Reliable appropriate topology design for multiple-processor systems
A Shift and Replace Graph which is a very appropriate candidate for the topology of a multiple-processor system is a function of two positive integers r and m, and is denoted as SRF(r,m). Pradhan and Reddy proved that the node connectivity of SRG(r,m) is at least r and also give a routing algorithm which generally requires 2m jumps if the number of node failures is no larger than r - 1. Later, Esfahanian and Hakimi proved that SRG(r,m) has maximum node connectivity 2r - 2 and give routing algorithms which require: (1) at most m + 3 + log/sub r/m jumps if 3 + log/sub r/m does not exceed m and the number of node failures is at most r - 1; (2) at most m + 5 + log/sub r/m jumps if 4 + log/sub r/m less than or equal to m and the number of node failures if less than or equal to 2r - 3; (3) all the other situations require no more than 2m jumps. By modifying the SRG(r,m), it is first proved that node connectivity of SRG(r,m) can be increased to: (1) 2r - 1 when r = 2, m = 2, and (2) 2r when (r = 2, m > 2) or (r > 2, m greater than or equal to 2, m greater than or equal to 2). The routing algorithms are also given for the modified SRG (r,m), which require at most 2m + 3 jumps when the number of node failures is less than or equal to 2r - 1.
- Research Organization:
- Stevens Inst. of Tech., Hoboken, NJ (USA)
- OSTI ID:
- 7231008
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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