Abstract
Interval routing is an attractive space-efficient routing method for point-to-point communication networks which found industrial applications in novel transputer routing technology.
Recently much effort is devoted to relate the efficiency (measured by dilation or stretch factor) to space requirements (measured by compactness or total memory bits) in a variety of compact routing methods [1, 5, 9, 10, 11, 15]. We add new results in this direction for interval routing.
For the shortest path interval routing we give a technique for obtaining lower bounds on compactness. We apply this technique to shuffle exchange graph of order n and get improved lower bound on compactness in the form Ω(n ½−ε ), where ε is arbitary positive constant. In [8] we applied this technique also to other interconnection networks, obtaining new lower bounds Ω(√n/log n) for cube connected cycles and butterfly, and Ω(n(log log n/log n)5) for star graph. Previous lower bounds for these networks were only constant [4]. For the dilation bounded interval routing we give a routing algorithm with the dilation [1.5D] and the compactness O(√n log n on n-node networks with the diameter D. It is the first nontrivial upper bound on the dilation bounded interval routing on general networks. Moreover, we construct a network on which each interval routing with dilation 1.5D − 3 needs compactness at least Ω(√n). It is an asymptotical improvement over the previous lower bounds in [15] and it is also better than independently obtained lower bounds in [16].
This research has been partially supported by the EC Cooperative Action IC 1000 (project AZTEC: Algorithms for Future Technologies) and by VEGA 1/4315/97.
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Kráľovič, R., Ružička, P., Štefankovič, D. (1997). The complexity of shortest path and dilation bounded interval routing. In: Lengauer, C., Griebl, M., Gorlatch, S. (eds) Euro-Par'97 Parallel Processing. Euro-Par 1997. Lecture Notes in Computer Science, vol 1300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0002742
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