Compact routing with stretch factor of less than three
Cowen gave a universal compact routing algorithm with a stretch factor of three and table-size of O(n(2/3) log(4/3) n) based on a simple and practical model [1]. (The table-size is later improved to O(n(1/2) log(3/2) n) [11].) This paper considers, using the same model, how the necessary table-size differs if the stretch factor must be less than three. It is shown that: (i) There is a routing algorithm with a stretch factor of two whose table-size is (n - rootn + 2) log n. (ii) There is a network for which any routing algorithm that follows the model and with a stretch factor of less than three needs a table-size of (n - 2 rootn) log n in at least one node. Thus, we can only reduce roughly an additive rootn log n (i.e., rootn table-entries) from the trivial table-size of n log n which obviously enables shortest-path routing. Furthermore it turns out that we can reduce only an additive log it (i.e., only one table-entry) from the. trivial n log n if we have to achieve a stretch factor of less than two. Thus the algorithm (i) is (roughly) tight both in its stretch factor and in its table-size.
compact routing stretch factor distributed algorithms