OpTree: An Efficient Algorithm for All-gather Operation in Optical Interconnect Systems

All-gather collective communication is one of the most important communication primitives in parallel and distributed computation, which plays an essential role in many HPC applications such as distributed Deep Learning (DL) with model and hybrid parallelism. To solve the communication bottleneck of All-gather, optical interconnection network can provide unprecedented high bandwidth and reliability for data transfer among the distributed nodes. However, most traditional All-gather algorithms are designed for electrical interconnection, which cannot fit well for optical interconnect systems, resulting in poor performance. This paper proposes an efficient scheme, called OpTree, for All-gather operation on optical interconnect systems. OpTree derives an optimal $m$-ary tree corresponding to the optimal number of communication stages, achieving minimum communication time. We further analyze and compare the communication steps of OpTree with existing All-gather algorithms. Theoretical results exhibit that OpTree requires much less number of communication steps than existing All-gather algorithms on optical interconnect systems. Simulation results show that OpTree can reduce communication time by 72.21%, 94.30%, and 88.58%, respectively, compared with three existing All-gather schemes, WRHT, Ring, and NE.Comment: This paper is under review at a conferenc

Wavelength routing of uniform instances in all-optical rings

AbstractWe consider the problem of routing uniform communication instances in switched optical rings that use wavelength-division multiplexing technology. A communication instance is called uniform if it consists exactly of all pairs of nodes in the graph whose distance is equal to one from a specified set S={d1,d2,…,dk}. When k=1 or 2, we prove necessary and sufficient conditions on the values in S relative to n for the optimal wavelength index to be equal to the optimal load in the ring Rn. When k=2, we show that for any uniform instance specified by {d1,d2}, there is an optimal wavelength assignment on the ring Rn, if n>(d1/q-2)d1+(d1/q-1)d2, where q=GCD(d1,d2). For general k and n, we show a (32)-approximation for the optimal wavelength index; this is the best possible for arbitrary S. We also show that an optimal assignment can always be obtained provided n is large enough compared to the values in S

Survivability in layered networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 195-204).In layered networks, a single failure at the lower (physical) layer may cause multiple failures at the upper (logical) layer. As a result, traditional schemes that protect against single failures may not be effective in layered networks. This thesis studies the problem of maximizing network survivability in the layered setting, with a focus on optimizing the embedding of the logical network onto the physical network. In the first part of the thesis, we start with an investigation of the fundamental properties of layered networks, and show that basic network connectivity structures, such as cuts, paths and spanning trees, exhibit fundamentally different characteristics from their single-layer counterparts. This leads to our development of a new crosslayer survivability metric that properly quantifies the resilience of the layered network against physical failures. Using this new metric, we design algorithms to embed the logical network onto the physical network based on multi-commodity flows, to maximize the cross-layer survivability. In the second part of the thesis, we extend our model to a random failure setting and study the cross-layer reliability of the networks, defined to be the probability that the upper layer network stays connected under the random failure events. We generalize the classical polynomial expression for network reliability to the layered setting. Using Monte-Carlo techniques, we develop efficient algorithms to compute an approximate polynomial expression for reliability, as a function of the link failure probability. The construction of the polynomial eliminates the need to resample when the cross-layer reliability under different link failure probabilities is assessed. Furthermore, the polynomial expression provides important insight into the connection between the link failure probability, the cross-layer reliability and the structure of a layered network. We show that in general the optimal embedding depends on the link failure probability, and characterize the properties of embeddings that maximize the reliability under different failure probability regimes. Based on these results, we propose new iterative approaches to improve the reliability of the layered networks. We demonstrate via extensive simulations that these new approaches result in embeddings with significantly higher reliability than existing algorithms.by Kayi Lee.Ph.D

Optical flow switched networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Includes bibliographical references (p. 253-279).In the four decades since optical fiber was introduced as a communications medium, optical networking has revolutionized the telecommunications landscape. It has enabled the Internet as we know it today, and is central to the realization of Network-Centric Warfare in the defense world. Sustained exponential growth in communications bandwidth demand, however, is requiring that the nexus of innovation in optical networking continue, in order to ensure cost-effective communications in the future. In this thesis, we present Optical Flow Switching (OFS) as a key enabler of scalable future optical networks. The general idea behind OFS-agile, end-to-end, all-optical connections-is decades old, if not as old as the field of optical networking itself. However, owing to the absence of an application for it, OFS remained an underdeveloped idea-bereft of how it could be implemented, how well it would perform, and how much it would cost relative to other architectures. The contributions of this thesis are in providing partial answers to these three broad questions. With respect to implementation, we address the physical layer design of OFS in the metro-area and access, and develop sensible scheduling algorithms for OFS communication. Our performance study comprises a comparative capacity analysis for the wide-area, as well as an analytical approximation of the throughput-delay tradeoff offered by OFS for inter-MAN communication. Lastly, with regard to the economics of OFS, we employ an approximate capital expenditure model, which enables a throughput-cost comparison of OFS with other prominent candidate architectures. Our conclusions point to the fact that OFS offers significant advantage over other architectures in economic scalability.(cont.) In particular, for sufficiently heavy traffic, OFS handles large transactions at far lower cost than other optical network architectures. In light of the increasing importance of large transactions in both commercial and defense networks, we conclude that OFS may be crucial to the future viability of optical networking.by Guy E. Weichenberg.Ph.D

