Many user interface toolkits use constraint solvers to maintain geometric relationships between graphic objects, or to connect the graphics to the application data structures. One efficient and flexible technique for maintaining constraints is multi-way local propagation, where constraints are represented by sets of method procedures. To satisfy a set of constraints, a local propagation solver executes one method from each constraint.SkyBlue is an incremental constraint solver that uses local propagation to maintain a set of constraints as individual constraints are added and removed. If all of the constraints cannot be satisfied, SkyBlue leaves weaker constraints unsatisfied in order to satisfy stronger constraints (maintaining a constraint hierarchy). SkyBlue is a more general successor to the DeltaBlue algorithm that satisfies cycles of methods by calling external cycle solvers and supports multi-output methods. These features make SkyBlue more useful for constructing user interfaces, since cycles of constraints can occur frequently in user interface applications and multi-output methods are necessary to represent some useful constraints. This paper discusses some of applications that use SkyBlue, presents times for some user interface benchmarks and describes the SkyBlue algorithm in detail.

Abstract The efficient satisfaction of constraints is essential to the performance of constraint‐based user interfaces. In the past, most constraint‐based user interfaces have used one‐way rather than multi‐way constraints because of a widespread belief that one‐way constraints were more efficient. In this paper we argue that many user interface construction problems are handled more naturally and elegantly by multi‐way constraints than by one‐way constraints. We present pseudocode for an incremental multi‐way constraint satisfaction algorithm, DeltaBlue, and describe experience in using the algorithm in two user interface toolkits. Finally, we provide performance figures demonstrating that multi‐way constraint solvers can be entirely competitive in performance with one‐way constraint solvers.