  Augmentative and Alternative Communication (AAC) systems allow people with
disabilities to provide input to devices which empower them to more fully
interact with their environment. Within AAC, switch scanning is a common
paradigm for spelling where a set of characters is highlighted and the user is
queried as to whether their target character is in the highlighted set. These
queries are used to traverse a decision tree which successively prunes away
characters until only a single one remains (the estimate). This work seeks a
decision tree which requires the fewest expected queries per decision sequence
(EQPD). In particular, we remove the constraint that the decision tree needs to
be a row-item or group-row-item style tree and minimize EQPD. We pose the
problem as a Huffman code with variable, integer cost and solve it with a mild
extension of Golin's method in "A dynamic programming algorithm for
constructing optimal prefix-free codes with unequal letter costs", IEEE
Transactions on Information Theory (1998). Additionally, we model the user on
the query level by their probability of detection and false alarm to derive
their expected performance on the character level given some decision tree. We
perform experiments which show that the min EQPD decision tree (Karp) may
reduce selection times, especially for timed (single switch) switch scanning.
