Papers by Behrooz Parhami
Swapped networks: unifying the architectures and algorithms of a wide class of hierarchical parallel processors
In this paper, we propose a new class of interconnection networks, called swapped networks, for g... more In this paper, we propose a new class of interconnection networks, called swapped networks, for general-purpose parallel processing. Swapped networks not only generate a wide class of high-performance interconnection networks, but also generalize, and serve to unify, many proposed parallel architectures as well as their algorithms. We show that swapped networks can efficiently emulate hypercubes, high-dimensional meshes, or generalized hypercubes, while having node degrees significantly smaller than the emulated network in each case. We also show that some subclasses of swapped networks can achieve asymptotically optimal diameters. Swapped networks are highly modularized, make the use of fixed-degree building blocks possible for any practically realizable system, and lead to the construction of high-performance scalable networks with reasonable cost
Further Properties of Cayley Digraphs and Their Applications to Interconnection Networks
Lecture Notes in Computer Science, 2006
Transactions on Emerging Telecommunications Technologies, 2020
To alleviate the computational burden of previous virtual network embedding (VNE) approaches when... more To alleviate the computational burden of previous virtual network embedding (VNE) approaches when the resource network scales up significantly, we propose an efficient node ranking strategy that considers both global and local topological characteristics of the substrate network in mapping virtual nodes to physical nodes. This method ranks the substrate network nodes in two stages. First, all nodes are ranked globally with respect to the stationary distribution of the entire network. Then, a connected subset of the ranked substrate nodes, forming the H‐admissible embedding subgraph, is extracted. Finally, the subgraph nodes are ranked according to a local node ranking vector derived from a random‐walking scheme. The local rank vector is resolved using discrete Green's function satisfying the Dirichelet boundary condition. The more accurate association of node demands and resources that our proposed method provides leads to both better acceptance ratio and lower computational ove...
Symmetry, 2018
Virtual network embedding (VNE) is a key technology in network virtualization. Advantages of netw... more Virtual network embedding (VNE) is a key technology in network virtualization. Advantages of network symmetry are well known in the design of load-balanced routing algorithms and in network performance analysis. Our work in this paper shows that benefits of graph symmetry also extend to the domain of network embedding. Specifically, we propose an efficient VNE method based on modular and structured agency guidance, a regular graph function. The proposed method, which is based on symmetric intermediate graphs, offers two main advantages. Firstly, characteristics of the intermediate structures enhance the computational efficiency of the VNE process. Secondly, the static agency network modeled with such intermediate structures improves the quality of the resulting embedding. These two advantages of our method are elaborated upon and verified by examples and simulations, respectively. In addition, we present a theoretical analysis explaining the reasons behind the benefits offered by such middleware.
The Computer Journal, 1998
Gaussian cubes are derived by removing links from a hypercube in a periodic fashion. By varying t... more Gaussian cubes are derived by removing links from a hypercube in a periodic fashion. By varying the partition parameter, one can obtain networks with different characteristics, while maintaining a basic framework for computation and communication. Unfortunately, such networks are in general not regular, making it difficult to derive their topological properties explicitly. In this paper, we study the diameter of Gaussian cubes and show the trade-off between cost and performance.
Biswapped Networks and Their Topological Properties
Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing (SNPD 2007), 2007
An Efficient Construction of Node Disjoint Paths in OTIS Networks
Lecture Notes in Computer Science
Hexagonal mesh and torus, as well as honeycomb and certain other pruned torus networks, are known... more Hexagonal mesh and torus, as well as honeycomb and certain other pruned torus networks, are known to belong to the class of Cayley graphs which are node-symmetric and possess other interesting mathematical properties. In this paper, we use Cayley-graph formulations for the aforementioned networks, along with some of our previous results on subgraphs and coset graphs, to draw conclusions relating to internode distance and network diameter. We also use our results to refine, clarify, and unify a number of previously published properties for these networks and other networks derived from them.
Parallel Processing Letters, 2012
We propose a symmetrical scheme, by drawing results from group theory, and use it to build a new ... more We propose a symmetrical scheme, by drawing results from group theory, and use it to build a new class of data center network models. The results are superior to current network models with respect to a number of performance criteria. Greater symmetry in networks is important, as it leads to simpler structure and more efficient communication algorithms. It also tends to produce better scalability and greater fault tolerance. Our models are general and are expected to find many applications, but they are particularly suitable for large-scale data-center networks.
