Michel Gangnet and Burton Rosenberg. Constraint programming and graph algorithms. In Second International Symposium on Articial Intelligence and Mathematics, January 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....effects of the assignment locally) Local propagation algorithms may use a number of techniques, including propagation of degrees of freedom, propagation of conflict [Steele Jr. 1980; Gosling 1983; Freeman Benson et al. 1990; Sannella 1994b] mark sweep [Hill 1993] and bipartite graph matching [Gangnet and Rosenberg 1992]: 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 [Sutherland 1963] and ThingLab [Borning 1981] Unlike QuickPlan, these systems did not support either multi output ....

....Graph Matching. Bipartite matching selects a set of graph edges such that no edge QuickPlan 51 shares a common vertex (variable or constraint) The constraint connected to each edge outputs the variable connected to that edge. The algorithm of Gangnet and Rosenberg uses this technique [Gangnet and Rosenberg 1992]. Table 6 compares QuickPlan with the incremental planning algorithms that use these techniques. Table 6: Comparison of multi way, local propagation solvers. An algorithm satisfies the acyclic solution criterion if it is designed to find an acyclic solution in a potentially cyclic constraint ....

Gangnet, M. and Rosenberg, B. 1992. Constraint programming and graph algorithms. In Second International Symposium on Artificial Intelligence and Mathematics.

....motivating our work (Section 1.2) In Section 1.3 we introduce HCLP and present a proof of its noncompositional nature. We discuss bags in Section 1.4. In Section 2 we define BCH, including a definition of guards; we discuss BCH s relationship to HCLP and its complexity and incrementality. Section 3 contains FGH, the second part of our scheme, and includes the description of a particular filter function and a discussion of its complexity. Section 4 begins with an example which includes a comparison with HCLP, and then proves the equivalence of FGH and HCLP. Finally we draw conclusions and ....

....hold in general, almost without being mentioned. Therefore, the focus in previous CLP work has tended to be on incrementality alone, rather than on its relationship with compositionality. Query composition in logic programming and CLP p 1 (X) q 1 (X) p 2 (X) q 2 (X) p 3 (X) p(X) q(X) fP 1 , P 2 , P 3 g fQ 1 , Q 2 g p(X) q(X) fP i i Q j j i = 1; 2; 3; j = 1; 2g Figure 1: Composing queries in logic programming Consider the two programs in Figure 1. They may be logic programs or constraint logic programs. The subscripts 1,2,3 are not part of ....

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Michel Gangnet and Burton Rosenberg. Constraint Programming and Graph Algorithms. In 2nd International Symposium on Artificial Intelligence and Mathematics, January 1992.

.... But DeltaBlue cannot cope with multiple output variables or with cycles (see below) and SkyBlue copes with them only be invoking a separate solver (for example, one based on Gaussian elimination or the Simplex method) DeltaBlue has been shown to be optimal for its task by Gangnet and Rosenberg [35]. Both DeltaBlue and SkyBlue provide one solution chosen nondeterministically, as opposed to our work which provides all solutions. Borning has said [Private Communication] that in general his applications only need the first solution. The notion of a cycle arises due to the operational nature ....

....hierarchies with constraints, and consider semantics as well as implementations. Implementations and algorithms embodying standard HCLP semantics have been developed by Freeman Benson, Sannella et al. 29, 66, 67] and certain optimality properties have been proven by Gangnet and Rosenberg [35]. The work of Menezes, Barahona, and Codognet [60] is closely related to our interest in incremental versions of HCLP. We discuss this at greater length in Further work , Section 13.7. There has been a great deal of work in the general area of PCSP, including implementations and detailed ....

Michel Gangnet and Burton Rosenberg. Constraint Programming and Graph Algorithms. In 2nd International Symposium on Artificial Intelligence and Mathematics, January 1992.

