Exploiting Object-Based Parallelism on Multi-core Multi-processor Clusters

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1. What contributions have the authors mentioned in the paper "Optimal routing in binomial graph networks" ?

2. What have the authors stated for future works in "Optimal routing in binomial graph networks" ?

3. What are the topologies used in structured peer-to-peer networking?

4. What are the topological properties of a binomial graph?

Accepted Answer

This paper presents an optimal ( shortest path ) two-terminal routing algorithm for BMG networks.

Accepted Answer

There are several improvements that the authors plan for the near future.. Over the longer term, the authors hope that BMG will become the basic logical topology of the runtime environments within the FT-MPI and Open MPI libraries.

Accepted Answer

used in structured peer-to-peer networking based on distributed hash tables such as CAN [22], Chord [23], SkipNet [24], Kademlia [25], Viceroy [26], Pastry [27] and Tapestry [28], are also scalable and fault-tolerant.

Accepted Answer

Binomial graph (BMG) [29] provides desirable topological properties in terms of both scalability and faulttolerance for high performance computing such as reasonable degree, regular graph (every node has the same degree), low diameter, symmetric graph (in the sense that an average inter-nodal distance is the same from any source node) and low cost factor.

Accepted Answer

Counting the bit of a 32-bit integer can be performed by masking out four sets of eight bits in the given integer and indexing them into the LTB8 array.

Accepted Answer

by using the counter-clockwise links the authors can use only 2 hops by jumping to distance 8 (1000) on one direction and 1 (0001) on the other direction (7 = 8-1).

Accepted Answer

The number of loops (l) can be limited by the diameter of BMG, i.e., |d ± l × n| ≤ D × jk, where jk is the maximum power of 2 that is less than or equal to n.

Accepted Answer

To satisfy the requirements of such a dynamic environment (where the available number of resources is fluctuating), a scalable and fault-tolerant communication framework is needed.

Accepted Answer

several high performance computing platforms have been installed with more than 10,000 CPUs, such as Blue-Gene/L at LLNL, BGW at IBM and Columbia at NASA [1].

Accepted Answer

Instead of recomputing the next hop in every message transmission, the breadth-first search technique can use a routing table to keep the result of the next hop sorted by the shortest path from the node itself to all other nodes in BMG.

Accepted Answer

In conclusion, the routing for a distance of 110 in the clockwise direction can be performed within three hops, i.e., one jump in a clockwise direction with the distance 128 and two jumps in a counter-clockwise direction with the distance 2 respectively 16.

Accepted Answer

This procedure is repeatedly performed until there is no consecutive bit left or the result after adding the values is more than jm, where jm is a maximum power of 2 that is less than or equal to n.

Accepted Answer

Hence the equivalence class of distance is applied, i.e., distance d is the same as distance |d±(l×n)|, where l is number of loops and l ∈ N.

Accepted Answer

This figure indicates that an undirected chord rout-2if the number of nodes in the undirected Chord is not power of two, it will create roughly the same small groups of nodes such that the number of groups is a power of two and will use their routing algorithm [36] between those groups.ing algorithm is not optimal for BMG unless the number of nodes is a power of 2 or middle points between the power of 2 (e.g., 24, 48, 96, ...).

Accepted Answer

Find neighborID which has the estimated shortest distance to destID Require: 1 ≤ myID ≤ n ∧ 1 ≤ destID ≤ n, n ∈ N 1: Min ⇐ ∞ 2: Get neighborID of myID 3: for i = 0 to (Numbersofneighbor) − 1 do 4: Distance ⇐ |destID − neighborID[i]| 5: if Distance < Min then 6: Min ⇐ Distance 7: nextHopID=neighborID[i] 8: end if 9: end for 10: Return nextHopIDIn order to always stay on the shortest path from a source to a destination, messages must be delivered through a neighbor that has the estimated shortest hop to the destination unlike the original basic sub-optimal algorithm that estimates the shortest distance between neighbors and destination (i.e., a greedy algorithm).

Accepted Answer

Estimating the number of hops using the bit counting method might be too pessimistic, e.g., if a distance between a neighbor and a destination (|destID− neighborID|) is 7 (binary is 0111), the bit counting method will estimate the number of hops is 3, jumpingto nodes with distance 4 (0100), 2 (0010) and 1 (0001), respectively.

Exploiting Object-Based Parallelism on Multi-core Multi-processor Clusters

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Most frequently asked questions

1. What contributions have the authors mentioned in the paper "Optimal routing in binomial graph networks" ?

2. What have the authors stated for future works in "Optimal routing in binomial graph networks" ?

3. What are the topologies used in structured peer-to-peer networking?

4. What are the topological properties of a binomial graph?

5. How can The authorcount the bit of a 32-bit integer?

6. How many hops can be used by using the counter-clockwise links?

7. How many loops can be limited by the diameter of BMG?

8. What is the purpose of the communication framework?

9. How many CPUs have been installed at LLNL?

10. What is the way to calculate the overhead of a routing table?

11. How many hops can be performed to get a distance of 110?

12. How many times is the bit counting method repeated?

13. What is the equivalence class of distance?

14. What is the optimal routing algorithm for BMG?

15. What is the complexity of the basic unicast routing algorithm?

16. How many hops can be counted using the bit counting method?

Figures

Citations

Concurrent data processing in a distributed system

Concerto: A Program Parallelization, Orchestration and Distribution Infrastructure

Scalable runtime for MPI: efficiently building the communication infrastructure

Exploring object-level parallelism on chip multi-processors

Empirical assessment of the impact of using automatic static analysis on code quality

References

Introduction to Algorithms

Introduction to algorithms: 4. Turtle graphics

Chord: A scalable peer-to-peer lookup service for internet applications

Pastry: Scalable, Decentralized Object Location, and Routing for Large-Scale Peer-to-Peer Systems

The SPLASH-2 programs: characterization and methodological considerations

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