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<p><b>Abstract</b>—In this paper, we study the properties of the bus-based hypercube, denoted as <tmath>U(n,b)</tmath>, which is a kind of multiple-bus networks (MBN). <tmath>U(n,b)</tmath> consists of <tmath>2^{n}</tmath> processors and <tmath>2^{b}</tmath> buses, where <tmath>0\leq b\leq n-1</tmath>, and each processor is connected to either <tmath>\lceil{\frac{b+2}{2}}\rceil</tmath> or <tmath>\lceil{\frac{b+1}{2}}\rceil</tmath> buses. We show that the diameter of <tmath>U(n,b)</tmath> is <tmath>\lceil{\frac{b+1}{2}}\rceil</tmath> if <tmath>b\geq2</tmath>. We also present an algorithm to select the best neighbor processor via which we can obtain one shortest routing path. In <tmath>U(n,b)</tmath>, we show that if there exist some faults, the fault diameter <tmath>DF(n,b,f)\leq b+1</tmath>, where <tmath>f</tmath> is the sum of bus faults and processor faults and <tmath>0\leq f\leq\lceil{\frac{b-3}{2}}\rceil</tmath>. Furthermore, we also show that the bus-fault diameter <tmath>DB(n,b,f)\leq\lfloor{\frac{b}{2}}\rfloor+3</tmath>, where <tmath>0\leq f\leq\lceil{\frac{b-1}{2}}\rceil</tmath> and <tmath>f</tmath> is the number of bus faults. These results improve significantly the previous result that <tmath>DB(n,b,f)\leq b+2f+1</tmath>, where <tmath>f</tmath> is the number of bus faults.</p>
Multiple-bus network, hypercube, routing algorithm, diameter, fault tolerance.
Lee-Juan Fan, Chang-Biau Yang, Shyue-Horng Shiau, "Routing Algorithms on the Bus-Based Hypercube Network", IEEE Transactions on Parallel & Distributed Systems, vol. 16, no. , pp. 335-348, April 2005, doi:10.1109/TPDS.2005.49
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