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Text entry has been a bottleneck of nontraditional computing devices. One of the promising methods is the virtual keyboard for touch screens. Correcting previous estimates on virtual keyboard efficiency in the literature, we estimated the potential performance of the existing Qwerty, FITALY, and OPTI designs of virtual keyboards to be in the neighborhood of 28, 36, and 38 words per minute (wpm), respectively. This article presents 2 quantitative design techniques to search for virtual keyboard layouts. The first technique simulated the dynamics of a keyboard with digraph springs between keys, which produced a Hooke keyboard with 41.6 wpm movement efficiency. The second technique used a Metropolis random walk algorithm guided by a "Fitts-digraph energy" objective function that quantifies the movement efficiency of a virtual keyboard. This method produced various Metropolis keyboards with different shapes …