Michael Sannella. "SkyBlue: A Multi-Way Local Propagation Constraint Solver for User Interface Construction," ACM SIGGRAPH Symposium on User Interface Software and Technology, Proceedings UIST'94. Marina del Rey, CA, Nov, 1994b. pp. 137-146.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....supported multi way constraints. ThingLab was also a prototype instance object system. EVAL vite [Hudson 1993a] integrates constraints with C by using a preprocessor and a special sub language for the constraints. EVAL vite is a one way solver like Amulet s formula constraints. MultiGarnet [Sannella 1994b] integrated a multi way solver with Garnet s one way solver, and inspired Amulet s goal for providing an architecture to make this kind of investigation easier. Rendezvous [Hill 1994] was designed to help create multi user applications in Lisp. Like Amulet, Rendezvous allows multiple one way ....

Michael Sannella. "SkyBlue: A Multi-Way Local Propagation Constraint Solver for User Interface Construction," ACM SIGGRAPH Symposium on User Interface Software and Technology, Proceedings UIST'94. Marina del Rey, CA, Nov, 1994b. pp. 137-146.

....a single application to be delivered on devices as diverse as a desktop browser, a handheld PDA, and a voice interface raises unique challenges for the application designer. In an attempt to facilitate the development and maintenance of multi device applications, many development frameworks ( 5] [8], 12] 13] force developers to design applications using an abstract specification language that can be automatically transformed into executable applications for each target device. In the PIMA system [3] for example, rather than designing an application using a device specific widget set, ....

....25 30 0 5 5 10 10 15 15 20 20 25 25 30 30 35 35 40 40 45 45 50 Errors ( Number of pages 74 the PIMA framework can be extended to translate the abstract model to any of these target platforms. Although we considered formulating model recovery as a constraintsatisfaction problem (e.g. [8]) we believe that expressing these transformations as a set of rules is more natural. Our approach to building a model using a set of rules is similar to a standard forwardchaining rule engine, but with several differences. Most of the deduction rules are aggregation rules. For example, ....

Sannella, M, SkyBlue: A Multi-Way Local Propagation Constrain Solver for User Interface Construction, Proceedings of UIST '94, pp. 137-146.

....methods can be general sideeffect free procedures that ensure the satisfaction of the constraint, after their execution, by computing some of the constrained variables as a function of the others. Constraints are maintained using an efficient local propagation algorithm based on Skyblue [13] 14] [19], a domain independent solver able to maintain a hi erarchy of multi way, multi output dataflow constraints. The main drawback of such a local propagation algorithm is the limitation to acyclic onstraint graphs. However, as noted by Sannella et al. 21] cyclic constraint networks are seldom ....

....The execution of a daemon s action is sequential and each manipulation of the constraint graph (assignment, assertion and retraction of a constraint) advances the state man ager time for recording the variable s history. State manager time and animation 2 VB2 s current constraint solver [13][19] is unable to Find acyclic solutions of potentially cyclic constraint graphs. An algorithm that removes this limitation is presented in [22] time are kept separate: state manager time always goes forward and is used to keep track of the successive states of the system; animation time can instead ....

Sannella M (1994) Skyblue A Multi-Way Local Propagation Constraint Solver for User Interface Construction. Proc. UIST: 137-146.

....Value Selection. This chapter ends with a simple example illustrating the use of the value selection heuristic proposed. CHAPTER 3. FINITE DOMAIN CONSTRAINT PROGRAMMING 21 3. 2 TRANSFORMING CONSTRAINT HIERARCHIES INTO ORDINARY CONSTRAINT SYSTEM Previous work on solving constraint hierarchies [27, 5, 28, 15, 20] concentrates on speci c solvers for constraint hierarchies either in general or for speci c constraint systems. However, such preferential constraints are not available in most ordinary constraint systems and solvers. In this section, we present a general framework for transforming a constraint ....

....manage to nd better solutions for P2 within 2 hours of search using branch and bound. Problems Pessimistic HCDS Optimistic HCDS Solution Quality CPU Time (s) Solution Quality CPU Time (s) P1 [0 0 5 1442] 0.58 [0 0 5 1442] 0.58 P2 [0 2 25 11096] 1.56 [0 2 15 34168] 1.37 P3 [0 2 25 11096] 0. 8 [0 2 20 22442] 1.34 P4 [0 2 25 11096] 1.37 [0 2 20 22442] 1.27 P5 [0 3 21 14214] 3.61 [0 3 15 39386] 3.41 P6 3600 3600 P7 [0 4 31 48630] 13.21 [0 4 46 73942] 13.32 P8 [0 4 41 50107] 11.36 [0 4 56 73942] 12.23 Table 5.3: Performance of HCDS on Gate Allocation Problem Problems WalkSearch Solution ....

