. H. Jung, K. Mehlhorn. Parallel algorithms for computing maximal independent sets in trees and for updating minimum spanning trees, Information Processing Letters, Vol. 27, No. 5, 227-236(1988).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....employed by those algorithms. 9 Table 1. Performance of Parallel MST Algorithms Under Single Vertex Update Researchers PRAM model Time Complexity Work Vertex Insertion Pawagi Ramakrishnan [35] CREW O(log n) O(n 2 log n) Varman Doshi [44] CREW O(log n) O(n log n) Jung Mehlhorn [24] CRCW O(log n) O(n) Pawagi Kaser [33] CREW O(log n) O(n) Johnson Metaxas [22] EREW O(log n) O(n) Vertex Deletion Tsin [43] CREW O(log n) O(n 2 log n) Pawagi Kaser [33] CREW O(log n log 2 d) O(n 2 (1 log 2 d log n ) Shen Liang [39] CREW O(log n log d) O(n 2 ) ....

....the same time and processor bounds. The processor bound for the single vertex insertion has been improved by Varman and Doshi [44] to O(n) processors. However, the work of their algorithm is O(n log n) which is a O(log n) factor away from the optimal work of O(n) Later, Jung and Mehlhorn [24] gave an optimal algorithm to treat vertex insertions on the powerful CRCW PRAM model, requiring O(log n) time and Theta(n) total work. Recently, Johnson and Metaxas [22] proposed another optimal algorithm for vertex insertions on the weaker EREW PRAM model, having the same time and work bounds ....

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H. Jung and K. Mehlhorn. Parallel algorithms for computing maximal independent sets in trees and for updating minimum spanning trees. Information Processing Letters, 27(5):227--236, 1988.

.... be returned as soon as it is available [32, 40, 56] It is helpful to note here that, when no deadlines are imposed, computations for which inputs arrive while the algorithm is in progress are referred to as on line [27, 33, 35, 36] incremental [21, 22, 49, 59] dynamic [11, 12, 67] and updating [20, 23, 28, 38, 53, 54, 62, 66]. It is also important to note that our definition, while striving to be as general as possible, is particularly suitable for our purposes in this paper. Many other definitions exist; see, for example, the various interpretations of the notion of real time provided in [10, 42, 65] 2.2 Models of ....

H. Jung and K. Mehlhorn, Parallel algorithms for computing maximal independent sets in trees and for updating minimum spanning trees, Information Processing Letters , 27, 1988, 227--236.

.... be returned as soon as it is available [31, 39, 55] It is helpful to note here that, when no deadlines are imposed, computations for which inputs arrive while the algorithm is in progress are referred to as on line [26, 32, 34, 35] incremental [20, 21, 48, 58] dynamic [10, 11, 66] and updating [19, 22, 27, 37, 52, 53, 61, 65]. It is also important to note that our definition, while striving to be as general as possible, is particularly suitable for our purposes in this paper. Many other definitions exist; see, for example, the various interpretations of the notion of real time provided in [9, 41, 64] 2.2 Models of ....

H. Jung and K. Mehlhorn, Parallel algorithms for computing maximal independent sets in trees and for updating minimum spanning trees, Information Processing Letters, 27, 1988, 227--236.

.... returned as soon as it is available [21, 28, 37] It is helpful to note here that, when no deadlines are imposed, computations for which inputs arrive while the algorithm is in progress are referred to as on line [18, 22, 23, 24] incremental [14, 15, 32, 39] dynamic [7, 8, 44] and updating [13, 16, 19, 26, 34, 35, 41, 43]. 2.2 Real time optimization The first example of a computation for which a parallel solution is consistently better than a sequential one was provided by real time optimization. The realtime weighted spanning tree problem is defined as follows: 1. The minimum weight spanning tree (MST) of an ....

H. Jung and K. Mehlhorn, Parallel algorithms for computing maximal independent sets in trees and for updating minimum spanning trees, Information Processing Letters , 27, 1988, 227--236.

....uses n CREW PRAM processors. They use divide and conquer to split the problem into approximately p n equally sized subproblems which they solve recursively. Even though their idea is rather simple, the implementation details make the algorithm rather complex. More recently, Jung and Mehlhorn [5] have given an optimal solution for the more powerful CRCW PRAM model by reduction to an all sub expression evaluation problem. They use an optimal tree contraction algorithm as a subroutine, as do we. However, their approach to breaking cycles is different from ours. In our case, we are able to ....

