T. Hagerup. Towards optimal parallel bucket sorting. Inform. and Comput. 75, pp. 39-51(1987).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....subproblems are of size n, the overall algorithm runs in O(log log n) time. 2 We can now perform a stable sort of n integers in the range [0: n Gamma 1] in O(log n) time with n log log n= log n processors and O(n ) space on a PRIORITY ERCW(ack) PRAM as follows. As in the CRCW algorithm of [29] we use an n Theta n array (which is assumed to be initialized to zero) For each index i in the input, if element i has value j then a 1 is written into position (i; j) of the array. We then solve the chaining problem on the n Theta n array (interpreted as a 1 Theta n array) to obtain the ....

T. Hagerup. Towards optimal parallel bucket sorting. Inform. and Comp., 75:39--51, 1987.

....Triconnected Components, we note that steps 1, 2 and 4 can be performed optimally in logarithmic time. So can all of the steps in Step 3 except Step 3c, which requires identifying the parent star of a star in a star embedding. This step can be performed using the bucket sort algorithm of Hagerup [10]. It can also be performed optimally in logarithmic time using list ranking and making use of the fact that G c (P 0 i ) is planar. The details of this implementation are given in [8] They are omitted here, since the overall complexity of the algorithm is dominated by the need to perform bucket ....

T. Hagerup, "Towards optimal parallel bucket sorting," Information and Computation, vol. 75, pp. 39-51.

....of some of the steps required new insights into the problem. Our parallel algorithm can be made to run within the same time bound using O( n m) log log n log n ) processors by using the algorithm for finding connected components in [CV86] and the algorithm for integer sorting in [Hag87] Chapter 4 Smallest Triconnectivity Augmentation: Biconnected Graphs 4.1 Introduction In this chapter, we present a linear time sequential algorithm for finding a smallest augmentation to triconnect a biconnected graph. Our sequential algorithm has a similar structure to the one used in ....

.... linear number of processors on a CRCW PRAM [FRT93, Ram93] The algorithm for constructing the 3block tree can be made to run within the same time bound using a sublinear number of processors by using the algorithm for finding connected components in [CV86] and the algorithm for integer sorting in [Hag87] Implied Path in the 3 Block Tree Given two vertices u and v in a biconnected graph G, the implied path between u and v in 3 blk(G) is the path between the two fi vertices that corresponds to the two Tutte components that contain u and v, respectively. An example of an implied path in 3 blk(G) ....

[Article contains additional citation context not shown here]

T. Hagerup. Towards optimal parallel bucket sorting. Information and Computation, 75:39--51, 1987.

.... number of ones, Ram90] Several parallel deterministic and randomized algorithms, that run in time proportional to log n= log log n ( logarithmic level ) or slower, were given for sorting [AKS83] Bat68] BN89] Col88] Hir78] Pre78] RV87] and [SV81] and integer sorting [BDH 89] Hag87] Hag91a] MV90] MV91] RR89a] Ram90] and [Ram91] The lower bound in [BH87] implies that faster algorithms are possible only by relaxing the definition of the problem: 1) MS91] gave a doubly logarithmic level result, assuming the input comes from a certain random source; the output is ....

T. Hagerup. Towards optimal parallel bucket sorting. Information and Computation, 75:39--51, 1987.

....small constant. Cole [7] has given a practical deterministic method of sorting on an EREW comparison PRAM in time O(log n) using O(n) processors. Reif Rajasekaran [30] gave an optimal O(log n) time PRAM algorithm using O(n) processors for integer sorting where key length is log n and Hagerup [12] gave an O(log n) time algorithm using O(n log log n=log n) processors for integer sorting with O(log n) bits key. The known lower bound for list ranking is Omega Gamma 24 n=log log n) expected time (Beame Hastad [2] for all algorithms using polynomial number of processors on CRCW PRAM. ....

T.Hagerup, Towards optimal parallel bucket sorting, Inform. and Comput., 75(1987)39-51.

....the parallelization of some of the steps required new insights into the problem. Our parallel algorithm can be made to run within the same time bound using a sublinear number of processors by using the algorithm for finding connected components in [3] and the algorithm for integer sorting in [9]. ....

T. Hagerup, Towards optimal parallel bucket sorting, Information and Computation, 75 (1987), pp. 39--51.

....and in the naming assignment procedure for substrings over large alphabets [17] For other algorithms, the time increase in [39] was O(lg lg n) or O Gamma (lg lg n) 2 Delta , while our algorithm leaves the expected time unchanged. Such is the case in integer sorting over a polynomial range [33] and over a super polynomial range [5, 39] More applications are discussed in the conclusion section. 1.4 Outline The rest of the paper is organized as follows. Preliminary technicalities used in our algorithm and its analysis are given in Section 2. The algorithm template is presented in ....