[Article contains additional citation context not shown here]

M. Sannella. Skyblue: A multi-way local propagation constraint solver for user interface construction. In Proceedings of the ACM Symposium on User Interface Software and Technology, pages 137-146. The ACM Press, 1996.

....user interface applications, researchers have proposed various constraint satisfaction methods and constraint solvers. Particularly, they had studied local propagation (or dataflow) constraint solvers that perform computations according to input output relationships among variables [5, 25]. Such local propagation solvers have an advantage that they efficiently handle many kinds of constraints. However, they impose a serious limitation that they can hardly deal with simultaneous constraints and inequalities. Therefore, researchers have recently proposed numerical solvers for linear ....

....trial actually found a global optimal solution, and the average number of twists in the final graph layouts was 2.1. However, it might be possible to obtain a better result by using another implementation of simulated annealing. 3 RELATED WORK AND DISCUSSION Local propagation constraint solvers [5, 25] can be regarded as a method that realizes a module mechanism, because local propagation constraints can be defined as procedures or functions in ordinary programming languages. However, local propagation solvers impose a limitation that they can hardly deal with simultaneous constraints and ....

Sannella, M. SkyBlue: A multi-way local propagation constraint solver for user interface construction. In Proc. ACM UIST, 1994, 137--146.

....Constraints form a main category of behavior nodes. A constraint node is associated with the constrained object and establishes its constraints at the beginning of its lifetime, and removes the constraints when its lifetime ends. Constraint networks managed by constraint solvers (e.g. SkyBlue [13]) can be anchored in behavior graphs and connected to the flow of time and events by behavior nodes. Time dependent functions which are applied to parameters of graphics objects represent a main category of constraint nodes. A time constraint behavior node (MTimeCt) associates an attribute of a ....

M. Sannella. SkyBlue: A Multi-Way Local Propagation Constraint Solver for User Interface Construction. Proceedings of UIST'94, pp. 137-146.

....exercise was a version of the video game KLAX. 1 While the conceptual architecture contained a component whose purpose was layout and global constraint maintenance, KLAX constraints were implemented locally with inline code. The two constraint managers we selected for this exercise were SkyBlue [San94] and Amulet s one way formula constraint solver [MM95] The main reasons they were selected were availability of the source code and the fact that implementations for both existed in C C , the primary language of implementation in KLAX. Initially, a variation of the original KLAX architecture ....

....C. Multiple Constraint Managers in a Single Component LayoutManager 6 had some of its constraints defined in SkyBlue and others in Amulet. Combining multiple constraint solvers in a single system has only recently been identified as a potentially useful approach to constraint management [San94, MM95]. Integrating multiple constraint solvers in a single C2 component is certainly at a different level of granularity. However, this exercise sensitized us to several issues intrinsic to the interaction of heterogeneous constraint managers. Specifying constraints in different solvers over disjoint ....

M. Sannella. SkyBlue: A Multi-Way Local Propagation Constraint Solver for User Interface Construction. In Proceedings of the Seventh Annual ACM Symposium on User Interface Software and Technology, Marina del Ray, CA, November 1994, pages 137-146.

....level. For example, suppose we have the constraint A B C = 0. If A changes, the constraint solver must choose whether to change B , C , or both. One approach to eliminate this ambiguity is to divide constraints into hierarchies, or assign priority levels, or strengths to constraints [Sannella 94] Freeman Benson 90] Lopez 94a] Lopez 94b] The constraint solver then tries to satisfy as many constraints as Leonidas Deligiannidis Page 20 possible, solving the highest priority constraints first, and then the next highest, and so on. One issue that constraint hierarchies do not address is ....

....always up to date. Constraint Systems People have developed constraint solvers that support both lazy and or eager evaluations, incremental solving and one way and multi way constraint solvers. For example, the DeltaBlue [Freeman Benson 90] algorithm (an incremental version of Blue) and SkyBlue [Sannella 94] a more general successor of the DeltaBlue) maintain an evolving solution to the constraint hierarchy as constraints are added and removed. DeltaBlue minimizes the cost of finding a new solution after each change by exploiting its knowledge of the last solution. Both DeltaBlue and SkyBlue ....

