 Fast ....

H. Bast and T. Hagerup. Fast and reliable parallel hashing. In Proc. of the 3rd Ann. ACM Symp. on Parallel Algorithms and Architectures, pages 50--61, 1991.

.... dictionaries that use only one hash function to distribute the shared memory cells over the modules of the DMM have an inherent delay of Theta(log n= log log n) even if the hash function behaves like a random function (see [7] Faster static dictionaries are only known for PRAMs, see [16] and [3]. On such machines constant access time can be achieved using linear space. Karp et al. 13] were the first to consider shared memory simulations using two or more hash functions. They also present a fast implementation of write steps. The simulation runs on an arbitraryDMM with delay O(log log n) ....

....a basis in Section 4 to obtain very fast simulations on an arbitrary DMM. Definition 2.2 Let m n denote the number of keys distributed among n processors such that each processor has at most one key. The linear approximate compaction problem is to insert the keys into an array B of size 4m. In [3] and [16] a randomized algorithm for the LAC problem is presented and analyzed. Their algorithms are designed for a CRCW PRAM that uses n processors and O(n) shared memory cells. As noted in [13] such a PRAM can be simulated on an n processor arbitrary DMM with constant delay. So we get the ....

[Article contains additional citation context not shown here]

H. Bast and T. Hagerup, Fast and reliable parallel hashing, in: Proc. SPAA'95, 50-61.

.... on the properties of a particular p n universal class of hash functions which combines the constructions given in [5] and [13] The structure of these hash functions enables us to analyze the delay in our simulation using a powerful martingale tail estimate that was derived independently in [1] and [10] 2 Computation Models A PRAM consists of processors P 1 ; Pm and a shared memory with cells U = p] The processors work synchronously and have random access to the shared memory cells, each of which can store an integer. We consider EREW PRAMs where concurrent access to the ....

....i is equal to failure . HASH(SM;X) INPUT: A parallel hash table SM containing the set S and an array X of key value pairs (x i ; c(x i ) RESULT: If jS [ X j cn then this operation sets SM equal to a parallel hash table storing S [ X ; otherwise, the operation returns failure . The papers [1] and [9] give randomized algorithms for realizing a parallel hash table of capacity cn on an n processor PRAM. The inputs and outputs of the operations, as well as the parallel hash table itself, reside in the shared memory of the PRAM. The space required for the parallel hash table is c 0 n, ....

[Article contains additional citation context not shown here]

H. Bast and T. Hagerup. Fast and reliable parallel hashing. In Proc. of the 3rd Ann. ACM Symp. on Parallel Algorithms and Architectures, pages 50--61, 1991.

No context found.

Holger Bast and Torben Hagerup. Fast and reliable parallel hashing. In 3rd Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA '91), pages 50--61. ACM Press, 1991.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC