Efficient Communication in Folded Petersen Networks

Abstract

Fast and efficient communication is one of the most important requirements in today's multicomputers. When reaching a larger scale of processors, the probability of faults in the network increases, hence communication must be robust and fault tolerant. The recently introduced family of folded Petersen networks, constructed by iteratively applying the cartesian product operation on the well-known Petersen graph, provides a regular, node– and edge-symmetric architecture with optimal connectivity (hence maximal fault-tolerance), and logarithmic diameter. Compared to the closest sized hypercube, the folded petersen network has a smaller diameter, lower node degree and higher packing density. In this paper, we study fundamental communication primitives like single routing, permutation routing, one-to-all broadcasting, multinode-broadcasting (gossiping), personalized communications like scattering, and total exchange on the folded Petersen networks, considering two communication models, namely single link availability (SLA) and multiple link availability (MLA). We derive lower bounds for these problems and design optimal algorithms in terms of both time and the number of message transmissions. The results are based on the construction of minimal height spanning trees in the fault-free folded Petersen network. We further analyze these communication primitives in faulty networks, where processing nodes and transmission links cease working. This analysis is based on multiple arc-disjoint spanning trees, a construct also useful for analyzing other families of multicomputer networks.

An Edge-Isoperimetric Problem for Powers of the Petersen Graph

“…Note that P is a vertex-symmetric as well as an edge-symmetric graph. The graphs P n , known as folded Petersen networks, were proposed and extensively studied byÖhring and Das [9,[13][14][15][16] as a communication-efficient interconnection network topology for multiprocessors. By definition, P n is also regular, vertex-and edge-symmetric with 10 n vertices, degree 3n and diameter 2n.…”

New infinite family of regular edge-isoperimetric graphs

“…The applications include the wirelength problem, the bisection width and the edge congestion problem of graph embedding, modeling the brain, the cutwidth problem and graph partitioning. The graphs in Theorem 1.7 are called folded Petersen networks and have been studied in [20,22,21,18,13] as a communication-efficient interconnection network topology for multiprocessors. The graphs in Theorem 1.8 are called folded Petersen cubes and have been studied in [13,19].…”

“…The graphs in Theorem 1.7 are called folded Petersen networks and have been studied in [20,22,21,18,13] as a communication-efficient interconnection network topology for multiprocessors. The graphs in Theorem 1.8 are called folded Petersen cubes and have been studied in [13,19].…”

Routing and embeddings in cyclic Petersen networks: an efficient extension of the Petersen graph

“…1). Due to its unique and optimal properties, several network topologies based on the Petersen graph have been proposed and investigated in the literature [3,4,5,7,8,9,10,11,16].…”