[Article contains additional citation context not shown here]

Michael Sannella. "SkyBlue: A Multi-Way Local Propagation Constraint Solver for User Interface Construction". UIST `94 November 2-4, 1994, pages 137-146.

.... Theta 5=9 and F = 32 (9=5) Theta C. Note the use of the assignment operator = instead of the equality operator = Given F or C, the other can be computed by extracting the appropriate program. Constraint programming has been attractive in many application areas such as user interfaces [San94] modeling, and design [Med95, MM89, Ste93] due to its ability to encapsulate many different problems (view any of the variables as unknown) within a single constraint specification. Logic languages [CM84] are specific instances of constraint languages in that the constraints in logic languages ....

Michael Sannella. Skyblue: A multi-way local propagation constraint solver for user interface construction. In Proceedings of the 1994 ACM Symposium on User Interface Software and Technology, pages 137--146, 1994.

....g for constraint weights is defined as: g( C i ) j X c2C i w c e(c ) In this paper, we concentrate on the use of global comparators and more specifically weighted sum better. 2. 2 Transforming Hierarchies into Non hierarchical Systems Previous work on solving constraint hierarchies [18, 4, 19, 9, 12] concentrates on specific solvers for constraint hierarchies either in general or for specific constraint systems. However, such preferential constraints are not available in practical constraint systems and solvers. In this section, we present a general framework for transforming a constraint ....

M. Sannella. Skyblue: A multi-way local propagation constraint solver for user interface construction. In Proceedings of the ACM Symposium on User Interface Software and Technology, pages 137--146. The ACM Press, 1996.

....in a useful manner. In such applications, there is usually a constrint network with a given solution, which is perturbed, either by adding a constraint, or by changing the value of one or more of the variables. The goal is to find a new solution for the perturbed network. DeltaBlue [8] and SkyBlue [7] are constraint engines for graphic editors that support linear equalities in an efficient manner, as long as the constraint graph is acyclic. SkyBlue supports cycles in constraint graphs indirectly, by detecting them and calling an external mechanism, such as a simultaneous linear equation ....

M. Sannella. SkyBlue: A multi-way local propagation constraint solver for user interface construction. In Proc. 1994 ACM Symp. User Interface Software and Technology, pages 137--146, 1994.

.... [22] The other most common sort of constraint satisfaction algorithm for interactive graphics is a local propagation algorithm for multi way constraints (thus restricting the constraints to functional constraints only and acyclic constraint graphs) Recent examples include DeltaBlue [30] SkyBlue [29], and QuickPlan [32] these three algorithms also support constraint hierarchies. The DETAIL system [20] is quite closely related to Ultraviolet. Like Ultraviolet, it is designed for user interface applications, and is a kind of meta solver that supports different subsolvers. It supports multi way ....

Michael Sannella. SkyBlue: A multi-way local propagation constraint solver for user interface construction. In Proceedings of the 1994 ACM Symposium on User Interface Software and Technology, pages 137--146, 1994.

....been applied to other application areas including circuits [1] graphical interfaces [10, 11, 13, 14, 18, 25, 19] and spreadsheets. Multi way, multi output dataflow constraint systems have also been developed for graphical interfaces, including ThingLab [3, 8, 23] Kaleidoscope [7] and MultiGarnet [22, 21, 24]. Multi way constraints are more powerful than one way constraints, but one way constraints suffice for many applications and in general are more easily managed by programmers. Researchers have adopted various approaches to storage optimization for dataflow constraints. Constant propagation ....

SANNELLA, M. Skyblue: A multi-way local propagation constraint solver for user interface construction. In ACM SIGGRAPH Symposium on User Interface Software and Technology (Marina del Rey, CA, Nov. 1994), Proceedings UIST'94, pp. 137--146.

....closer to the conceptual level of specification of the interface, and at the same time overcomes limitations for its reusability. The technique we propose, Virtual Slots, can be implemented as an extension to languages like the ones used in systems such as Garnet, 4] Rendezvous, 1] SkyBlue, [5], or ThingLab II, 2] The use of Virtual Slots improves the language s power and expressivity, and makes some programming tasks easier. As a simple example that will allow us to introduce both the limitations of present languages, and the kind of solution we propose, we consider the development ....

