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149
Embedding of Tree Networks into Hypercubes
, 1985
"... The hypercube is a good host graph for the embedding of networks of processors because of its low degree and low diameter. Graphs such as trees and arrays can be embedded into a hypercube with small dilation and expansion costs, but there are classes of graphs which can be embedded into a hypercube ..."
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Cited by 26 (0 self)
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The hypercube is a good host graph for the embedding of networks of processors because of its low degree and low diameter. Graphs such as trees and arrays can be embedded into a hypercube with small dilation and expansion costs, but there are classes of graphs which can be embedded into a hypercube only with large expansion COSt or large dilation cost.
Optimal Distributed Algorithms in Unlabelled Tori and Chordal Rings
, 1996
"... We study the message complexity of distributed algorithms in Tori and Chordal Rings when the communication links are unlabelled, which implies that the processors do not have "Sense of Direction". We introduce the paradigm of handrail which allows messages to travel with a consistent direction. We g ..."
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Cited by 25 (12 self)
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We study the message complexity of distributed algorithms in Tori and Chordal Rings when the communication links are unlabelled, which implies that the processors do not have "Sense of Direction". We introduce the paradigm of handrail which allows messages to travel with a consistent direction. We give a distributed algorithm which confirms the conjecture that the Leader Election problem for unlabelled Tori of N processors can be solved using #(N) messages instead of O(N log N ). Using the same handrail paradigm, we solve the Election problem using #(N) messages in unlabelled chordal rings with one chord (of length approximately # N ). This solves a longstanding open problem of the minimal number of unlabelled chords required to decrease to decrease the O(N log N) message complexity. For each topology, we give an algorithm to compute the Sense of Direction in #(N) messages (improving the O(N log N) previous results). This proves the more fundamental result that any global...
A comparison of shared and nonshared memory models of parallel computation
 Proceedings of the IEEE
, 1991
"... Four algorithms are analyzed in the shared and nonshared (distributed) memory models ofparallel computation. The analysis shows that the shared memory model predicts optimality for algorithms and programming styles that cannot be realized on any physical parallel computers. Programs based on these t ..."
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Cited by 23 (4 self)
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Four algorithms are analyzed in the shared and nonshared (distributed) memory models ofparallel computation. The analysis shows that the shared memory model predicts optimality for algorithms and programming styles that cannot be realized on any physical parallel computers. Programs based on these techniques are inferior to programs wrinen in the nonshared memory model. The “unit ” cost charged for a reference to shared memory is argued to be the source of the shared memory model’s inaccuracy. The implications of these observations are discussed. I.
DualCubes: A New Interconnection Network For HighPerformance Computer Clusters
, 2000
"... The binary hypercube, or ncube, has been widely used as the interconnection network in parallel computers. However, the major drawback of the hypercube is the increase in the number of communication links for each node with the increase in the total number of nodes in the system. This paper introdu ..."
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Cited by 21 (19 self)
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The binary hypercube, or ncube, has been widely used as the interconnection network in parallel computers. However, the major drawback of the hypercube is the increase in the number of communication links for each node with the increase in the total number of nodes in the system. This paper introduces a new interconnection network for largescale distributed memory multiprocessors called dualcube. This network mitigates the problem of increasing number of links in the largescale hypercube network while keeps most of the topological properties of the hypercube network. We investigate the topological properties of the dualcube, compare them with other hypercubelike networks, and establish the basic routing and broadcasting algorithms for dualcubes. 1.
Perfect Dominating Sets
, 1990
"... A dominating set S of a graph G is perfect if each vertex of G is dominated by exactly one vertex in S. We study the existence and construction of PDSs in families of graphs arising from the interconnection networks of parallel computers. These include trees, dags, seriesparallel graphs, meshes, to ..."
