A Load Balancing Strategy with Migration Cost for Independent Batch of Tasks (BoT) on Heterogeneous Multiprocessor Interconnection Networks

In high performance computing, heterogeneous Multiprocessor Interconnection Networks (MINs) are used for processing of compute intensive applications. These applications are distributed on the heterogeneous computational processors of MINs arranged in specific geometrical shape. MINs are also used for transfer task between two processors in a heterogeneous multistage network for better load balancing. Load balancing algorithm plays a vital role in interconnection network in order to minimize the load imbalance on the processors. In this paper, a Load Balancing Strategy with Migration cost (LBSM) is proposed to execute an independent batch of tasks on various heterogeneous MINs viz. MetaCube, X-Torus and Folded Crossed Cube having the objective of minimizing the load imbalance on processors. In simulation study, LBSM is compared with its previous work DLBS and superior performance is shown with the considered parameters under study. Further, the performance analysis of LBSM has been conducted on MetaCube, X-Torus and Folded Crossed Cube and results have been reported accordingly.

Some new models for multiprocessor interconnection networks

A multiprocessor system can be modeled by a graph G. The vertices of G correspond to processors while edges represent links between processors. To find suitable models for multiprocessor interconnection networks (briefly MINs), one can apply tools and techniques of spectral graph theory. In this paper, we extend some of the existing results and present several graphs which could serve as models for efficient MINs based on the small values of the previously introduced graph tightness. These examples of possible MINs arise as a result of some well-known and widely used graph operations. We also examine the suitability of strongly regular graphs (briefly SRGs) to model MINs, and prove the uniqueness of some of them.

MULTIPROCESSOR INTERCONNECTION NETWORKS WITH SMALL TIGHTNESS

Homogeneous multiprocessor systems are usually modelled by undirected graphs. Vertices of these graphs represent the processors, while edges denote the connection links between adjacent processors. Let G be a graph with diameter D, maximum vertex degree Δ, the largest eigenvalue λ1 and m distinct eigenvalues. The products mΔ and (D+1)λ1 are called the tightness of G of the first and second type, respectively. In recent literature it was suggested that graphs with a small tightness of the first type are good models for the multiprocessor interconnection networks. In a previous paper we studied these and some other types of tightness and some related graph invariants and demonstrated their usefulness in the analysis of multiprocessor interconnection networks. We proved that the number of connected graphs with a bounded tightness is finite. In this paper we determine explicitly graphs with tightness values not exceeding 9. There are 69 such graphs and they contain up to 10 vertices. In addition we identify graphs with minimal tightness values when the number of vertices is n = 2,…, 10.

Application of some graph invariants to the analysis of multiprocessor interconnection networks

Let G be a graph with diameter D, maximum vertex degree ?, the largest eigenvalue ?1 and m distinct eigenvalues. The products m? and (D+1) ?1 are called the tightness of G of the first and second type, respectively. In the recent literature it was suggested that graphs with a small tightness of the first type are good models for the multiprocessor interconnection networks. We study these and some other types of tightness and some related graph invariants and demonstrate their usefulness in the analysis of multiprocessor interconnection networks. Tightness values for graphs of some standard interconnection networks are determined. We also present some facts showing that the tightness of the second type is a relevant graph invariant. We prove that the number of connected graphs with a bounded tightness is finite.