A class of hierarchical graphs as topologies for interconnection networks

We study some topological and algorithmic properties of a recently defined hierarchical interconnection network, the hierarchical crossed cube HCC(k,n), which draws upon constructions used within the well-known hypercube and also the crossed cube. In particular, we study: the construction of shortest paths between arbitrary vertices in HCC(k,n); the connectivity of HCC(k,n); and one-to-all broadcasts in parallel machines whose underlying topology is HCC(k,n) (with both one-port and multi-port store-and-forward models of communication). Moreover, (some of) our proofs are applicable not just to hierarchical crossed cubes but to hierarchical interconnection networks formed by replacing crossed cubes with other families of interconnection networks. As such, we provide a generic construction with accompanying generic results relating to some topological and algorithmic properties of a wide range of hierarchical interconnection networks

A Structured Table of Graphs with Symmetries and Other Special Properties

We organize a table of regular graphs with minimal diameters and minimal mean path lengths, large bisection widths and high degrees of symmetries, obtained by enumerations on supercomputers. These optimal graphs, many of which are newly discovered, may find wide applications, for example, in design of network topologies.Comment: add details about automorphism grou

The failure tolerance of mechatronic software systems to random and targeted attacks

This paper describes a complex networks approach to study the failure tolerance of mechatronic software systems under various types of hardware and/or software failures. We produce synthetic system architectures based on evidence of modular and hierarchical modular product architectures and known motifs for the interconnection of physical components to software. The system architectures are then subject to various forms of attack. The attacks simulate failure of critical hardware or software. Four types of attack are investigated: degree centrality, betweenness centrality, closeness centrality and random attack. Failure tolerance of the system is measured by a 'robustness coefficient', a topological 'size' metric of the connectedness of the attacked network. We find that the betweenness centrality attack results in the most significant reduction in the robustness coefficient, confirming betweenness centrality, rather than the number of connections (i.e. degree), as the most conservative metric of component importance. A counter-intuitive finding is that "designed" system architectures, including a bus, ring, and star architecture, are not significantly more failure-tolerant than interconnections with no prescribed architecture, that is, a random architecture. Our research provides a data-driven approach to engineer the architecture of mechatronic software systems for failure tolerance.Comment: Proceedings of the 2013 ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2013 August 4-7, 2013, Portland, Oregon, USA (In Print

Topological Characterization of Hamming and Dragonfly Networks and its Implications on Routing

Current HPC and datacenter networks rely on large-radix routers. Hamming graphs (Cartesian products of complete graphs) and dragonflies (two-level direct networks with nodes organized in groups) are some direct topologies proposed for such networks. The original definition of the dragonfly topology is very loose, with several degrees of freedom such as the inter- and intra-group topology, the specific global connectivity and the number of parallel links between groups (or trunking level). This work provides a comprehensive analysis of the topological properties of the dragonfly network, providing balancing conditions for network dimensioning, as well as introducing and classifying several alternatives for the global connectivity and trunking level. From a topological study of the network, it is noted that a Hamming graph can be seen as a canonical dragonfly topology with a large level of trunking. Based on this observation and by carefully selecting the global connectivity, the Dimension Order Routing (DOR) mechanism safely used in Hamming graphs is adapted to dragonfly networks with trunking. The resulting routing algorithms approximate the performance of minimal, non-minimal and adaptive routings typically used in dragonflies, but without requiring virtual channels to avoid packet deadlock, thus allowing for lower-cost router implementations. This is obtained by selecting properly the link to route between groups, based on a graph coloring of the network routers. Evaluations show that the proposed mechanisms are competitive to traditional solutions when using the same number of virtual channels, and enable for simpler implementations with lower cost. Finally, multilevel dragonflies are discussed, considering how the proposed mechanisms could be adapted to them

Output consensus of nonlinear multi-agent systems with unknown control directions

In this paper, we consider an output consensus problem for a general class of nonlinear multi-agent systems without a prior knowledge of the agents' control directions. Two distributed Nussbaumtype control laws are proposed to solve the leaderless and leader-following adaptive consensus for heterogeneous multiple agents. Examples and simulations are given to verify their effectivenessComment: 10 pages;2 figure