....graph rather than individual constraints. We can view the constraints and constrained variables as forming a bipartite graph. Each variable and each constraint is represented by a node, with an edge from a constraint node to a variable node if the variable is constrained by the constraint [11]. The constraint graph is acyclic iff this bipartite graph is acyclic. All of these properties are declarative attributes of the constraints or the constraint graph, rather than of the constraint satisfaction algorithm. Naturally, however, the different properties place different requirements on ....

Michel Gangnet and Burton Rosenberg. Constraint programming and graph algorithms. In Second International Symposium on Artificial Intelligence and Mathematics, January 1992.

....the reverse order (i.e. executing rst the methods that were chosen last) This algorithm has been used in SketchPad [ Sutherland, 1963 ] and QuickPlan [ Vander Zanden, 1996 ] 3) A third approach is related to the classical problem of graph matching. It gives the Maximum matching algorithm [ Gangnet and Rosenberg, 1992 ] 3 Dioeerent types of constraint planning problems Existing local propagation algorithms solve dioeerent planning problems that imply various tradeooes between expressiveness and performance: ffl required constraints only, or both required and preferential constraints that are satis ed if ....

.... by 3 Setsj [ Papadimitriou, 1994 ] problem method restriction single output complexity proof algorithms acp1 yes yes P [Sutherland, 1963] PDOF, DeltaBlue acp2 yes no P [Vander Zanden, 1996] QuickPlan acp3 no yes NPC [Maloney, 1991] 3 acp4 no no NPC [Maloney, 1991] 1 and 2 cp1 yes yes P [Gangnet Rosenberg, 1992] Maximum matching cp2 yes no SkyBlue cp3 no yes cp4 no no Table 1: Computational complexity of constraint planning problems. Cycles in the constraint graph are allowed. Constraints are required (not preferential) Every problem depends on three characteristics: 1) a problem that ....

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Michel Gangnet and Burton Rosenberg. Constraint programming and graph algorithms. In 2 nd International Symposium on Artiøcial Intelligence and Mathematics, January 1992.

.... constraint hierarchies, our original description of constraint hierarchies is in reference [4] DeltaBlue, an efficient, incremental algorithm for finding a locally predicate better solution to a constraint hierarchy using local propagation is described in [20] and further analyzed in [43] [25], and [57] Constraint hierarchies as described in reference [4] have subsequently been used in a number of systems, including ThingLab II [43, 44] TRIP and TRIP II [37, 76] the Constraint Window System [16] and Multi Garnet [56] In addition to early conference publications [4, 7] constraint ....

Michel Gangnet and Burton Rosenberg. Constraint Programming and Graph Algorithms. In Second International Symposium on Artificial Intelligence and Mathematics, January 1992.

....of the DAG, the solver will fail if that constraint cannot be satisfied without undoing other previously satisfied constraints. We expect to improve the solver and to eventually implement a more powerful algorithm, such as Delta Blue [Freeman Benson 90] or the algorithm described in [Gangnet 92] This has become necessary because of scenes that include lots of constraints or situations where the solver fails on relatively simple cases. For instance, depending on the arbitrary orientation initially given to the constraints, the current solver may not succeed. 5 Related work Early ....

....allow the user to create conflicting constraints. An alternative solution would be to allow this, and then to partition the conflicting constraints using a preference level. Constraint solvers have been developed that can solve constraint systems with this type of hierarchy [Freeman Benson 90, Gangnet 92] Another area of investigation is in tuning the types and ordering of the rules. This could be done through a rule browser that would allow the developer to easily change the conditions and ordering of the rules by direct manipulation. Rockit could be made user adaptive. Since it is possible ....

Michel Gangnet and Burt Rosenberg. Constraint Programming and Graph Algorithms. In Second International Symposium on Artificial Intelligence and Mathematics, Ft. Lauderdale, January 1992.

