Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010

Peer Reviewe

Dagstuhl News January - December 2011

"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic

Joint optimization of topology, switching, routing and wavelength assignment

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 279-285).To provide end users with economic access to high bandwidth, the architecture of the next generation metropolitan area networks (MANs) needs to be judiciously designed from the cost perspective. In addition to a low initial capital investment, the ultimate goal is to design networks that exhibit excellent scalability - a decreasing cost-per-node-per-unit-traffic as user number and transaction size increase. As an effort to achieve this goal, in this thesis we search for the scalable network architectures over the solution space that embodies the key aspects of optical networks: fiber connection topology, switching architecture selection and resource dimensioning, routing and wavelength assignment (RWA). Due to the inter-related nature of these design elements, we intended to solve the design problem jointly in the optimization process in order to achieve over-all good performance. To evaluate how the cost drives architectural tradeoffs, an analytical approach is taken in most parts of the thesis by first focusing on networks with symmetric and well defined structures (i.e., regular networks) and symmetric traffic patterns (i.e., all-to-all uniform traffic), which are fair representations that give us suggestions of trends, etc.(cont.) We starts with a examination of various measures of regular topologies. The average minimum hop distance plays a crucial role in evaluating the efficiency of network architecture. From the perspective of designing optical networks, the amount of switching resources used at nodes is proportional to the average minimum hop distance. Thus a smaller average minimum hop distance translates into a lower fraction of pass-through traffic and less switching resources required. Next, a first-order cost model is set up and an optimization problem is formulated for the purpose of characterizing the tradeoffs between fiber and switching resources. Via convex optimization techniques, the joint optimization problem is solved analytically for (static) uniform traffic and symmetric networks. Two classes of regular graphs - Generalized Moore Graphs and A-nearest Neighbors Graphs - are identified to yield lower and upper cost bounds, respectively. The investigation of the cost scalability further demonstrates the advantage of the Generalized Moore Graphs as benchmark topologies: with linear switching cost structure, the minimal normalized cost per unit traffic decreases with increasing network size for the Generalized Moore Graphs and their relatives.(cont.) In comparison, for less efficient fiber topologies (e.g., A-nearest Neighbors) and switching cost structures (e.g., quadratic cost), the minimal normalized cost per unit traffic plateaus or even increases with increasing network size. The study also reveals other attractive properties of Generalized Moore Graphs in conjunction with minimum hop routing - the aggregate network load is evenly distributed over each fiber. Thus, Generalized Moore Graphs also require the minimum number of wavelengths to support a given uniform traffic demand. Further more, the theoretical works on the Generalized Moore Graphs and their close relatives are extended to study more realistic design scenarios in two aspects. One aspect addresses the irregular topologies and (static) non-uniform traffic, for which the results of Generalized Moore networks are used to provide useful estimates of network cost, and are thus offering good references for cost-efficient optical networks. The other aspect deals with network design under random demands. Two optimization formulations that incorporate the traffic variability are presented.(cont.) The results show that as physical architecture, Generalized Moore Graphs are most robust (in cost) to the demand uncertainties. Analytical results also provided design guidelines on how optimum dimensioning, network connectivity, and network costs vary as functions of risk aversion, service level requirements, and probability distributions of demands.by Kyle Chi Guan.Ph.D

Inductive Pattern Formation

With the extended computational limits of algorithmic recursion, scientific investigation is transitioning away from computationally decidable problems and beginning to address computationally undecidable complexity. The analysis of deductive inference in structure-property models are yielding to the synthesis of inductive inference in process-structure simulations. Process-structure modeling has examined external order parameters of inductive pattern formation, but investigation of the internal order parameters of self-organization have been hampered by the lack of a mathematical formalism with the ability to quantitatively define a specific configuration of points. This investigation addressed this issue of quantitative synthesis. Local space was developed by the Poincare inflation of a set of points to construct neighborhood intersections, defining topological distance and introducing situated Boolean topology as a local replacement for point-set topology. Parallel development of the local semi-metric topological space, the local semi-metric probability space, and the local metric space of a set of points provides a triangulation of connectivity measures to define the quantitative architectural identity of a configuration and structure independent axes of a structural configuration space. The recursive sequence of intersections constructs a probabilistic discrete spacetime model of interacting fields to define the internal order parameters of self-organization, with order parameters external to the configuration modeled by adjusting the morphological parameters of individual neighborhoods and the interplay of excitatory and inhibitory point sets. The evolutionary trajectory of a configuration maps the development of specific hierarchical structure that is emergent from a specific set of initial conditions, with nested boundaries signaling the nonlinear properties of local causative configurations. This exploration of architectural configuration space concluded with initial process-structure-property models of deductive and inductive inference spaces. In the computationally undecidable problem of human niche construction, an adaptive-inductive pattern formation model with predictive control organized the bipartite recursion between an information structure and its physical expression as hierarchical ensembles of artificial neural network-like structures. The union of architectural identity and bipartite recursion generates a predictive structural model of an evolutionary design process, offering an alternative to the limitations of cognitive descriptive modeling. The low computational complexity of these models enable them to be embedded in physical constructions to create the artificial life forms of a real-time autonomously adaptive human habitat

Quasi-Kautz Digraphs for Peer-to-Peer Networks

The topological properties of peer-to-peer overlay networks are critical factors that dominate the performance of these systems. Several nonconstant and constant degree interconnection networks have been used as topologies of many peer-to-peer networks. The Kautz digraph is one of these topologies that have many desirable properties. Unlike interconnection networks, peer-topeer networks need a topology with an arbitrary order and degree, but the Kautz digraph does not possess these properties. In this paper, we propose MOORE: the first effective and practical peer-to-peer network based on the quasi-Kautz digraph with Oðlog d nÞ diameter and constant degree under a dynamic environment. The diameter and average routing path length, respectively, are shorter than that of CAN, butterfly, and cube-connected cycle, and are close to that of the de Bruijn and Kautz digraphs. The message cost of node joining and departing operations are at most 2:5d log d n and ð2:5d þ 1Þ log d n, and only d and 2d nodes need to update their routing tables. MOORE can achieve optimal diameter, high performance, good connectivity, and low congestion, evaluated by formal proofs and simulations