Journal of Systems Science and Systems Engineering, 2007
Journal of Interconnection Networks, 2012
The node-to-set parallel routing problem for a k-connected network Γ is as follows: given a node ... more The node-to-set parallel routing problem for a k-connected network Γ is as follows: given a node s and k other nodes {t1, t2, … , tk} in Γ, find k node-disjoint paths connecting s and ti, for 1 ≤ i ≤ k. From the viewpoint of applications in synthesizing fast and resilient collective communication operations, it is desirable to make the parallel paths as short as possible. Building such paths is a nontrivial problem for a general network. Optical transpose interconnection system (OTIS, also known as swapped) networks, a class of hierarchical structures built of n identical n-node factor networks, are known to be maximally fault-tolerant for any connected factor network, implying that they have maximal connectivity. We propose a general algorithm for the node-to-set parallel routing problem in OTIS/swapped networks that yields paths of length no greater than D + 4 in O(Δ2 + Δf(n)) time, where D and Δ represent the diameter and degree of the OTIS network and O(f(n)) is the time complex...
Journal of Computer and System Sciences, 2007
Despite numerous interconnection schemes proposed for distributed multicomputing, systematic stud... more Despite numerous interconnection schemes proposed for distributed multicomputing, systematic studies of classes of interprocessor networks, that offer speed-cost tradeoffs over a wide range, have been few and far in between. A notable exception is the study of Cayley graphs that model a wide array of symmetric networks of theoretical and practical interest. Properties established for all, or for certain subclasses of, Cayley graphs are extremely useful in view of their wide applicability. In this paper, we obtain a number of new relationships between Cayley (di)graphs and their subgraphs and coset graphs with respect to subgroups, focusing in particular on homomorphism between them and on relating their internode distances and diameters. We discuss applications of these results to well-known and useful interconnection networks such as hexagonal and honeycomb meshes as well as certain classes of pruned tori.
Information Processing Letters, 1998
Information Processing Letters, 2010
The class of swapped or OTIS (optical transpose interconnect system) networks, built of n copies ... more The class of swapped or OTIS (optical transpose interconnect system) networks, built of n copies of an n-node cluster by connecting node i in cluster j to node j in cluster i for i = j, has been studied extensively. One problem with such networks is that node i of cluster i has no intercluster link. This slight asymmetry complicates a number of algorithms and hinders both theoretical investigations and practical pursuits, such as building parallel node-disjoint paths for fault tolerance. We introduce biswapped networks that are fully symmetric and have cluster connectivity very similar to swapped/OTIS networks. We derive basic topological parameters, present a simple distributed shortest-path routing algorithm, and point to a number of other interesting properties under investigation for biswapped networks.
Discrete Applied Mathematics, 2007
In this paper, we extend known relationships between Cayley digraphs and their subgraphs and cose... more In this paper, we extend known relationships between Cayley digraphs and their subgraphs and coset graphs with respect to subgroups to obtain a number of general results on homomorphism between them. Intuitively, our results correspond to synthesizing alternative, more economical, interconnection networks by reducing the number of dimensions and/or link density of existing networks via mapping and pruning. We discuss applications of these results to well-known and useful interconnection networks such as hexagonal and honeycomb meshes, including the derivation of provably correct shortest-path routing algorithms for such networks.
Course: ECE 257A – Fault-Tolerant Computing, University of California, Santa Barbara, Fall 2006, ... more Course: ECE 257A – Fault-Tolerant Computing, University of California, Santa Barbara, Fall 2006, Enrollment Code 49585 Catalog entry: 257A. Fault-Tolerant Computing. (4) PARHAMI. Prerequisite: ECE 154. Lecture, 4 hours. Basic concepts of dependable computing. Reliability of nonredundant and redundant systems. Dealing with circuit-level defects. Logic-level fault testing and tolerance. Error detection and correction. Diagnosis and reconfiguration for system-level malfunctions. Degradation management. Failure modeling and risk assessment. (F) Instructor: Behrooz Parhami, Room 5155 Harold Frank Hall (Engr I), Phone 805-893-3211, [email protected] Meetings: Tuesdays and Thursdays, 10:00-11:30 AM, Phelps 1431 Consultation: Open office hours, held in Room 5155 Harold Frank Hall (Engr I) – Tuesdays 11:30-1:00, Thursdays 8:30-10:00 Motivation: Dependability concerns are integral parts of engineering design. Ideally, we would like our computer systems to be perfect, always yielding timely...
Proceedings 15th International Parallel and Distributed Processing Symposium. IPDPS 2001
International Parallel and Distributed Processing Symposium/International Parallel Processing Symposium, 2001
We solve an open question posed by Akers and Krishna- murthy in 1986 (1, 3) concerning VLSI layou... more We solve an open question posed by Akers and Krishna- murthy in 1986 (1, 3) concerning VLSI layout of star graphs. We show that the area of the optimal layout of an N-node star graph, hierarchical cubic network (HCN), or hierarchi- cal folded-hypercube network (HFN) is N2 16 o N2 un- der the Thompson model, or under the extended grid
The Journal of Supercomputing, 2009
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Papers by Behrooz Parhami