....PDOF) selects the methods in the reverse order (selecting rst the methods to be executed last) It has been used in SketchPad [Sutherland 63] and QuickPlan [Vander Zanden 96] 3) A third approach is related to the classical problem of graph matching. It gives the Maximummatching algorithm [Gangnet 92] 3 Types of constraint planning problems Existing local propagation algorithms solve dioeerent planning problems that imply various tradeooes between simplicity and power: ffl required constraints only, or both required and preferential constraints that are satis ed if possible ffl ....

.... imposed or relaxed (see de nition 3 below) problem method restriction single output complexity proof algorithms acp1 yes yes P [Sutherland 63] PDOF, DeltaBlue acp2 yes no P [Vander Zanden 96] QuickPlan acp3 no yes NPC [Maloney 91] 3 acp4 no no NPC [Maloney 91] 1 and 2 cp1 yes yes P [Gangnet 92] Maximum matching cp2 yes no SkyBlue cp3 no yes cp4 no no Table 1: Computational complexity of constraint planning problems. Cycles in the constraint graph are allowed. Constraints are required (not preferential) Every problem depends on three characteristics: 1) a problem that ....

[Article contains additional citation context not shown here]

Michel Gangnet, Burton Rosenberg. Constraint programming and graph algorithms. In Second International Symposium on Artiøcial Intelligence and Mathematics, Jan. 1992.

....constraint graph must be acyclic. These restrictions allow all of DeltaBlue s operations incrementally adding and removing a constraint, extracting a plan, and executing that plan to have O(NM ) worst case complexity, so that the algorithm scales smoothly to handle large problems. References [31, 19] prove that removing either of these restrictions turns the constraint satisfaction problem into an NP complete one, making the worst case running time exponential in the number of constraints. While the restriction on methods with multiple outputs is not usually an obstacle, the occasional user ....

Michel Gangnet and Burton Rosenberg. Constraint Programming and Graph Algorithms. In Second International Symposium on Artificial Intelligence and Mathematics, January 1992.

....of variables and constraints forms a constraint graph, which is assumed to be acyclic. We can construct a bipartite graph by having a vertex for each variable and each constraint, and an edge from a constraint vertex to a variable vertex if the variable is constrained by the constraint [Gangnet Rosenberg 92] The constraint graph is said to be acyclic if the corresponding bipartite graph is acyclic. Each variable has a lower and an upper bound, which are initially Gamma1 and 1 respectively. As with our previous algorithms DeltaBlue and SkyBlue, every variable has an implicit stay constraint at ....

Michel Gangnet and Burton Rosenberg. Constraint programming and graph algorithms. In Second International Symposium on Artificial Intelligence and Mathematics, January 1992.

....of variables and constraints forms a constraint graph, which is assumed to be acyclic. We can construct a bipartite graph by having a vertex for each variable and each constraint, and an edge from a constraint vertex to a variable vertex if the variable is constrained by the constraint [5]. The constraint graph is said to be acyclic if the corresponding bipartite graph is acyclic. Each variable has a lower and an upper bound, which are initially Gamma1 and 1 respectively. As with our previous algorithms DeltaBlue and SkyBlue, every variable has an implicit stay constraint at the ....

....both the presentation and implementation of the algorithm. Finally we define the tighten message to variables (with an interval argument) to tighten the bounds on the variable if possible, given the argument. For example, if a variable currently has the bounds [3,10] if we tighten it using [5,8], its new bounds will be [5,8] On the other hand, if a variable current has the bounds [3,10] and we tighten it using [50,100] its new bounds will be the singleton interval [10,10] since 10 is the number within the interval [3,10] that minimizes the distance to the interval [50,100] The ....

[Article contains additional citation context not shown here]

Michel Gangnet and Burton Rosenberg. Constraint programming and graph algorithms. In Second International Symposium on Artificial Intelligence and Mathematics, January 1992.

....work will extend SkyBlue to call a specialized constraint solver to solve the constraints around a cycle, and continue using local propagation to satisfy the rest of the constraints. SkyBlue is currently being used as the constraint solver in Multi Garnet [15] a package that ex 1 Reference [7] presents another algorithm that solves constraint hierarchies, with roughly the same power and limitations as DeltaBlue. 0.00 100.00 A 0.00 100.00 B 22.45 122.45 A 0.00 100.00 B 0.00 81.89 A 0.00 272.56 B Figure 1: A scatterplot built using SkyBlue constraints: The initial scatterplot, the ....