T. Hagerup. Towards optimal parallel bucket sorting. Information and Computation, 75:39--51, 1987.

....and in the naming assignment procedure for substrings over large alphabets [17] For other algorithms, the time increase in [39] was O(lg lg n) or O Gamma (lg lg n) 2 Delta , while our algorithm leaves the expected time unchanged. Such is the case in integer sorting over a polynomial range [33] and over a super polynomial range [5, 39] More applications are discussed in the conclusion section. 1.4 Outline The rest of the paper is organized as follows. Preliminary technicalities used in our algorithm and its analysis are given in Section 2. The algorithm template is presented in ....

T. Hagerup. Towards optimal parallel bucket sorting. Information and Computation, 75:39--51, 1987.

....are of size p n, the overall algorithm runs in O(log log n) time. 2 We can now perform a stable sort of n integers in the range [0: n Gamma 1] in O(log n) time with n log log n= log n processors and O(n 2 ) space on a PRIORITY ERCW(ack) PRAM as follows. As in the CRCW algorithm of [29] we use an n Theta n array (which is assumed to be initialized to zero) For each index i in the input, if element i has value j then a 1 is written into position (i; j) of the array. We then solve the chaining problem on the n Theta n array (interpreted as a 1 Theta n 2 array) to obtain the ....

T. Hagerup. Towards optimal parallel bucket sorting. Inform. and Comp., 75:39--51, 1987.

....are of size p n, the overall algorithm runs in O(log log n) time. 2 We can now perform a stable sort of n integers in the range [0: n Gamma 1] in O(log n) time with n log log n= log n processors and O(n 2 ) space on a PRIORITY ERCW(ack) PRAM as follows. As in the CRCW algorithm of [36] we use an n Theta n array (which is assumed to be initialized to zero) For each index i in the input, if element i has value j then a 1 is written into position (i; j) of the array. We then solve the chaining problem on the n Theta n array (interpreted as a 1 Theta n 2 array) to obtain the ....

T. Hagerup. Towards optimal parallel bucket sorting. Inform. and Comp., 75:39--51, 1987.

....for any constant c 1 [RR89] The integer sorting algorithm of Rajasekaran and Reif cannot be extended for m polynomial in n. For m = poly(n) Hagerup provided an O(log n) time and O(n 1 ffl ) space (for any fixed ffl 0) parallel algorithm, using n log log n= log n priority CRCW processors [Hag87] No optimal parallel algorithm is known for this range. Our sorting algorithm clearly belongs in the second approach. Using data structures presented by van Emde Boas, Kaas and Zijlstra [vKZ77] Johnson [Joh82] dealt with priority queues problems, where the priorities are drawn from the integer ....

....processors; and (2) O(log n (log log m) 2 ) time and O(n 2 m ffl ) space (ffl 0) using n(log log m) 2 log n arbitrary CRCW processors. Some of the ideas we use in the deterministic algorithms of Section 2 go back to [vKZ77] These ideas were inspired also by the algorithms of [Hag87] and [Joh82] Johnson s algorithm has the same complexity as our deterministic serial algorithm. However, our sorting algorithm has two advantages: it is simpler and parallelizable. The so called DNN algorithm of Section 2 implies efficient algorithms for the ordered chaining and for the ordered ....

[Article contains additional citation context not shown here]

T. Hagerup. Towards optimal parallel bucket sorting. Information and Computation, 75:39--51, 1987.

....of each of the sets of identical edges is kept as useful while the rest are nullified as redundant. This is done as follows: First, we sort the edge list of each component in lexicographical order. We note that there are O(log n) time, n processor, sorting algorithms for both the CREW PRAM model [8, 2, 14] and the CREW PPM model [13] Then, blocks of redundant edges are identified and nullified. This step takes O(log n) time using m processors. ffl The edge list of each component is prepared by deleting all the null edges. Each of these steps take O(log n) parallel running time. So, the total ....

T. Hagerup. Towards optimal parallel bucket sorting. Informaton and Computation, 75:39--51, 1987.

No context found.

T. Hagerup. Towards optimal parallel bucket sorting. Inform. and Comput. 75, pp. 39-51(1987).

No context found.

T. Hagerup, Towards optimal parallel bucket sorting, Inform. and Comput., 75, 39-51(1987).

No context found.

T. Hagerup, Towards optimal parallel bucket sorting, Inform. and Comput. 75, pp. 3951 (1987).

No context found.

Hagerup, T., Toward optimal parallel bucket sorting, Information and Computation 75 (1987), pp. 39--51.

No context found.

Hagerup, T., Toward optimal parallel bucket sorting, Information and Computation 75 (1987), pp. 39--51.

No context found.

Hagerup, T., Toward optimal parallel bucket sorting, Information and Computation 75 (1987), pp. 39--51.

No context found.

Hagerup,T., "Towards Optimal Parallel Bucket Sorting," Information and Computation 75, 1987, pp.39-51.

No context found.

T. Hagerup, "Towards optimal parallel bucket sorting," Inform. and Comput. , vol. 75, 1987, pp. 39-51.

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