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Cited by 18 (2 self)
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A dominating set S of a graph G is perfect if each vertex of G is dominated by exactly one vertex in S. We study the existence and construction of PDSs in families of graphs arising from the interconnection networks of parallel computers. These include trees, dags, seriesparallel graphs, meshes, tori, hypercubes, cubeconnected cycles, cubeconnected paths, and de Bruijn graphs. For trees, dags, and seriesparallel graphs we give linear time algorithms that determine if a PDS exists, and generate a PDS when one does. For 2 and 3dimensional meshes, 2dimensional tori, hypercubes, and cubeconnected paths we completely characterize which graphs have a PDS, and the structure of all PDSs. For higher dimensional meshes and tori, cubeconnected cycles, and de Bruijn graphs, we show the existence of a PDS in infinitely many cases, but our characterization is not complete. Our results include distance ddomination for arbitrary d. 1 Introduction Suppose G = (V; E) is a graph with vertex se...
Periodically regular chordal rings
 IEEE Transactions on parallel and Distributed Systems
, 1999
"... AbstractÐChordal rings have been proposed in the past as networks that combine the simple routing framework of rings with the lower diameter, wider bisection, and higher resilience of other architectures. Virtually all proposed chordal ring networks are nodesymmetric, i.e., all nodes have the same i ..."
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Cited by 16 (9 self)
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AbstractÐChordal rings have been proposed in the past as networks that combine the simple routing framework of rings with the lower diameter, wider bisection, and higher resilience of other architectures. Virtually all proposed chordal ring networks are nodesymmetric, i.e., all nodes have the same in/out degree and interconnection pattern. Unfortunately, such regular chordal rings are not scalable. In this paper, periodically regular chordal (PRC) ring networks are proposed as a compromise for combining low node degree with small diameter. By varying the PRC ring parameters, one can obtain architectures with significantly different characteristics (e.g., from linear to logarithmic diameter), while maintaining an elegant framework for computation and communication. In particular, a very simple and efficient routing algorithm works for the entire spectrum of PRC rings thus obtained. This flexibility has important implications for key system attributes such as architectural scalability, software portability, and fault tolerance. Our discussion is centered on unidirectional PRC rings with in/outdegree of 2. We explore the basic structure, topological properties, optimization of parameters, VLSI layout, and scalability of such networks, develop packet and wormhole routing algorithms for them, and briefly compare them to competing fixeddegree architectures such as symmetric chordal rings, meshes, tori, and cubeconnected cycles. Index TermsÐChordal rings, fault tolerance, greedy routing, hierarchical parallel architectures, interconnection networks, routing algorithms, skip links. 1
Efficient collective communications in dualcube. The
 Journal of Supercomputing
"... The binary hypercube, or ncube, has been widely used as the interconnection network in parallel computers. However, the major drawback of the hypercube is the increase in the number of communication links for each node with the increase in the total number of nodes in the system. This paper introdu ..."
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Cited by 15 (13 self)
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The binary hypercube, or ncube, has been widely used as the interconnection network in parallel computers. However, the major drawback of the hypercube is the increase in the number of communication links for each node with the increase in the total number of nodes in the system. This paper introduces a new interconnection network for largescale parallel computers called dualcube. This network mitigates the problem of increasing number of links in the largescale hypercube network while keeps most of the topological properties of the hypercube network. Design of efficient routing algorithms for collective communications is the key issue for any interconnection networks. In this paper, we show that collective communications can be done efficiently in dualcube. KEY WORDS Interconnection networks, hypercube, collective communication, broadcast and personalized communication 1.
On Crossing Numbers Of Hypercubes And Cube Connected Cycles
, 1993
"... . We prove tight bounds for crossing numbers of hypercube and cube connected cycles (CCC) graphs. Key Words: crossing number, cube connected cycles, hypercube, lower bound CR Categories: F.1.2 [Modes of Computations] Parallelism, G.2.2. [Graph Theory] Network problems 1 ..."
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Cited by 15 (3 self)
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. We prove tight bounds for crossing numbers of hypercube and cube connected cycles (CCC) graphs. Key Words: crossing number, cube connected cycles, hypercube, lower bound CR Categories: F.1.2 [Modes of Computations] Parallelism, G.2.2. [Graph Theory] Network problems 1
Extracting and Implementing List Homomorphisms in Parallel Program Development
 Science of Computer Programming
, 1997
"... this paper, we study functions called list homomorphisms, which represent a particular pattern of parallelism. ..."
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Cited by 12 (0 self)
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this paper, we study functions called list homomorphisms, which represent a particular pattern of parallelism.