A Network Configuration Algorithm Based on Optimization of Kirchhoff Index

Abstract

Abstract-Traditionally, a parallel application is partitioned, mapped and then routed on a network of compute nodes where the topology of the interconnection network is fixed and known beforehand. Such a topology often comes with redundant links to accommodate the communication patterns of a wide range of applications. With recent advances in technology for optical circuit switches, it is now possible to construct a network with much fewer links, and to make the link endpoints configurable to suit the communication pattern of a given application. While this is economical (saving both links and the power to run them), it raises the difficult problem of how to configure the network and how to reconfigure it quickly when the application's communication pattern changes.In this paper, we propose the Kirchhoff index (KI) of a certain weighted graph related to the interconnection network as a proxy for its communication throughput. Our usage of this metric is based on a theoretical analogy between resistances in an electrical network and communication loads in the interconnection network. We show how mathematical techniques for reducing KI can be used to configure a network in a dramatically shorter time as compared to the current state-of-the-art scheme.

Exactly scale-free scale-free networks

“…Scale-free networks are usually identified by the histogram of node degrees having a power-law tail. Many naturally occurring networks 1 have been identified as having a scale-free property: citation and collaboration networks [3,4], airline networks [5], protein-protein interaction [6], metabolic pathways [7], the world-wide web and internet [8].…”

Co-optimizing application partitioning and network topology for a reconfigurable interconnect

“…As for the iterations themselves, we note that a proxy function has been proposed [3] to evaluate the efficacy of a topology without explicitly computing the partitioning, mapping and routing solution. This proxy function (based on Kirchhoff index of a certain weighted graph related to the interconnection network) is significantly faster to compute and can be easily parallelized.…”

Data-Intensive Workflow Optimization Based on Application Task Graph Partitioning in Heterogeneous Computing Systems

“…Moreover, the algorithm is designed for coarse-grained applications in which communication costs are negligible and the execution environment is homogeneous while PDWA addresses communicationintensive applications in heterogeneous computing system. An approach for streaming-based application is proposed in [11], that considers network topology graph to optimize its configuration with maximum throughput. A theoretical analogy between loads on communication links and the resistances in an electrical circuit is used to define a metric, Kirchhoff Index (KI), as a proxy for the throughput of the network.…”

“…Similarly, P 2 is mapped to u 1 . The pipelined schedule with latency 76 is The application task graph splits into P n partitions; 10 / * Optimization of partitions * / while Inter-partition edge weights e ij > e th do 11 Shift the task v i or v j to any other partition such 12 that inter-partition edge weight always less than e th ; endw 13 Return P n partitions; Return M mapped P partitions; 8 obtained by PDWA, which is shown in Fig. 3a.…”