Parallel directed graph algorithms on directional processor arrays with reconfigurable bus systems

Kuo, Chi-Jung; Hsu, Cheng–Che; Fang, Wei-Chen

doi:10.1007/bf03037435

Cited by 2 publications

(4 citation statements)

References 12 publications

(1 reference statement)

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“…In Figure 6, the numbers in the two 4-th rows are the indexes of parents and we construct the tree with root vertex V 4 as shown in Figure 7. For example, the white thick nodes in the right R-Mesh, processor (4, 2, 4) and processor (4,3,4) in Figure 6, will be merged by < 1, . .…”

Section: Cyclic Checking Algorithmmentioning

confidence: 99%

“…For example, there are reconfigurable mesh, directional reconfigurable mesh, processor arrays with reconfigurable bus systems, complete directional processor arrays with reconfigurable bus systems, reconfigurable multiple bus machine, directional reconfigurable multiple bus machine, and etc. As we know, many constant-time undirected graph algorithms have be proposed on R-Mesh, PARBS, and RMBM [1,2,6,8,10] and many constanttime digraph algorithms have be proposed on DR-Mesh, CD-PARBS, directional RMBM [3,6,8]. The main difference between directional and non-directional models is that DR-Mesh, CD-PARBS, and directional RMBM can control the data flow in each segment of a bus.…”

Section: Introductionmentioning

confidence: 99%

“…The main difference between directional and non-directional models is that DR-Mesh, CD-PARBS, and directional RMBM can control the data flow in each segment of a bus. This is the most important reason why researchers proposed the directional models, and therefore they can resolve the digraph problems on such models [3,6,8]. Besides digraph algorithms on the directional models, the algebraic path problems (APP) of digraphs, such as transitive closure, all pairs shortest paths, and minimum spanning tree, can be resolved in O(log n) time by using the matrix multiplication algorithm on the non-directional models [4,8].…”

Section: Introductionmentioning

confidence: 99%

“…The second approach for some digraph problems is using the directional models. On such models, researchers can design the O(1) time digraph algorithms for their specified digraph problems [3,6,8]. The constant-time algorithms on the directional models for digraph problems which are based on the s-t connectivity algorithm have the outstanding feature: the digraph is embedded in an n × n directional reconfigurable model, a signal is sent from a specified processor (s, s) representing the source vertex s, and the target vertex t is connected to the source vertex s if and only if processor (t, t) received the signal.…”

Section: Introductionmentioning

confidence: 99%

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The Transitive Closure and Related Algorithms of Digraph on the Reconfigurable Architecture

Pan

Lin

2011

Parallel Process. Lett.

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The reconfigurable architecture is a parallel computation model that consists of many processor elements (PEs) and a reconfigurable bus system. There are many variant proposed reconfigurable architectures, for example, reconfigurable mesh (R-Mesh), directional reconfigurable mesh (DR-Mesh), processor arrays with reconfigurable bus systems (PARBS), complete directional processor arrays with reconfigurable bus systems (CD-PARBS), reconfigurable multiple bus machine (RMBM), directional reconfigurable multiple bus machine (directional RMBM), and etc. In this paper, a transitive closure (TC) algorithm of digraph is proposed on the models without the directional capability (non-directional). Some related digraph problems, such as strongly connected digraph, strongly connected component (SCC), cyclic checking, and tree construction, can also be resolved by modifying our transitive closure algorithm. All the proposed algorithms are designed on a three-dimensional (3-D) n×n×n non-directional reconfigurable mesh, n is the number of vertices in a digraph D, and can resolve the respective problems in O(log d(D)) time, d(D) is the diameter of the digraph D. The cyclic checking problem can be further reduced to O(log c(D)) time, c(D) is the minimum distance of cycles in the digraph D. There exist two different approaches: the matrix multiplication approach on the non-directional models for algebraic path problems (APP) and s-t connectivity approach on the directional models. In this paper, we will use the tree construction algorithm to prove those two approaches are insufficient to resolve all digraph problems and demonstrate why our approach is so important and innovative for digraph problems on the reconfigurable models.

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Section: Cyclic Checking Algorithmmentioning

confidence: 99%