Ternary content addressable memories (TCAMs) are frequently used for fast matching of packets against a given ruleset. While TCAMs can achieve fast matching, they are plagued by high update costs that can make them unusable in a high churn rate environment. We present, in this paper, a systematic and in-depth analysis of the TCAM update problem. We apply partial order theory to derive fundamental constraints on any rule ordering on TCAMs, which ensures correct checking against a given ruleset. This theoretical insight enables us to fully explore the TCAM update algorithms design space, to derive the optimal TCAM update algorithm (though it might not be suitable to be used in practice), and to obtain upper and lower bounds on the performance of practical update algorithms. Having lower bounds, we checked if the smallest update costs are compatible with the churn rate observed in practice, and we observed that this is not always the case. We therefore developed a heuristic based on ruleset splitting, with more than a single TCAM chip, that achieves significant update cost reductions (1.05~11.3x) compared with state-of-the-art techniques.