M.J. Dent and R.E. Mercer. Minimal forward checking. In Proceedings of the Sixth International Conference on Tools with Artificial Intelligence, pages 432--438, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....these algorithms. And fourth, although we do not have space to present the details here, it provides us with a uniform way of implementing n ary versions of many different binary CSP algorithms (including algorithms that have not yet been extended to the n ary case, e.g. Minimal Forward checking [5] and BackMarking [6] 2 Background and Notation A CSP consists of a set of variables fV 1 ; Vn g and a set of constraints fC 1 ; Cm g. Each variable V has a finite domain of values Dom[V ] and can be assigned a value v, indicated by V v, if and only if v 2 Dom[V ] Let A be ....

M. J. Dent and R. E. Mercer. Minimal forward checking. In 6th IEEE International Conference on Tools with Artificial Intelligence, pages 432--438, New Orleans, 1994. Available via anonymous ftp from ftp://csd.uwo.ca/pub/csd-technical-reports/374/tai94.ps.Z.

....against the domains of the other variables and inconsistent elements are removed; this way, only consistent values remain. If a domain becomes empty, inconsistency is detected. The Forward Checking algorithm has been improved by considering a lazy version, called Minimal Forward Checking (MFC) [4], where domain elements are checked by constraints only if it is required by the search. The idea behind MFC is the observation that FC s effectiveness is mainly due to the domain wipe out test, i.e. FC finds out inconsistencies early by showing that a domain is empty. However, in order to ....

....performs a computation with many similarities to a standard CSP solver. In fact, the ICSP solver can be implemented on top of a CSP solver [2] or on a stand alone language. Thus, the same measures used in the CSP field can be employed to obtain the ICSP solver computation time. As in many works [9, 11, 4] we employed the number of constraint checks as a measure of the ICSP solver computation time: m ICSP = c i c n ICSP chk where c i c is the (average) time employed to perform a constraint check and n ICSP checks is the number of constraint checks performed by the ICSP solver. 4.2 Esteem ....

M.J. Dent and R.E. Mercer. Minimal forward checking. In Proc. of ICTAI94, 1994.

....this paper, the discussion is confined to binary CSPs only. Forward checking (FC) is considered as one of the most efficient search methods to solve CSPs. Enhancements have been proposed in order to make it more efficient [15, 16] One recent result of this effort is minimal forward checking (MFC) [4] (and a similar idea has been proposed in [22] MFC is interesting since given the same variable and value orderings, it always performs fewer or the same number of compatibility checks than that of FC. In this paper, we suggest an algorithm which enhances MFC with the capability of backmarking ....

....propagation scheme, FC only needs to find one value in the domain of each future variable which is compatible with the committed labels. This is the principle of introducing delayed evaluation in FC based algorithms. We refer to this class of algorithms as lazy algorithms. As mentioned in [4, 2], MFC can be extended with Prosser s type of partial backmarking [17] and CBJ. Two types of savings can be achieved in BM [14] a) if the current variable s label was found incompatible with a past variable s label, unless that past variable s label has been changed the compatibility check ....

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Dent, M. & Mercer, R.E. Minimal Forward Checking. In Proceedings 6th IEEE International Conference on Tools with Artificial Intelligence, 1994.

....of domain wipeout with backmarking corresponds to the well known imperative algorithm called forward checking. Because our cache table construction is lazy, we have actually rediscovered ( for free ) minimal (or lazy) forward checking, itself a recent discovery in the imperative literature [5]. Figure 11 shows code for implementing domain wipeout. To gather a list of wipedDomains and test whether it is non empty is straightforward. The interesting question is what conflict set to assign to the node n if domain wipeout has occurred. Since it is always valid to throw additional ....

....problem. 12 Related Work Hughes [9] gives a lazy development of minimax tree search. Bird and Wadler [3] treat the n queens problem using generate and test and lazy lists. Laziness (not in the context of lazy languages) has been used for improving the efficiency of existing CSP algorithms [15, 5], but as far as we know laziness has not been previously been used to modularize any of the CSP algorithms presented here. Queens 5 6 7 8 9 10 11 12 13 bjbm 276 909 3158 11928 49369 210210 975198 4938324 26709008 bjfc 279 916 3182 12229 51314 218907 1026826 5231284 28387767 bm 276 944 3236 ....

M. J. Dent and R. Mercer. Minimal forward checking. In Prec. of the Int'l Conference on Tools with Artificial Intelligence, pages 432--438, New Orleans, Louisiana, 1994. IEEE Computer Society.