....the right path are always included into the new MST. Therefore, the solution of the binarized problem shows a corresponding unique and unambiguous solution to the general problem. 2 Similar binarization techniques to the one described have been used in [4] 11] and [13] Another technique [5] plants a balanced binary tree over the v i s with v as the root. The internal nodes and the internal edges have weights as those in the right path in the previously described technique. Both constructions require the list ranking algorithm [19, 20] which runs within the desired bounds. ....

H. Jung and K. Mehlhorn. Parallel algorithms for computing maximal independent sets in trees and for updating minimum spanning trees. Information Processing Letters, 27(5):227--236, April, 28 1988.

....of computing a solution. The newly arrived data must be incorporated in the solution at hand. The final solution is to be returned by a certain deadline. Real time computations form a subclass of a larger class of problems known variably as on line, incremental , dynamic, and updating computations [7, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 30, 31, 32, 36, 38, 40, 41]. What distinguishes a real time problem from problems in the larger class is the presence of deadlines by which the input is to be processed, by which the output is to be produced, and so on. 3 Modern Cryptography The purpose of contemporary cryptography is the protection of digital ....

H. Jung and K. Mehlhorn, Parallel algorithms for computing maximal independent sets in trees and for updating minimum spanning trees, Information Processing Letters , 27, 1988, 227--236.

....simultaneously in constant time. Varman and Doshi [19] presented an efficient solution that works in the same parallel time, but uses n CREW PRAM processors. Even though their idea is rather simple, the implementation details make the algorithm rather complex. More recently, Jung and Mehlhorn [9] have given an optimal solution for the more powerful CRCW PRAM model by reduction to an expression evaluation problem. They use an optimal tree contraction algorithm as a subroutine, as do we. However, their approach to breaking cycles is different from ours and appears to require concurrent ....

....require concurrent writing if the running time of O(log n) is to be preserved. In our case, we are able to restrict consideration of cycles to those with no more than four vertices and, as we will show, they can 1 We denote log 2 n by lg n. be treated without concurrent writing. Simulating the [9] algorithm without concurrent writing slows down its performance by a factor of lg n. As indicated above, the model of parallel computation we will use throughout this paper is the EREW PRAM (exclusive read exclusive write parallel random access machine) 10] Representation. Upon introducing ....

H. Jung and K. Mehlhorn. Parallel algorithms for computing maximal independent sets in trees and for updating minimum spanning trees. IPL, 27(5):227--236, April, 28 1988.

....only 2n 2k Gamma 3 edges, some edges are removed more than once , so to speak. This can be done in O(1) time and at most (n k) Theta Gamma n k Gamma1 2 Delta processors on the CRCW PRAM using the MAXIMUM rule for resolving write conflicts. Variants of this algorithm are described in [10, 20, 26, 27, 30, 33, 34]. Additional examples of real time optimization problems can be easily developed along the same lines outlined in this paper. These include the problems listed in section 2.1, namely, those calling for the computation of shortest paths, maximum sum subsequences, and minimum weight matchings. ....

H. Jung and K. Mehlhorn, Parallel algorithms for computing maximal independent sets in trees and for updating minimum spanning trees, Information Processing Letters , 27, 1988, 227--236.

....vertex in V . We want to compute a new MST T 0 = V [ fzg; E 0 ) The updating MST problem arizes often in practice in very diverse areas that vary from VLSI design and Artificial Intelligence to Operations Research and Economics. The problem has been addressed in the past in both the parallel [PR86, VD86, JM88, JM92a] and sequential settings. Optimal sequential algorithms have been given in [SP75, CH78] GPS87] JM92a] JM92a] JM92b] JM91] CV89] AV84] MR86] Growth Control Schedule [CV88] ADKP89] TV85] Augmentation Edge list M.S.T. M.I.S. connectivity 2 edge Updating M.S.T. Multiple Planar graphs ....

H. Jung and K. Mehlhorn. Parallel algorithms for computing maximal independent sets in trees and for updating minimum spanning trees. Information Processing Letters, 27(5):227--236, April, 28 1988.

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. H. Jung, K. Mehlhorn. Parallel algorithms for computing maximal independent sets in trees and for updating minimum spanning trees, Information Processing Letters, Vol. 27, No. 5, 227-236(1988).

No context found.

. H. Jung, K. Mehlhorn. Parallel algorithms for computing maximal independent sets in trees and for updating minimum spanning trees, Information Processing Letters, Vol. 27, No. 5, 227-236(1988).

No context found.

H. Jung and K. Mehlhorn, Parallel algorithms for computing maximal independent sets in trees and for updating minimum spanning trees, Information Processing Letters , 27, 1988, 227--236.

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