  Traffic splitting is a required functionality in networks, for example for
load balancing over paths or servers, or by the source's access restrictions.
The capacities of the servers (or the number of users with particular access
restrictions) determine the sizes of the parts into 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 consuming and are often also required for other tasks such as
classification and routing. In the longest-prefix model (LPM), Draves et al.
(INFOCOM 1999) find a minimal representation of a function, and Sadeh et al.
(INFOCOM 2019) find a minimal representation of a partition. In certain
situations, range-functions are of special interest, that is, all the addresses
with the same target, or action, are consecutive. In this paper we show that
minimizing the amount of TCAM entries to represent a partition comes at the
cost of fragmentation, such that for some partitions some actions must have
multiple ranges. Then, we also study the case where each target must have a
single segment of addresses.
