Awerbuch, B. and Shiloach, Y. New connectivity and MSF algorithms for ultracomputer and PRAM. Proc. of  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of [19] from a purely parallel model to the model of this paper. A brief description of the algorithm of [19] is given in the Appendix. The idea of breaking cycles (in the pointer graphs ) using a method different from the common one (used, e.g. in [19] as well as from the method used in [1] (within an algorithm for computing a minimum spanning tree, which is in itself a variant of [19] Compared to [19] we use hook on smalles as opposed to hook on smaller. This idea simplified the algorithm by saving a second round of hookings in each iteration. Such a second round was needed ....

....tree did not shortcut) in the current iteration; without such a second round, the parallel running time went up from O(logn) to linear in n. Unlike the parallel computation 15 model in [19] the distributed model of the current paper readily allows to provide the smallest value. Compared to [1] we use hook on smallest known, as opposed to hook on absolute smallest used in [1] We cannot use the method of [1] since in the directed model, a vertex may not be aware of its minimum outgoing arc. The vertex may learn of that arc by a message from the other endpoint of that arc, however, ....

[Article contains additional citation context not shown here]

B. Awerbuch, and Y. Shiloach. New Connectivity and MSF Algorithms for Ultracom- puter and PRAM. IEEE transactions on Computers, Vol. 36, pp. 1258-1263, 1987.

....of processors and the PRAM. Before discusing our results, we discus the most significant previous results for the problem of checking the correctness of an MST. Throughout this chapter, let n be the number of nodes in the graph G, and m be the number of edges in G. In addition, let N = n m. In [9], Alon and Schieber present an O(n(n) m) time sequential algorithm for checking MSTs, where O( n) is any function from a class of very slow growing functions (of which O(log (n) otherwise known as the iterated log function, is a member) They show how their algorithm can be implemented to ....

Awerbuch, B., and Shiloach, Y., "New Connectivity and MSF Algorithms for Ultracomputer and PRAM", IEEE ICPP 1983 pp. 175-179.

....2D40 and 3D20 have a large number of components, graphs of type 2D60, 3D40 and AD3 are highly connected, and most graphs of type AD3E consist of one component only. 3. 1 Parallel algorithm There has been a lot of publications on parallel distributed algorithms for the connected components problem [16, 17, 18, 7, 2]. Most of these algorithms were designed for PRAM. Algorithm. We chose the algorithm by Krishnamurthy e.a. 7] because it seemed easy to implement and practical results for comparison were provided. It is a refinement of the algorithm by Shiloach and Vishkin [2] In the following we only give an ....

Awerbuch, B., Y. Shiloach, New connectivity and MSF algorithms for Ultracomputer and PRAM, International Conference on Parallel Processing, 1983, pp. 175-179.

....points in 3 space. iii) can be obtained in O(log n) time from the Voronoi diagram. iv) can be obtained by running a minimal spanning tree algorithm on the edges of Delaunay triangulation which is the dual graph of the Voronoi diagram. This algorithm uses the stronger Priority CRCW model as in [3] 2 7 Bounding random bits 7.1 Chebychev s inequality The commonly used form of Chebychev s inequality has the form: P rob[ jX j t) 2 t 2 . This simple fact was exploited by Chor and Goldreich [5] for their 2 point sampling theorem where they consider the following scenario. To ....

B. Awerbuch and Y. Shiloach. New connectivity and msf algorithms for ultracomputer and pram. Proc. of the Int'l Conf. on Parallel Processing, pages 175-179, 1983.

....problem. Hirschberg et. al [Hir76, HCS79, CLC82] showed an O(n 2 ) work algorithm for CREW PRAMs. This algorithm starts with the adjacency matrix of the graph and shrinks the graph based on local connectiviety information at each step, recomputing the new matrix each time. Shiloach et. al [SV82, AS87] use a similar idea for sparse graphs. This CRCW PRAM algorithm starts with a list of edges, forming trees of connected vertices and grafting smaller trees to form larger trees till all vertices of a component are in the same tree. The work complexity of this algorithm is O( m n) log n) m being ....

B. Awerbuch and Y. Shiloach. New connectivity and msf algorithms for ultracomputer and pram. IEEE Transactions on Computers, 36(10):1258--1263, 1987.

