E. Freuder (1988). Backtrack-free and backtrack-bounded search. In Kanal and Kumar, editors, Search in Artificial Intelligence, Springer-Verlag.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....can be brought to bear. Researchers within and outside the field of artificial intelligence have identified many such classes and developed efficient algorithms for them. Such methods range from algorithms for solving tree structured binary constraint satisfaction problems in polynomial time [7] to methods for solving arithmetic equations. The use of such specialized algorithms removes the possibility that a search engine spends a long time solving a problem that is essentially easy. The drawback of these methods is of course that they are extremely brittle; a small change in the problem ....

Eugene C. Freuder. Backtrack-free and backtrack-bounded search. In Laveen N. Kanal and Vipin Kumar, editors, Search in Artificial Intelligence. SpringerVerlag, 1988. 148

....that a few simple, fast tests on partially generated hypotheses will eliminate large numbers of globally inconsistent hypotheses. Of course, it would be ideal if satisfying the set of local unary and binary tests would guarantee global consistency, but this is not always the case. Freuder [10] considers k consistent problems, wherein satisfying constraints over all sets of k tuples of pairings guarantees global consistency) The following quantities are used: ffl There are M model features in the model. ffl On average, p v M of these are visible in the scene (less than M by ....

E. Freuder. Backtrack-Free and Backtrack-Bounded Search. in L. Kanal and V. Kumar (eds), Search in Artificial Intelligence. pp343-369, New York:Springer-Verlag, 1988.

.... system is an NP hard problem, much work has focussed on the identification of tractable classes of constraint problems, that can be solved in polynomial time (see [113, 120, 174] for an overview of many algorithms) Such classes are usually identified by a precise graph structure (like a tree [65, 148, 52]) or by a precise combination of algebraic operators [106] Recently, graph decomposition strategies and also constraint propagation techniques have been used also for continuous constraint problems [22, 151, 42] and for problems where constraints represent differential equations [54] For some ....

E. C. Freuder. Backtrack-free and backtrack-bounded search. In Kanal and Kumar, editors, Search in Artificial Intelligence, pages 343--369. Springer-Verlag, 1988.

....combinations of values. Since many problems in AI and other areas of computer science can be formulated as CSPs, it has been a research subject for a long time and researchers have approached the subject in different directions: searching for the CSP s solutions from the possible solution space ([10, 7, 3]) reducing a CSP to a simpler and equivalent CSP ( 13, 14, 15, 9, 1] and synthesizing solutions from partial solutions ( 6, 21, 22, 17] Solution synthesis finds all solutions for a given CSP. It can also be used to find all partial solutions with respect to a particular subset of variables. ....

....blocks. These nodes are called separating nodes. For example, the separating nodes of the graph in Figure 1 (A) are V 1 ; V 2 ; V 3 ; V 4 ; V 5 , and V 6 A binary CSP is associated with a simple constraint graph, which has been well studied and widely used for analyzing and solving binary CSPs [7, 4, 2]. A general CSP is associated with a constraint hypergraph, but the topological V V V V V V V V V V V V V V V V 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 B3 B4 B5 B6 B7 B1 B2 (A) A connected graph (B) A block tree Fig. 1. A graph and its block tree properties of ....

E. Freuder. Backtrack-free and backtrack-bounded search. In L. Kanal and V. Kumar, editors, Search in Artificial Intelligence, pages 343--369. SpringerVerlag, New York, 1988.

....vertices. Definition 5 The width of a constraint graph is the minimum width of all the orderings of that graph. In our case, the constraint graph has a width = 1, since once an abstract path has been selected, the constraint graph is a simple chain. This holds because of the following theorem [5, 6]: Theorem 1 (Freuder)At least one of the orderings of a tree structured constraint graph has a width equal to 1. The DAC algorithm uses node consistency and arc consistency to make the graph strongly 2consistent. Therefore, the following theorem proves that the DAC algorithm does not require any ....

....1 (Freuder)At least one of the orderings of a tree structured constraint graph has a width equal to 1. The DAC algorithm uses node consistency and arc consistency to make the graph strongly 2consistent. Therefore, the following theorem proves that the DAC algorithm does not require any search [5, 6]: Theorem 2 (Freuder) If a constraint graph is strongly k consistent, and k , where is the width of the constraint graph, then there exists a search order that is backtrack free. 6 Conclusions This paper has described a multi agent paradigm to support the QoS based inter domain routing ....

