This paper presents an asymptotically optimal online algorithm for compressing the Forwarding Information Base (FIB) of a router under a stream of updates (namely insert rule, delete rule, and change port of prefix). The objective of the algorithm is to dynamically aggregate forwarding rules into a smaller but equivalent set of rules while taking into account FIB update costs. The problem can be regarded as a new variant of ski rental on the FIB trie, and we prove that our deterministic algorithm is 3.603-competitive. Moreover, a lower bound of 1.636 is derived for any online algorithm.
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