....vertex will only be visited once. A new frontier is generated by collecting all the neighbors of the current frontier vertices in parallel and removing any that have already been visited. This is 4 5 6 7 9 11 12 14 13 15 10 0 1 2 3 8 (a) Step Frontier 0 [0] 1 [1, 4] 2 [2, 5, 8] 3 [3, 6, 9, 12] 5 [7, 10, 13] 6 [11, 14] 7 [15] b) 4 5 6 7 9 11 12 14 13 15 10 0 1 2 3 8 (c) Figure 6: Example of Parallel Breadth First Search. a) A graph G. b) The frontier at each step of the BFS of G with s = 0. c) A BFS tree. not sufficient on its own, however, since multiple vertices might collect the same ....

....although the depth has increased. 4.3.3 Improved Versions of Connected Components There are many improvements to the two basic connected component algorithms we described. Here we mention some of them. The deterministic algorithm can be improved to run in O(log n) depth with the same work bounds [10, 68]. The basic idea is to interleave the hooking steps with the shortcutting steps. The one tricky aspect is that we must always hook in the same direction (i.e. from smaller to larger) so as not to create cycles. Our previous technique to solve the star graph problem therefore does not work. ....

Baruch Awerbuch and Yossi Shiloach. New connectivity and MSF algorithms for Ultracomputer and PRAM. In Proceedings International Conference on Parallel Processing, pages 175--179, 1983.

....computer science theory courses as an application of depth first and breadth first search. Parallel solutions have received a great deal of attention from both theorists and practical computer scientists, and have proven difficult. Theoretical work shows good results on the CRCW PRAM model[3, 10, 11, 24], which assumes uniform memory access time and arbitrary bandwidth to any memory location. This material is based upon work supported under a National Science Foundation Presidential Faculty Fellowship Award, a Graduate Research Fellowship, and Infrastructure Grant number CDA 8722788, as well ....

B. Awerbuch, Y. Shiloach, "New Connectivity and MSF Algorithms for Ultracomputer and PRAM," International Conference on Parallel Processing, 1983, pp. 175-179.

....Note that the above strategy still yields a valid MH when we insert an item starting from any empty leaf of address different from N 0 M . In particular, the deletion algorithm described in the following subsection creates a hole in the structure at the target leaf of the root, L = ML [1]. The hole is then refilled by performing an insertion starting from L. The following procedure INSERT implements the above ideas. Parameter L is the address of a leaf, while parameter I is the item to be inserted. INSERT uses the auxiliary vectors VH and VL to perform operations on the elements ....

....simply considering k as a leaf node and running a slight variant of INSERT with parameters k and v. The details of the algorithm are omitted for the sake of brevity. 2.2 Deletion The algorithm for deleting the root of an MH M proceeds in three phases: 1. Let 1 = fn 1 = 1; n h = L = ML [1]g be the min path of the root of M . The root item MH [1] is returned and the target leaf of the root L = ML [1] is broadcast to all the processors. 2. Nodes n 2 ; n h are shifted one position above, that is, MH [n i ] MH [n i 1 ] for technical reasons, we set M [n h ] 1) Note that ....

[Article contains additional citation context not shown here]

B.Auerbuch and Y.Shiloach, New Connectivity and MSF Algorithms for Ultracomputer and PRAM, in: Proc. of the 1983 Int. Conf. on Parallel Processing (1983) 298-319.

....solutions are well understood and commonly used as an application of depth first and breadth first search. Parallel solutions have received a great deal of attention from theorists, and have proven difficult. Algorithms such as Shiloach Vishkin obtain good results with the CRCW PRAM model [3, 11, 12, 28], which assumes uniform memory access time and Copyright 1995 by the Association for Computing Machinery, Inc. ACM) Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for ....

B. Awerbuch, Y. Shiloach, "New Connectivity and MSF Algorithms for Ultracomputer and PRAM," International Conference on Parallel Processing, 1983, pp. 175-179.