E. Freuder, "Backtrack-Free and Backtrack-Bounded Search". In Search in Artificial Intelligence, ed. L. Kanal and V. Kumar, 343-369. New York: Springer-Verlag.

....formalism to specify many kinds of real life problems. In fact, problems ranging from map coloring, vision, robotics, job shop scheduling, VLSI design, etc. can easily be cast as CSPs and solved using one of the many techniques that have been developed for such problems or subclasses of them [Fre78, Fre88, MF85, Mac77, Mon74]. However, they also have evident limitations, mainly due to the fact that they are not very flexible when trying to represent real life scenarios where the knowledge is not completely available nor crisp. In fact, in such situations, the ability of stating whether an instantiation of values to ....

E. C. Freuder. Backtrack-free and backtrack-bounded search. In Kanal and Kumar, editors, Search in Artificial Intelligence. Springer-Verlag, 1988.

....DA j nA (nA Gamma1) 2 . Let N be the maximal amount of boundary nodes in the network of a provider, i.e. N = max domains A nA . Therefore, the complexity of the arc consistency process is bound by O(j P j N 6 ) The following theorem proves that the DAC algorithm does not require any search (Freuder 1988; 1984) Theorem 1 (Freuder82) If a constraint graph is strongly k consistent, and k , where is the width of the constraint graph, then there exists a search order that is backtrack free. In our case, the constraint graph has a width = 1, since once an abstract path has been selected, the ....

.... constraints (which are for instance the ones fixed in the currently used contracts) In a future scenario NPI could supply an automated mechanism to route and negotiate the allocation of demands across 4 At least one of the orderings of a tree structured constraint graph has a width equal to 1 (Freuder 1988; 1984) Scenario APC time T time 4 ND 5 ID 18 msec 146 msec 4 ND 11 ID 50 msec 569 msec 8 ND 8 ID 23 msec 483 msec 8 ND 16 ID 138 msec 507 msec Table 1: DAC time performance. distinct domains without the need for human intervention. This would require further work to integrate NPI in a real ....

Freuder, E. 1988. Backtrack-free and backtrackbounded search. In Kanal, L., and Kumar, V., eds., Search in Artificial Intelligence. New York: SpringerVerlag.

....If there exists such a tree for a TCN C according to def. 6 there exists an efficient algorithm for finding finite solutions of C which is just needed for the task of monitoring real time systems. The algorithm bases on the algorithm for tree structured binary constraint nets given e.g. in [6]. The principle of the algorithm is a follows: At each point of time t k = k Deltat the values of some variables are predefined (those of the visible variables) The states of all transition systems of the net can be combined in a state vector. At t k a set of state vectors is still possible, at ....

E.C. Freuder. Backtrack-free and backtrackbounded search. In L. Kanal and V. Kumar, editors, Search in Artificial Intelligence, pages 341-- 369. Springer, New York, 1988.

....which performs a depth first search in a tree where the nodes are the variable instantiations and each branch from the root to a leaf involves all the variables. It has been widely recognized that such a procedure can perform very badly if the given problem has a lot of syntactic redundancy [10, 6]. Here we mean that an object of a CSP is (syntactically) redundant whenever its removal does not change the solution of the CSP. Many preprocessing algorithms [11, 10, 5, 4, 8] have been developed in order to remove redundancy in the definition of the constraints. In this paper we analyze a ....

....constraint, given in term of tuples of values of the domain, and the visible variables are marked by a star. Then, the solution of this problem is the set fha; big, or, alternatively, the set of equations fx = a; y = bg. a,a b,c a,b z y x n n n Figure 1: A CSP. A CSP is k consistent [6] if, for each k 1 variables, and values for them which are allowed by all the constraints involving subsets of them, and for each other variable, there is at least a value locally allowed for such k th variable which is compatible with all the other k 1 variables. In this line, arc consistency is ....

[Article contains additional citation context not shown here]

E. Freuder. Backtrack-free and backtrackbounded search. In Kanal and Kumar, editors, Search in Artificial Intelligence. Springer-Verlag, 1988.

.... propagation and has been formalized in various levels of so called local consistencies: arc consistency, path consistency, k consistency and has been related to ATMS nogood inference in [dK89] Adding enough induced constraints may even lead to backtrack free or backtrack bounded search [Fre88] 1.2 Dynamic constraint satisfaction problems Definition 1.4 A dynamic constraint satisfaction problem P is a sequence P 0 ; P ff ; of static CSPs each resulting from a change in the preceding one [Bes91] This change may be a restriction (a new constraint is imposed on a subset ....