Michel Gangnet and Burton Rosenberg. Constraint Programming and Graph Algorithms. In Second International Symposium on Artificial Intelligence and Mathematics, January 1992.

....are constrained by constraints connected with the edges, and the directed edges 4 In the papers on DeltaBlue [22, 58, 76] they do not associate constraint hierarchies with bipartite graphs. However, such a connection is often convenient to explain a certain kind of local propagation algorithms [25]. CHAPTER 3. GENERALIZED LOCAL PROPAGATION 33 a b c d strong required required strong weak weak Figure 3.3: Walkabout strengths. show selected methods by pointing output variables. Symbols associated with constraints give their strengths, and ones attached to variables depict their walkabout ....

Gangnet, M. and B. Rosenberg, "Constraint Programming and Graph Algorithms," in Proceedings of Second International Symposium on Artificial Intelligence and Mathematics, Jan. 1992.

.... But DeltaBlue cannot cope with multiple output variables or with cycles (see below) and SkyBlue copes with them only be invoking a separate solver (for example, one based on Gaussian elimination or the Simplex method) DeltaBlue has been shown to be optimal for its task by Gangnet and Rosenberg [4]. Both DeltaBlue and SkyBlue provide one solution chosen non deterministically, as opposed to our work which provides all solutions. Borning has said [Private Communication] that in general his applications only need the first solution. The notion of a cycle arises due to the operational nature ....

Michel Gangnet and Burton Rosenberg. Constraint Programming and Graph Algorithms. In 2nd International Symposium on Artificial Intelligence and Mathematics, January 1992.

....of variables and constraints forms a constraint graph, which is assumed to be acyclic. We can construct a bipartite graph by having a vertex for each variable and each constraint, and an edge from a constraint vertex to a variable vertex if the variable is constrained by the constraint [9]. The constraint graph is said to be acyclic if the corresponding bipartite graph is acyclic. Each variable has a lower and an upper bound, which are initially Gamma1 and 1 respectively. As with our previous algorithms DeltaBlue and SkyBlue, every variable has an implicit stay constraint at ....

Michel Gangnet and Burton Rosenberg. Constraint programming and graph algorithms. In Second International Symposium on Artificial Intelligence and Mathematics, January 1992.

....in the construction of the DAG, the solver will fail if that constraint cannot be satisfied without undoing other previously satisfied constraints. We expect to improve the solver and to eventually implement a more powerful algorithm, such as Delta Blue [7] or the algorithm described in [8]. This has become necessary because of scenes that include lots of constraints or situations where the solver fails on relatively simple cases. For instance, depending on the arbitrary orientation initially given to the constraints, the current solver may not succeed. Research Report No. 17 ....

....Currently, we do not allow the user to create conflicting constraints. An alternative solution would be to allow this, and then to partition the conflicting constraints using a preference level. Constraint solvers have been developed that can solve constraint systems with this type of hierarchy [7, 8]. Another area of investigation is in tuning the types and ordering of the rules. This could be done through a rule browser that would allow the developer to easily change the conditions and ordering of the rules by direct manipulation. Rockit could be made user adaptive. Since it is possible to ....

Michel Gangnet and Burt Rosenberg. Constraint Programming and Graph Algorithms. In Second International Symposium on Artificial Intelligence and Mathematics, Ft. Lauderdale (January 1992).

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Michel Gangnet and Burton Rosenberg. Constraint programming and graph algorithms. In Second International Symposium on Articial Intelligence and Mathematics, January 1992.

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Michel Gangnet and Burton Rosenberg, `Constraint programming and graph algorithms', Second International Symposium on Artificial Intelligence and Mathematics, January 1992.

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