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T9-like keyboards (i.e., 3×3 layouts) have been commonly used on small touchscreen devices to mitigate the problem of tapping tiny keys with imprecise finger touch (e.g., T9 is the default keyboard on Samsung Gear 2). In this paper, we proposed a computational approach to design optimal T9-like layouts by considering three key factors: clarity, speed, and learnability. In particular, we devised a clarity metric to model the word collisions (i.e., words with identical tapping sequences), used the Fitts-Digraph model to predict speed, and introduced a Qwerty-bounded constraint to ensure high learnability. Founded upon rigorous mathematical optimization, our investigation led to Optimal-T9, an optimized T9-like layout which outperformed the original T9 and other T9-like layouts. A user study showed that its average input speed was 17% faster than T9 and 26% faster than a T9-like layout from literature. Optimal-T9 also …