....learned also gets a justification. The other improvement is on the quality of learning: Dechter full shallow k th order learning algorithm enforces in fact a subset of strong k consistency. Our k th order nogood recording algorithm enforces a subset of strong (k; n Gamma j) consistency [Fre88] on the j th variable in the ordering used, a property much stronger than strong k consistency. It will, for example, built a justification of inconsistency for any inconsistent CSP. The following pseudo code defines the algorithm more precisely. Such as it is defined, it will find the first ....

Eugene C. Freuder, Backtrack-free and backtrack-bounded search, Search in Artificial Intelligence (L. Kanal and V. Kumar, eds.), Springer-Verlag, 1988, pp. 343--369.

....the general problem is NP complete, one of the main research issues has been devoted to finding fast preprocessing algorithm that can make the search for a solution efficient in important practical cases. Such algorithms (Mackworth, 1977) Montanari, 1974) Freuder, 1978) Dechter and Pearl, 1987) (Freuder, 1988) were found to be so convenient (Mackworth and Freuder, 1985) that another main research direction focussed on finding so called islands of tractability , that is, classes of constraint problems where one of the preprocessing algorithms is enough to solve the problem. Examples of some of the ....

E. C. Freuder. Backtrack-free and backtrack-bounded search. In Kanal and Kumar, editors, Search in Artificial Intelligence. Springer-Verlag, 1988.

....to specify many kinds of real life problems. In fact, problems ranging from map coloring, vision, robotics, job shop scheduling, VLSI design, etc. can easily be cast as CSPs and solved using one of the many techniques that have been developed for such problems or subclasses of them [Fre78, Fre88, MF85, Mac77, Mon74] However, they also have evident limitations, mainly due to the fact that they do not appear to be very flexible when trying to represent real life scenarios where the knowledge is not completely available nor crisp. In fact, in such situations, the ability of stating whether ....

....precisely, we define the notion of constraint solving over any semiring. Specific choices of the semiring will then give rise to different instances of the framework, which may correspond to known or new constraint solving schemes. In classical CSPs, so called local consistency techniques [Fre78, Fre88, Mac92, Mac77, Mon74, MR91] have been proved to be very effective when approximating the solution of a problem. In this paper we study how to generalize these techniques to our framework, and we provide sufficient conditions over the semiring operations which assure that they can also be ....

[Article contains additional citation context not shown here]

E. C. Freuder. Backtrack-free and backtrack-bounded search. In Kanal and Kumar, editors, Search in Artificial Intelligence. Springer-Verlag, 1988.

.... The network domain A is the source xor the destination domain: j d j N The network domain A is a transit domain : j d j N(N Gamma1) 2 The network domain A is source and destination domain: j d j = 1 In order to obtain a solution DAC does not require any search. Theorem [Freuder82] [4, 3] If a constraint graph is strongly k consistent, and K , where is the width of the constraint graph, then there exists a search order that is backtrack free. The DAC algorithm uses node consistency and arc consistency to make the graph strongly 2consistent. In particular = 1 since the ....

....The DAC algorithm uses node consistency and arc consistency to make the graph strongly 2consistent. In particular = 1 since the constrained graph, once a global path has been selected, is a simple chain (at least one of the ordering of a tree structured constraint graphs have width equal to 1 [4, 3]) 4. Conclusions This paper shows how Constraint Satisfaction techniques can support the qos based multidomain routing process for allocating demands which cross distinct networks. The complexity of the problem increases when considering further QoS parameters, such as delay, loss probability, ....

E. Freuder, "Backtrack-Free and Backtrack-Bounded Search". In Search in Artificial Intelligence, ed. L. Kanal and V. Kumar, 343-369. New York: Springer-Verlag.

.... context free productions (because their synchronization requirements do not match with those of the productions of adjacent processes) This could lead to a great speed up in the overall search for a solution, especially when the graph representing the current system state has special topologies [Fre88]. In classical constraint solving over finite domains, constraints are usually stored in one memory. Thus local consistency algorithms are usually centralized. However, it is easy to see that such algorithms have an intrinsic distributed nature, since one can consider agents corresponding to ....

.... general only local consistency is achieved (and not global consistency, which would mean that the problem is solved) The first local consistency algorithms have been called arc consistency [Mac77] and path consistency [Mon74] Later, both of them were generalized to the concept of k consistency [Fre88]: a CSP is k consistent if, for each k 1 variables, and values for them which are allowed by all the constraints involving subsets of them, and for each other variable, there is at least a value locally allowed for such k th variable which is compatible with all the other k 1 variables. In this ....