....in terms of work and steps is also critical in being able to compose the complexities. In addition to the examples in this paper, many other algorithms have been coded in Nesl, including quicksort, radixsort, mergesort, the Shiloach Vishkin and Awerbuch Shiloach connected components algorithms [25, 2], a randomized work efficient list ranking algorithm [19] various tree operations based on Euler tours [26] an algorithm for matching parentheses in a string, and a graph separator algorithm [18] Acknowledgments I would like to thank Marco Zagha, Tim Freeman, Jay Sipelstein, Margaret ....

Baruch Awerbuch and Yossi Shiloach. New connectivity and msf algorithms for ultracomputer and pram. In Proceedings International Conference on Parallel Processing, pages 175--179, 1983.

....used by the algorithms in this paper is stored in vectors (one dimensional arrays) in the shared memory and that each processor is assigned to one element of the vector. When executing an operation, the i th processor operates on the i th element of a vector. For example, in the operation: A = [5 1 3 4 3 9 2 6] B = 2 5 3 8 1 3 6 2] C A B = 7 6 6 12 4 12 8 8] each processor reads its respective value from the vectors A and B, sums the values, and writes the result into the destination vector C. Initially, we assume that the P RAM always has as many processors as vector elements. The scan primitives ....

....in this paper is stored in vectors (one dimensional arrays) in the shared memory and that each processor is assigned to one element of the vector. When executing an operation, the i th processor operates on the i th element of a vector. For example, in the operation: A = 5 1 3 4 3 9 2 6] B = [2 5 3 8 1 3 6 2] C A B = 7 6 6 12 4 12 8 8] each processor reads its respective value from the vectors A and B, sums the values, and writes the result into the destination vector C. Initially, we assume that the P RAM always has as many processors as vector elements. The scan primitives can be used to scan ....

[Article contains additional citation context not shown here]

Baruch Awerbuch and Yossi Shiloach. New connectivity and MSF algorithms for Ultracomputer and PRAM. In Proceedings ACM Symposium on Theory of Computing, pages 175--179, 1985.

....PRINS CRCW model and has variants with reasonable work efficiency for sparse and dense graphs. The initial presentation of the algorithm, A 0 , is for the CREW PRAM model of computation and is based on ideas found in the CRCW PRAM algorithms for sparse graphs developed by Shiloach et al. in [SV82, AS87] For a graph G with n vertices and m edges, A 0 requires at most O(log n) parallel steps and performs O( n m) log n) work (hence, like [SV82, AS87] is not quite work efficient) A 0 differs from [SV82, AS87] in that it can be adapted to a 2 D mesh connected communication model in which all ....

.... CREW PRAM model of computation and is based on ideas found in the CRCW PRAM algorithms for sparse graphs developed by Shiloach et al. in [SV82, AS87] For a graph G with n vertices and m edges, A 0 requires at most O(log n) parallel steps and performs O( n m) log n) work (hence, like [SV82, AS87] is not quite work efficient) A 0 differs from [SV82, AS87] in that it can be adapted to a 2 D mesh connected communication model in which all CREW operations are replaced by parallel row and column operations. In the case of the MasPar MP 1 and MP 2 machines that are the implementation ....

[Article contains additional citation context not shown here]

B. Awerbuch and Y. Shiloach. New connectivity and MSF algorithms for Ultracomputer and PRAM. IEEE Transactions on Computers, 36(10):1258--1263, 1987.

....jdg cs.cmu.edu Abstract This paper presents a comparison of the pragmatic aspects of some parallel algorithms for finding connected components, together with optimizations on these algorithms. The algorithms being compared are two similar algorithms by Shiloach Vishkin [22] and Awerbuch Shiloach [2], a randomized contraction algorithm based on algorithms by Reif [21] and Phillips [20] and a hybrid algorithm [11] Improvements are given for the first two to improve performance significantly, although without improving their asymptotic complexity. The hybrid combines features of the others ....

.... Much of the previous pragmatic work has been restricted to the 2D and 3D grids that are of interest in these areas, e.g. 1, 7, 8, 12, 17, 16, 18, 26] This paper compares implementations and provides optimizations of four algorithms, those of Shiloach Vishkin (SV) 22] Awerbuch Shiloach (AS) [2], a random mate (RM) algorithm [10] and a hybrid (HY) of the previous three [11] The first two algorithms are quite similar and require O(m log n) work and O(log n) time. The randomized algorithm combines the random mating of Reif [21] with the graph contraction of Phillips [20] and requires ....