Sannella, M.: SkyBlue: A Multi-Way Local Propagation Constraint Solver for User Interface Construction. In Proceedings UIST'94, pp. 137-146, November 1994.

....variety of systems, is that of local propagation algorithms for multiway constraints, constraint hierarchies, functional constraints only, and no cycles. These algorithms provide a good balance between expressiveness and efficiency; recent examples include DeltaBlue [Sannella et al. 93] SkyBlue [Sannella 94] and QuickPlan [Vander Zanden 96] In local propagation algorithms, each constraint has a set of methods that can be used to satisfy the constraint. When a method is executed, it sets one of the constrained variables to a value such that the constraint is satisfied. All of the constraints in a ....

Michael Sannella. SkyBlue: A multi-way local propagation constraint solver for user interface construction. In Proceedings of the 1994 ACM Symposium on User Interface Software and Technology, pages 137--146, 1994.

....and used in a variety of systems, is that of local propagation algorithms for multi way constraints, constraint hierarchies, functional constraints only, and no cycles. These algorithms provide a good balance between expressiveness and efficiency; examples include DeltaBlue [8] SkyBlue [7], Detail [6] and QuickPlan [9] In local propagation algorithms, each constraint has a set of methods that can be used to satisfy the constraint. When a method is executed, it sets one of the constrained variables to a value such that the constraint is satisfied. All of the constraints in a ....

Michael Sannella. SkyBlue: A multi-way local propagation constraint solver for user interface construction. In Proceedings of the 1994 ACM Symposium on User Interface Software and Technology, pages 137--146, 1994.

....architecture. Center: To do list with item indicating a problem with Status Logic. Right: Implementation Architecture. Small shapes attached to components are user interface affordances for making connections. 10 of 16 porating a research off the shelf constraint management system, SkyBlue [29], into the application. Constraint management code, such as specifying the left and right boundaries of palette s movement and ensuring that the tiles on the palette move along with the palette, was dispersed throughout the original application. This variation replaced that code with SkyBlue ....

M. Sannella. "SkyBlue: A Multi-Way Local Propagation Constraint Solver for User Interface Construction." In Proceedings of the Seventh Annual ACM Symposium on User Interface Software and Technology, pages 137--146, Marina del Rey, California, November 1994.

....object data directly, they only use public methods of objects. We opt for not accessing object data directly in order to be independent from the implementation of the glyph class, to allow objects to be distributed over the network, and to maintain encapsulation. Current constraint solvers (e.g. [24]) are based on atomic variables; using object data directly as these variables would violate the encapsulation principle. Instead, we define several controller classes which install a communication between protocol constraints and constrainable glyphs. Typically constraints are contained in the ....

Michael Sannella. SkyBlue: A Multi-Way Local Propagation Constraint Solver for User Interface Construction. Dept. of Computer Science and Engineering, FR-35, Univ. of Washington, 1994.

....to strengths. It is adopted in recent constraint solvers for GUIs such as Cassowary and QOCA [12] Local propagation gradually solves hierarchies by repeatedly selecting uniquely satisfiable constraints. It is used in various constraint solvers for GUIs including DeltaBlue [22] and SkyBlue [73]. CHAPTER 1. INTRODUCTION 6 First, to see the refining method, suppose we have the following constraint hierarchy: required x = y strong y = z 1 medium z = 0 weak z = 1: This is solved as follows: First, by satisfying the strongest constraint required x = y, the method reduces the set 2 ....

....identify the overall dependency among cells with a partial order among blocks. Then we can perform GLP in a unique manner as is with conventional local 1 The SkyBlue algorithm also realizes simultaneous satisfaction by invoking cycle solvers, but provides no features for relaxing constraints [72, 73]. CHAPTER 4. THE DETAIL CONSTRAINT SOLVER 36 (a) x y strong 3 = y x (b) x y strong 3 = y x weak 1 = y x (c) x strong 0 = x strong 2 = x Figure 4.1: Constraint cells. required t = 1 1 A weak t = u u 1 B weak v = 0 v 1 E strong t v = w w 2 weak w = x required x ....

[Article contains additional citation context not shown here]

Sannella, M., "SkyBlue: A Multi-Way Local Propagation Constraint Solver for User Interface Construction," in Proceedings of the ACM Symposium on User Interface Software and Technology (UIST), Nov. 1994, pp. 137--146.

