Optimal Representations of a Traffic Distribution in Switch Memories

Traffic splitting is a required functionality in networks, for example for load balancing over multiple paths or among different servers. The capacity of each server or path implies the distribution by which traffic should be split. A recent approach implements traffic splitting within the ternary content addressable memory (TCAM), which is often available in switches. It is important to reduce the amount of memory allocated for this task since TCAMs are power hungry and are often also required for other tasks such as classification and routing. For splitting a universe of $2^{W}$ addresses into k pieces of particular sizes, we give a simple algorithm that computes an optimal representation in $\tilde{O}(wk)$ time. Furthermore, we prove that a recently published load balancer, called Niagara, which also runs in $\tilde{O}(wk)$ time is in fact optimal. That is, both our algorithm and Niagara produce the smallest possible TCAM that splits the traffic exactly to the required pieces, where the only previously known algorithm for computing optimal exact representation has running time exponential in k. Finally, we rely on our optimal $\tilde{O}(wk)$ runtime algorithm to investigate through extensive experiments the amount of TCAM memory required to represent traffic splitting in typical scenarios.