We study a variant of Interval Routing [SK85, LT86] where the routing range associated with every link is represented by a linear (i.e., contiguous) interval with no wrap around. This kind of routing schemes arises naturally in the study of dynamic Prefix Routing [BLT90]. Linear Interval Routing schemes are precisely the Prefix Routing schemes that use an alphabet of one symbol. We characterize the type of networks that admit optimum Linear Interval Routing schemes. It is shown that several well-known interconnection networks such as hypercubes, certain n-tori, and n-dimensional grids all with unit-cost links, have optimum Linear Interval Routing schemes. We also introduce the multi-label Linear Interval Routing schemes where each link may contain more than one label, and we prove several characterization results for these schemes
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