....management system 1 INTRODUCTION A constraint is a relationship to be maintained among a set of variables. For example, A B=C represents the relationship that C is the sum of A and B. Constraints are widely recognized as a useful tool for user interface construction [1] 4] 10] 14] 20] [21], 23] 26] Through constraints, relationships among user interface components and their applications can be defined declaratively, leaving the task of maintaining the relationships to a constraint solver, an algorithm that determines a plan for computing constrained values in a way that is ....

....line drawings. Algebraic transformations were used to eliminate cycles in the constraint graph. When propagation encountered a cycle, the transformation system attempted to replace each cycle with a single complex constraint (i.e. executed through the use of a cycle solver) The SkyBlue algorithm [21] provides support for solving hierarchies of multi way, multi output constraints, and has been applied in the Garnet toolkit [22] Multi output constraints provide a convenient way to group multiple related computations into a single constraint. SkyBlue allows cyclic relationships to be formed ....

Michael Sannella. SkyBlue: A Multi-way Local Propagation Constraint Solver for User Interface Construction. In proceedings of the ACM SIGGRAPH Symposium on User Interface Software and Technology, pages 137-146, November 1994.

....multi way relationships has given impetus to research aimed at making multi way constraints more palatable to programmers. These efforts have focused on making multi way constraints efficient and predictable. Incremental planning algorithms have been devised to address the performance issue [13, 40, 48]. Constraint hierarchies have been introduced to address the predictability issue [5, 7] Constraint hierarchies allow users to attach strengths to constraints, indicating how strongly the user wants particular constraints satisfied. If the constraint solver cannot satisfy all the constraints, it ....

.... then considering the effect that this assignment has on constraints that share variables with this constraint (thus propagating the effects of the assignment locally) Local propagation algorithms may use a number of techniques, including propagation of degrees of freedom, propagation of conflict [44, 18, 13, 40], mark sweep [21] and bipartite graph matching [15] Propagation of degrees of freedom. Propagation of degrees of freedom is the technique used by QuickPlan. Examples of systems that use this technique include SketchPad [45] and QuickPlan 39 Binary Tree Visualizer ###### ###### ###### ....

[Article contains additional citation context not shown here]

Michael Sannella=. SkyBlue: A Multi-Way Local Propagation Constraint Solver for User Interface Construction. ACM SIGGRAPH Symposium on User Interface Software and Technology, Proceedings UIST'94, Marina del Rey, CA, Nov., 1994, pp. 137-146.

.... objects [28] Our system uses instead multi way local propagation constraints, which offer support for two way communication between objects while remaining efficient enough to ensure the responsiveness of the system [17; 18; 27] TBAG [14] also uses multi way constraints maintained by Skyblue [27], but its functional approach concentrates more on modeling time varying behaviors than on creating interactive systems. Much effort has been spent in developing powerful numerical solvers for computer graphics (e.g. 7; 15; 16] This work is complementary to ours, which focuses more on ....

Sannella M (1994) Skyblue: A Multi-Way Local Propagation Constraint Solver for User Interface Construction. Proc. UIST : 137-146.

....and used in a variety of systems, is that of local propagation algorithms for multi way constraints, constraint hierarchies, functional constraints only, and no cycles. These algorithms provide a good balance between expressiveness and efficiency; recent examples include DeltaBlue [19] SkyBlue [18], and QuickPlan [20] In local propagation algorithms, each constraint has a set of methods that can be used to satisfy the constraint. When a method is executed, it sets one of the constrained variables to a value such that the constraint is satisfied. All of the constraints in a traditional ....

Michael Sannella. SkyBlue: A multi-way local propagation constraint solver for user interface construction. In Proceedings of the 1994 ACM Symposium on User Interface Software and Technology, pages 137-- 146, 1994.

.... to describe over constrained realworld problems by specifying constraints with hierarchical strengths or preferences [1, 2] and have been applied to various research areas such as constraint logic programming [11, 13] constraint imperative programming [3] and graphical user interfaces [8, 9]. Intuitively, in a constraint hierarchy, the stronger a constraint is, the more it influences the solutions of the hierarchy. For example, the hierarchy of the constraints strong x = 0 and weak x = 1 yields the solution x 0. This property enables programmers to specify preferential or default ....