E. Freuder. Backtrack-free and backtrack-bounded search. In Kanal and Kumar, editors, Search in Artificial Intelligence. Springer-Verlag, 1988.

....formalism to specify many kinds of real life problems. In fact, problems ranging from map coloring, vision, robotics, job shop scheduling, VLSI design, etc. can easily be cast as CSPs and solved using one of the many techniques that have been developed for such problems or subclasses of them [Fre78, Fre88, MF85, Mac77, Mon74]. However, they also have evident limitations, mainly due to the fact that they are not very flexible when trying to represent real life scenarios where the knowledge is not completely available nor crisp. In fact, in such situations, the ability of stating whether an instantiation of values to ....

E. C. Freuder. Backtrack-free and backtrack-bounded search. In Kanal and Kumar, editors, Search in Artificial Intelligence. Springer-Verlag, 1988.

....formalism to specify many kinds of real life problems. In fact, problems ranging from map coloring, vision, robotics, job shop scheduling, VLSI design, etc. can easily be cast as CSPs and solved using one of the many techniques that have been developed for such problems or subclasses of them [11, 12, 23, 25, 26]. However, they also have evident limitations, mainly due to the fact that they are not very flexible when trying to represent real life scenarios where the knowledge is not completely available nor crisp. In fact, in such situations, the ability of stating whether an instantiation of values to ....

....interpreted as cost, or degrees of preference, or probabilities, or others) and the two operations define a way to combine constraints together. Specific choices of the semiring will then give rise to different instances of the framework. In classical CSPs, so called local consistency techniques [11, 12, 23, 24, 26, 27] have been proved to be very effective when approximating the solution of a problem. In this paper we study how to generalize this notion to this framework, and we provide some sufficient conditions over the semiring operations which guarantee that such algorithms can also be fruitfully applied to ....

[Article contains additional citation context not shown here]

E. Freuder. Backtrack-free and backtrack-bounded search. In Kanal and Kumar, editors, Search in Artificial Intelligence. Springer-Verlag, 1988.

.... context free productions (because their synchronization requirements do not match with those of the productions of adjacent processes) This could lead to a great speed up in the overall search for a solution, especially when the graph representing the current system state has special topologies [12]. In classical constraint solving over finite domains, constraints are usually stored in one memory. Thus local consistency algorithms are usually centralized. However, it is easy to see that such algorithms have an intrinsic distributed nature, since one can consider agents corresponding to ....

.... Thus in general only local consistency is achieved (and not global consistency, which would mean that the problem is solved) The first local consistency algorithms have been called arc consistency [25] and path consistency [29] Later, both of them were generalized to the concept of k consistency [12]: a CSP is k consistent if, for each k 1 variables, and values for them which are allowed by all the constraints involving subsets of them, and for each other variable, there is at least a value locally allowed for such k th variable which is compatible with all the other k 1 variables. In this ....

E. Freuder. Backtrack-free and backtrack-bounded search. In Kanal and Kumar, editors, Search in Artificial Intelligence. Springer-Verlag, 1988.

....efficient algorithms which obtain an approximation of their solution. These algorithms are called relaxation algorithms . Some examples are the path consistency algorithm by Montanari ( 173] the arc consistency algorithm proposed by Mackworth ( 172] the k consistency algorithm of Freuder ([171]) and the directional k consistency and the adaptive consistency of Dechter and Pearl ( 170] All relaxation algorithms can be seen as mere instances of a scheme, which we proposed in ( 174] Among the instances of such scheme, there are some which are powerful enough to completely solve ....

Freuder E., "Backtrack-free and backtrack-bounded search", on Search in Artificial Intelligence, Kanal and Kumar eds., Springer-Verlag, 1988.

.... context free productions (because their synchronization requirements do not match with those of the productions of adjacent processes) This could lead to a great speed up in the overall search for a solution, especially when the graph representing the current system state has special topologies [20]. In classical constraint solving over finite domains, constraints are usually stored in one memory. Thus local consistency algorithms are usually centralized. However, it is easy to see that such algorithms have an intrinsic distributed nature, since one can consider agents corresponding to ....