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

Optical control plane: theory and algorithms

In this thesis we propose a novel way to achieve global network information dissemination in which some wavelengths are reserved exclusively for global control information exchange. We study the routing and wavelength assignment problem for the special communication pattern of non-blocking all-to-all broadcast in WDM optical networks. We provide efficient solutions to reduce the number of wavelengths needed for non-blocking all-to-all broadcast, in the absence of wavelength converters, for network information dissemination. We adopt an approach in which we consider all nodes to be tap-and-continue capable thus studying lighttrees rather than lightpaths. To the best of our knowledge, this thesis is the first to consider “tap-and-continue” capable nodes in the context of conflict-free all-to-all broadcast. The problem of all to-all broadcast using individual lightpaths has been proven to be an NP-complete problem [6]. We provide optimal RWA solutions for conflict-free all-to-all broadcast for some particular cases of regular topologies, namely the ring, the torus and the hypercube. We make an important contribution on hypercube decomposition into edge-disjoint structures. We also present near-optimal polynomial-time solutions for the general case of arbitrary topologies. Furthermore, we apply for the first time the “cactus” representation of all minimum edge-cuts of graphs with arbitrary topologies to the problem of all-to-all broadcast in optical networks. Using this representation recursively we obtain near-optimal results for the number of wavelengths needed by the non-blocking all-to-all broadcast. The second part of this thesis focuses on the more practical case of multi-hop RWA for non- blocking all-to-all broadcast in the presence of Optical-Electrical-Optical conversion. We propose two simple but efficient multi-hop RWA models. In addition to reducing the number of wavelengths we also concentrate on reducing the number of optical receivers, another important optical resource. We analyze these models on the ring and the hypercube, as special cases of regular topologies. Lastly, we develop a good upper-bound on the number of wavelengths in the case of non-blocking multi-hop all-to-all broadcast on networks with arbitrary topologies and offer a heuristic algorithm to achieve it. We propose a novel network partitioning method based on “virtual perfect matching” for use in the RWA heuristic algorithm

Methods for improving resilience in communication networks and P2P overlays

Resilience to failures and deliberate attacks is becoming an essential requirement in most communication networks today. This also applies to P2P Overlays which on the one hand are created on top of communication infrastructures, and therefore are equally affected by failures of the underlying infrastructure, but which on the other hand introduce new possibilities like the creation of arbitrary links within the overlay. In this article, we present a survey of strategies to improve resilience in communication networks as well as in P2P overlay networks. Furthermore, our intention is to point out differences and similarities in the resilience-enhancing measures for both types of networks. By revising some basic concepts from graph theory, we show that many concepts for communication networks are based on well-known graph-theoretical problems. Especially, some methods for the construction of protection paths in advance of a failure are based on very hard problems, indeed many of them are in NP and can only be solved heuristically or on certain topologies. P2P overlay networks evidently benefit from resilience-enhancing strategies in the underlying communication infrastructure, but beyond that, their specific properties pose the need for more sophisticated mechanisms. The dynamic nature of peers requires to take some precautions, like estimating the reliability of peers, redundantly storing information, and provisioning a reliable routing

Using GRASP and GA to design resilient and cost-effective IP/MPLS networks

The main objective of this thesis is to find good quality solutions for representative instances of the problem of designing a resilient and low cost IP/MPLS network, to be deployed over an existing optical transport network. This research is motivated by two complementary real-world application cases, which comprise the most important commercial and academic networks of Uruguay. To achieve this goal, we performed an exhaustive analysis of existing models and technologies. From all of them we took elements that were contrasted with the particular requirements of our counterparts. We highlight among these requirements, the need of getting solutions transparently implementable over a heterogeneous network environment, which limit us to use widely standardized features of related technologies. We decided to create new models more suitable to fit these needs. These models are intrinsically hard to solve (NP-Hard). Thus we developed metaheuristic based algorithms to find solutions to these real-world instances. Evolutionary Algorithms and Greedy Randomized Adaptive Search Procedures obtained the best results. As it usually happens, real-world planning problems are surrounded by uncertainty. Therefore, we have worked closely with our counterparts to reduce the fuzziness upon data to a set of representative cases. They were combined with different strategies of design to get to scenarios, which were translated into instances of these problems. Finally, the algorithms were fed with this information, and from their outcome we derived our results and conclusions

Optimised Design and Analysis of All-Optical Networks

This PhD thesis presents a suite of methods for optimising design and for analysing blocking probabilities of all-optical networks. It thus contributes methodical knowledge to the field of computer assisted planning of optical networks. A two-stage greenfield optical network design optimiser is developed, based on shortest-path algorithms and a comparatively new metaheuristic called simulated allocation. It is able to handle design of all-optical mesh networks with optical cross-connects, considers duct as well as fibre and node costs, and can also design protected networks. The method is assessed through various experiments and is shown to produce good results and to be able to scale up to networks of realistic sizes. A novel method, subpath wavelength grouping, for routing connections in a multigranular all-optical network where several wavelengths can be grouped and switched at band and fibre level is presented. The method uses an unorthodox routing strategy focusing on common subpaths rather than individual connections, and strives to minimise switch port count as well as fibre usage. It is shown to produce cheaper network designs than previous methods when fibre costs are comparatively high. A new optical network concept, the synchronous optical hierarchy, is proposed, in which wavelengths are subdivided into timeslots to match the traffic granularity. Various theoretical properties of this concept are investigated and compared in simulation studies. An integer linear programming model for optical ring network design is presented. Manually designed real world ring networks are studied and it is found that the model can lead to cheaper network design. Moreover, ring and mesh network architectures are compared using real world costs, and it is found that optical cros..