....algorithm [11] and a hierarchical constraint logic programming language CHAL [10] Local propagation gradually solves hierarchies by repeatedly selecting uniquely satisfiable constraints. It is mainly used in constraint solvers for graphical user interfaces such as DeltaBlue [4] SkyBlue [9], and DETAIL [6] First, to illustrate the refining method, suppose we have a hierarchy consisting of required x = y, strong y = z 1, medium z = 0, and weak z = 1. This is solved as follows: first, by satisfying the strongest constraint required x = y, the method reduces the set 2 of all ....

[Article contains additional citation context not shown here]

Sannella, M., "SkyBlue: A Multi-Way Local Propagation Constraint Solver for User Interface Construction," in UIST'94, ACM, Nov. 1994, pp. 137--146.

....new kinds of constraint solvers (e.g. Vander Zanden 92] Hill 93] Gleicher 93] Therefore, in addition to the standard solver described above, Amulet is designed to support other constraint systems at the same time. Since two different constraint solvers were made to work together in Garnet [Sannella 94] we believe that this will work, but how to schedule the various solvers is an open research issue, especially when multiple solvers want to set the same slot. 3.4. Opal Output Model The graphical object layer of Amulet is called Opal, which stands for Object Programming Aggregate Layer. Opal ....

Michael Sannella, "SkyBlue: A Multi-Way Local Propagation Constraint Solver for User Interface Construction," Proceedings UIST'94: ACM SIGGRAPH Symposium on User Interface Software and Technology. Nov, 1994, Marina del Rey, CA, pp. 137-146

....methods can be general sideeffect free procedures that ensure the satisfaction of the constraint, after their execution, by computing some of the constrained variables as a function of the others. Constraints are maintained using an efficient local propagation algorithm based on Skyblue [13] 14][19], a domain independent solver able to maintain a hierarchy of multi way, multi output dataflow constraints. The main drawback of such a local propagation algorithm is the limitation to acyclic onstraint graphs. However, as noted by Sannella et al. 21] cyclic constraint networks are seldom ....

....The execution of a daemon s action is sequential and each manipulation of the constraint graph (assignment, assertion and retraction of a constraint) advances the state manager time for recording the variable s history. State manager time and animation 2 VB2 s current constraint solver [13][19] is unable to find acyclic solutions of potentially cyclic constraint graphs. An algorithm that removes this limitation is presented in [22] time are kept separate: state manager time always goes forward and is used to keep track of the successive states of the system; animation time can ....

Sannella M (1994) Skyblue A Multi-Way Local Propagation Constraint Solver for User Interface Construction. Proc. UIST: 137-146.

....and integrating constraints with a prototype instance object system originated in Garnet [29] EVAL vite [8] integrates constraints with C by using a preprocessor and a special sub language for the constraints. EVAL vite is a one way solver like Amulet s formula constraints. MultiGarnet [28] integrated a multi way solver with Garnet s oneway solver, and inspired Amulet s goal for providing an architecture to make this kind of investigation easier. Rendezvous [7] was designed to help create multi user applications in Lisp. Like Amulet, Rendezvous allows multiple one way constraints to ....

M. Sannella. "SkyBlue: A Multi-Way Local Propagation Constraint Solver for User Interface Construction," in ACM SIGGRAPH Symposium on User Interface Software and Technology. 1994. Marina del Rey, CA: pp. 137-146. Proceedings UIST'94.

....and integrating constraints with a prototype instance object system originated in Garnet [30] EVAL vite [8] integrates constraints with C by using a preprocessor and a special sub language for the constraints. EVAL vite is a one way solver like Amulet s formula constraints. MultiGarnet [29] integrated a multi way solver with Garnet s oneway solver, and inspired Amulet s goal for providing an architecture to make this kind of investigation easier. Rendezvous [7] was designed to help create multi user applications in Lisp. Like Amulet, Rendezvous allows multiple one way constraints to ....

M. Sannella. "SkyBlue: A Multi-Way Local Propagation Constraint Solver for User Interface Construction," in Proceedings UIST'94: ACM SIGGRAPH Symposium on User Interface Software and Technology. 1994. Marina del Rey, CA: pp. 137146.

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Sannella, Michael. SkyBlue: A Multi-way Local Propagation Constraint Solver for User Interface Construction. In Proceedings of the ACM SIGGRAPH Symposium on User Interface Software and Technology, pages 137-146, November 1994.

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