[Article contains additional citation context not shown here]

B. Awerbuch and Y. Shiloach. New connectivity and MSF algorithms for Ultracomputer and PRAM. In Proceedings of the International Conference on Parallel Processing, pages 175--179, 1983.

....arbitrary CRCW ( SV82a] one of the processors succeeds, but we do not know in advance which one. In the priority CRCW ( Gol82] the smallest numbered among the processors succeeds. The above three CRCW models are considered standard. Next we mention two non standard models. In the min CRCW PRAM ( AS83] the processor that tries to write the minimum value succeeds. In the fetch add CRCW PRAM ( Vis83a] the values are added to the value already written in the shared memory location and all sums obtained in the (virtual) serial process are recorded. Finally, in an exclusive read exclusive write ....

B. Awerbuch and Y. Shiloach. New connectivity and MSF algorithms for Ultracomputer and PRAM. In Proc. International Conference on Parallel Processing, pages 175--179, 1983.

....Science Carnegie Mellon University Pittsburgh, PA 15213 Abstract This paper presents a pragmatic comparison of three parallel algorithms for finding connected components, together with optimizations on these algorithms. Those being compared are two similar algorithms by Awerbuch and Shiloach [2] and by Shiloach and Vishkin [19] and a randomized contraction algorithm by Blelloch [7] based on algorithms by Reif [18] and Phillips [17] Major improvements are given for the first two which significantly reduces the super linear component of their work complexity. An improvement is also given ....

....the connected components of a graph, some of which are provably work optimal. Much less work has pursued the pragmatic aspects of these algorithms. This paper compares implementations and provides optimizations of three algorithms, those of Shiloach and Vishkin [19] Awerbuch and Shiloach (A S) [2], and a random mate (RM) algorithm of Blelloch [7] The former two algorithms are quite similar and require O(m log n) work. The latter randomized algorithm uses the random mating of Reif [18] combined with the graph contraction of Phillips [17] This algorithm is also O(m log n) work in the ....

[Article contains additional citation context not shown here]

Awerbuch, B. and Shiloach, Y. New Connectivity and MSF Algorithms for Ultracomputer and PRAM. In Proceedings of the International Conference on Parallel Processing, pages 175-179. 1983.

No context found.

Awerbuch, B. and Shiloach, Y. New connectivity and MSF algorithms for ultracomputer and PRAM. Proc. of

No context found.

B. Awerbuch and Y. Shiloach, New connectivity and MSF algorithms for ultracomputer and PRAM, IEEE Trans. Computers 36 (1987) 1258-1263.

No context found.

Baruch Awerbuch and Yossi Shiloach. New connectivity and MSF algorithms for Ultracomputer and PRAM. In Proceedings International Conference on Parallel Processing, pages 175--179, 1983.

No context found.

B. Awerbuch, and Y. Shiloach. New connectivity and MSF algorithms for Ultracomputer and PRAM. IEEE transactions on Computers, Vol. 36, pp. 1258-1263, 1987.

No context found.

B. Awerbuch and Y. Shiloach. New connectivity and MSF algorithms for Ultracomputer and PRAM. IEEE Trans. on Computers, 36:1258--1263, 1987.

No context found.

B. Awerbuch, and Y. Shiloach. New Connectivity and MSF Algorithms for Ultracomputer and PRAM. IEEE transactions on Computers, Vol. 36, pp. 1258-1263, 1987.

No context found.

B. Awerbuch and Y. Shiloach. New Connectivity and MSF Algorithms for Ultracomputer and PRAM. IEEE Trans. on Computers 36, (1987), 1258--1263.

No context found.

Awerbuch, B. and Shiloach, Y. "New connectivity and MSF algorithms for ultracomputer and PRAM" International conference on parallel processing, 1983, p175-179.

No context found.

B. Awerbuch and Y. Shiloach. New connectivity and MSF algorithms for Ultracomputer and PRAM. IEEE Transactions on Computers 36 #1987#, pp. 1258# 1263.

No context found.

Awerbuch, B. and Shiloach, Y. "New connectivity and MSF algorithms for ultracomputer and PRAM" International conference on parallel processing, 1983, p175-179.

First 50 documents

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