Jonathan Stanton1Spring 2004 / Lecture 19Network IICS 184Network TopologiesDepartment of Computer ScienceGeorge Washington UniversityJonathan Stanton2Spring 2004 / Lecture 19Network Topologies• Interconnection networks:– Parallel– Clusters• Peer to peer systems:– All to all–Tree– Multistage• Distributed Hash Tables:– Use virtual topologyJonathan Stanton3Spring 2004 / Lecture 191) Geometry: a graph structure that inspires aDHT design– Tree, Hypercube, Ring, Butterfly, Debruijn2) Distance function: captures a geometricstructure– d(id1, id2) for any two node identifiers3) Algorithm: rules for selecting neighbors androutes using the distance functionThree Aspects of DHTJonathan Stanton4Spring 2004 / Lecture 19“Ideal” Networked set ofComputersP+MP+MP+MP+MP+MP+MP+MP+MP+MP+MP+MP+MP+MP+MP+MP+MJonathan Stanton5Spring 2004 / Lecture 19“Ideal” Computer…PPPPPPPPMMMMMMMM…Jonathan Stanton6Spring 2004 / Lecture 19“Ideal” ComputerJonathan Stanton7Spring 2004 / Lecture 19“Ideal” ComputerJonathan Stanton8Spring 2004 / Lecture 19“Ideal” Parallel ComputerJonathan Stanton9Spring 2004 / Lecture 19Non-Ideal networks• To be cost effective or implementable oftencompromises are required:– Fewer links– Lower dimensionality or out-degree– Smaller units– SimplerJonathan Stanton10Spring 2004 / Lecture 19Buses• • Simple and cost-effective for small-scale multiprocessors• • Not scalable (limited bandwidth; electrical complications)P PPBusJonathan Stanton11Spring 2004 / Lecture 19Crossbars• • Each port has link to every other port• + Low latency and high throughput• - Cost grows as O(N^2) so not very scalable.• - Difficult to arbitrate and to get all data lines into and out of a centralizedcrossbar.• • Used as building block for other networks.PPPPM M M MCrossbarJonathan Stanton12Spring 2004 / Lecture 19Rings• • Cheap: Cost is O(N).• + High overall bandwidth• - High latency O(N)P PPP P PRingJonathan Stanton13Spring 2004 / Lecture 19Trees• Cheap: Cost is O(N).• Latency is O(logN).• Easy to layout as planar graphs (e.g., H-Trees).• For random permutations, root can become bottleneck.• To avoid root being bottleneck, notion of Fat-TreesH-TreeFat TreeJonathan Stanton14Spring 2004 / Lecture 19Multistage Logarithmic Networks• Key Idea: have multiple layers of switches between destinations.• Cost is O(NlogN); latency is O(logN); throughput is O(N).• Generally indirect networks.• Many variations exist (Omega, Butterfly, Benes, ...).Jonathan Stanton15Spring 2004 / Lecture 19Mesh of TreesJonathan Stanton16Spring 2004 / Lecture 19Mesh of TreesJonathan Stanton17Spring 2004 / Lecture 19Hypercubed = 0N = 1d = 1N = 2d = 2N = 4d = 3N = 8d = 4N = 16Jonathan Stanton18Spring 2004 / Lecture 19Hypercube010010011011000000001001110110111111100100101101Jonathan Stanton19Spring 2004 / Lecture 19Cube-Connected CyclesJonathan Stanton20Spring 2004 / Lecture 19k-ary n-cubes• • Generalization of hypercubes (k-nodes in a string)• • Total # of nodes = N = k^n.• • k > 2 reduces # of channels at bisection, thus allowing for widerchannels but more hops.4-ary 3-cubeJonathan Stanton21Spring 2004 / Lecture 19Butterfly (FFT) Network0120000001010011100101110111000001010011100101110111Jonathan Stanton22Spring 2004 / Lecture 19ButterfliesJonathan Stanton23Spring 2004 / Lecture 19Decomposing a ButterflyJonathan Stanton24Spring 2004 / Lecture 19Decomposing a ButterflyJonathan Stanton25Spring 2004 / Lecture 19Decomposing a ButterflyJonathan Stanton26Spring 2004 / Lecture 19Decomposing a ButterflyJonathan Stanton27Spring 2004 / Lecture 19Decomposing a Butterfly IIJonathan Stanton28Spring 2004 / Lecture 19Decomposing a Butterfly IIJonathan Stanton29Spring 2004 / Lecture 19Decomposing a Butterfly IIJonathan Stanton30Spring 2004 / Lecture 19Decomposing a Butterfly IIJonathan Stanton31Spring 2004 / Lecture 19Decomposing a Butterfly IIJonathan Stanton32Spring 2004 / Lecture 19Decomposing a Butterfly IIJonathan Stanton33Spring 2004 / Lecture 19Decomposing a Butterfly IIJonathan Stanton34Spring 2004 / Lecture 19Routing on a Butterfly0120000001010011100101110111000001010011100101110111Jonathan Stanton35Spring 2004 / Lecture 19Tree in Butterfly0120000001010011100101110111000001010011100101110111Jonathan Stanton36Spring 2004 / Lecture 19Tree in Butterfly0120000001010011100101110111000001010011100101110111Jonathan Stanton37Spring 2004 / Lecture 19Information Slide• Lecture slides can be obtained at the course