Cluster computing is now an accepted form of supercomputing. A cluster is a collection of computing nodes interconnected by a high-speed network using a network switch or a number of network switches. Each cluster node is either a workstation, a PC, or a symmetric multiprocessor.
A few years back we proposed a new cluster design that is symmetric and every pair of computing nodes is connected by a single switch.
We based the construction of a cluster using a graph with diameter 1 or 2. The graph in the figure below is called a circulant graph of order 8. It consists of 8 nodes denoted by 0, 1, 2, 3, 4, 5, 6 ,7 and 12 edges connecting each of the pairs {0, 1}, {0, 4}, {0, 7}, {1, 2}, {1, 5}, {2, 3}, {2, 6}, {3, 4}, {3, 7}, {4, 5}, {5, 6}, {6, 7}.
We construct a cluster with 8 network switches and 48 computers. Each network switch has 24 ports and each computer has 4 Network Interface Cards (NICs) to connect to 4 network switches. The cluster is shown below with 8 switches denoted by S0, S1, S2, S3, S4, S5, S6 and S7 and the 48 computers are denoted by 0, 1, 2, ..., 47.
The constructed cluster has the following properties:
- There are 48 computers with 8 network switches.
- With 48 computers, we have a total of 1,128 pairs of computers. All of these pairs are connected by at least one switch. In fact, there are 288 pairs joined by exactly one switch, 720 pairs joined by exactly two switches, and 120 pairs joined by exactly 4 switches.
- If a 100 Mbps ethernet is used, the bidirectional bandwitch per pair of computers is 391.48Mbps.
- The bisection bandwidth of the cluster reaches 9.6Gbps.
- The bisection bandwith per computer reaches 200 Mbps.
by Felix P. Muga II
Associate Professor, Mathematics Department, Ateneo de Manila University
Senior Fellow, Center for People Empowerment in Governance
The Mathematics of Networks
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