Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, June 16, 2015, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Christof Lutteroth (University of Auckland)

Tiling Algebra for Constraint-based Layout Editing

The constraint-based layout model is a very powerful model to describe a wide range of graphical user interface (GUI) layouts, based on linear constraints. However, the advantages of the constraint-based layout model come at a price: layout designers have to ensure layouts are sound, i.e. they are solvable and items in the layout do not overlap each other. Keeping a layout sound is non-trivial since editing one constraint may have undesirable effect on other constraints. In this talk I present a new formalism for constraint-based layouts, which we call a tiling algebra. Editing operations on layouts are specified as algebraic operations, which guarantees that these operations keep a layout sound. We propose to model tiling operations with two operators that are isomorphic cancellative semigroup operators with involution if seen as binary operators. While these semigroup operators alone cover an interesting subset of layouts, called fragments, we show that there are more involved layouts, such as the pinwheel layout, which cannot be modeled with these operators alone. We introduce a third operator which is isomorphic to a Boolean conjunction. Finally we discuss symmetry properties and show the involutions of the semigroups and the isomorphism between both semigroups form the symmetry group D_4.

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