.... Thus in general only local consistency is achieved (and not global consistency, which would mean that the problem is solved) The first local consistency algorithms have been called arc consistency [29] and path consistency [35] Later, both of them were generalized to the concept of k consistency [20]: a CSP is k consistent if, for each k 1 variables, and values for them which are allowed by all the constraints involving subsets of them, and for each other variable, there is at least a value locally allowed for such k th variable which is compatible with all the other k 1 variables. In this ....

[Article contains additional citation context not shown here]

E. Freuder. Backtrack-free and backtrack-bounded search. In Kanal and Kumar, editors, Search in Artificial Intelligence. Springer-Verlag, 1988.

....formalism to specify many kinds of reallife problems. In fact, problems ranging from map coloring, vision, robotics, job shop scheduling, VLSI design, etc. can easily be cast as CSPs and solved using one of the many techniques that have been developed for such problems or subclasses of them [ Freuder, 1978; 1988; Mackworth and Freuder, 1985; Mackworth, 1977; Montanari, 1974 ] However, they also have evident limitations, mainly due to the fact that they are not very flexible when trying to represent real life scenarios where the knowledge is not completely available nor crisp. In fact, in such ....

....as cost, or degrees of preference, or probabilities, or others) and the two operations define a way to combine constraints together. Specific choices of the semiring will then give rise to different instances of our framework. In classical CSPs, the so called local consistency techniques [ Freuder, 1978; 1988; Mackworth, 1988; 1977; Montanari, 1974; Montanari and Rossi, 1991 ] have been proved to be very effective when approximating the solution of a problem. In this paper we study how to generalize this notion to our framework, and we provide some sufficient conditions over the semiring operations ....

[Article contains additional citation context not shown here]

E. Freuder. Backtrack-free and backtrack-bounded search. In Kanal and Kumar, editors, Search in Artificial Intelligence. Springer-Verlag, 1988.

....one or all value assignments for the constraints network such that all the constraints are satisfied together. As beeing expected, various techniques for solving CSP s have been developed; these include backtraking, arc consistancy (Waltz [13] Mackworth [11] path consistan cy (Freuder [6] On other hand, symmetries for boolean constraints are well studied in (Benhamou and Sais [2,3] They showed that it is a real improvment for efficiency of several automated deduction algorithms. In this paper we develop the concept of symmetry for CSP s. Symmetrical domain values will be in a ....

E. Freuder. Backtrack-free and backtrack bounded search. In Kanal, Laveen and Kumar, Vipin, editors 1988, Search in Artificial Intelligence. Springer-Verlag, New York., 1988.

....variables to k (k 2) variables. Thus, k consistency implies that the domains of k mutually constraining variables have been pruned of values such that all remaining combinations of variable assignments are guaranteed to satisfy all constraints between the k variables. It has been proven [36], that after preprocessing a constraint graph with width 3 w to establish k consistency for k w the constraint graph can be solved by backtrack free search. While this result is theoretically interesting, it is nevertheless of only limited value in practice; the cost of establishing ....

E.C. Freuder. Backtrack-Free and Backtrack-Bounded Search. In L. Kanal and V. Kumar, editors, Search in Artificial Intelligence. Springer, 1988.

....which has a better semiring value for such n 1 variables. Otherwise the assumption that the initial tuple was the best one for the n variables will be contradicted. This discussion leads to the main result of this section, which again is an extension of a result already known for classical CSPs [7]: if we have an SCSP with a total order over the semiring values, and such a SCSP is SAC consistent and has the shape of a tree, then the optimal solution can be found in time linear in the number of its variables. In fact, in a tree shaped SCSP, all variables have either degree 1 (the leaves) ....

E. C. Freuder. Backtrack-free and backtrack-bounded search. In Kanal and Kumar, editors, Search in Artificial Intelligence, pages 343--369. SpringerVerlag, 1988.

....Tree structured problems. Local consistency methods have been used to support polynomial algorithms for CSPs with tree or tree like structure [8] 15] 27] When problems do not have such structure it may still be useful to view them as containing or being contained in such structures [6] 8] 9] [13] [15] 28] A problem is tree structured if the graph that results from viewing variables as vertices and constraints between variables as edges between vertices (the constraint graph) is tree structured. The idea of utilizing a tree which represents a subproblem is particularly attractive in the ....

E. C. Freuder. Backtrack-free and backtrack-bounded search. In L. Kanal and V. Kumar, editors, Search in Artificial Intelligence, pages 343--369. Springer, New York, NY, 1988.

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E. Freuder (1988). Backtrack-free and backtrack-bounded search. In Kanal and Kumar, editors, Search in Artificial Intelligence, Springer-Verlag.

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