....from the results we prove here. We will discuss Prosser s work in more detail in Section 3. In Section 4 we briefly discuss an improved version of forward checking first pro posed by Zweben and Eskey [ZE89] and subsequently presented independently, and in greater detail, by Dent and Mercer [DM94]. Dent and Mercer call their improved algorithm minimal forward checking (MFC) MFC was proposed as a lazy version of forward checking which avoids doing checks until they are absolutely necessary. MFC provably never does worse than the original FC algorithm. Its gains over plan FC are typically ....

....MFC was proposed as a lazy version of forward checking which avoids doing checks until they are absolutely necessary. MFC provably never does worse than the original FC algorithm. Its gains over plan FC are typically modest (10 40 in our own experiments, which seems to be in fair agreement with [DM94]) but are nevertheless worthwhile. We re discovered this algorithm not by thinking about lazy evaluation, but instead as a corollary of our results connecting backmarking and forward checking. As we show, there is a strong sense in which minimal forward checking is a logical hybrid of regular ....

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M. J. Dent and R. E. Mercer. Minimal forward checking. In 6th IEEE International Conference on Tools with Artificial Intelligence, pages 432--438, New Orleans, 1994. Available via anonymous ftp from ftp://csd.uwo.ca/pub/csd-technicalreports /374/tai94.ps.Z.

....efficient ways to implement each component. In particular, we can look for more efficient ways to do DWO detection. We have previously shown in [BG95] that applying this principle leads naturally to the minimal forward checking (or lazy forward checking) algorithm developed by Dent and Mercer [DM94]. This algorithm does not forward check every value of all of the future variables this is more work than is required to detect a DWO. Rather, it simply ensures that every future variable has at least one value consistent with the current set of assignments. A change to the DWO component also ....

M. J. Dent and R. E. Mercer. Minimal forward checking. In 6th IEEE International Conference on Tools with Artificial Intelligence, pages 432--438, New Orleans, 1994. Available via anonymous ftp from ftp://csd.uwo.ca/pub/csd-technicalreports /374/tai94.ps.Z.

....(they have a large number of solutions) but have thousands of variables. On such problems the lookahead that forward checking does is too time consuming, and the benefits too small, as future dead ends are rarely uncovered. It may be better do perform minimal forward checking as suggested in [3], or backtracking or backjumping with no lookahead component. Taking a larger perspective than we adopt in the body of this paper, the ideal might be an algorithm always does the right amount of looking ahead, from as little as backtracking, through forward checking and full looking ahead, to ....

M. J. Dent and R. E. Mercer. Minimal forward checking. Technical Report 374, The University of Western Ontario, Dept. of Computer Science, 1993.

....excessive search effort that might have been wasted by FC, it may perform worse than FC in some occasions. Figure 1 depicts the constraint graph of an example CSP which causes such a problem. Traces of the execution of FC and LFC on the CSP are given in Figures 2 and 3 in a similar manner as in [Dent Mercer 94] The ticks ( and crosses ( represent successful and unsuccessful compatibility checks respectively. The Checks entry in each row of the tables represents the number of compatibility checks performed in that step. In Figure 3, domain values are shown with the list of current and past ....

....1 ) 2 3 1 1 7 X 1 = 1 X 2 = 3 2 3 1 (X 2 ) 1 8 X 1 = 1 X 2 = 3 X 3 = 2 3 1 (X 2, X 3 ) 1 9 X 1 = 1 X 2 = 3 3 (X 1 ) 1 (X 2 ) 1 10 X 1 = 1 X 2 = 3 X 3 = 3 1 (X 2, X 3 ) 1 Total 13 Figure 3. Trace of execution of LFC 3 Minimal forward checking with backmarking As mentioned in [Dent Mercer 94] backmarking [Gaschnig 77] can be used to improve MFC. Two types of saving can be made by BM [Nadel 89] a) if an instantiation of the current variable was found incompatible with a past variable s label, unless that past variable s label has been changed, otherwise the compatibility check ....

[Article contains additional citation context not shown here]

Dent, M. & Mercer, R.E. 1994. Minimal Forward Checking. In Proceedings 6th IEEE International Conference on Tools with Artificial Intelligence.

....as they are appreciably harder to search than problems that are generated outside of the phase transition. Both Smith and Prosser propose that Smith s model of hard binary CSPs be used to compare CSP algorithms empirically. This has already been done by many authors 1 [ Dechter and Meiri, 1994; Dent and Mercer, 1994; Frost and Dechter, 1994a; 1994b; Prosser, 1995 ] We believe that the underlying structure of a problem needs to be included into models of hard problems. Smith Dyer (1995) also conclude that local graph topology needs to be included in order to better model the transition point. With this in ....

....parameters. 2. 1 The Global Constraint Tightness Model Smith s model of hard random binary CSPs is parameterized by a 4 tuple hn; m; p 1 ; p 2 i where n is the number of variables, m is the global domain size (every 1 These authors found the crossover point independently of Smith, except for Dent Mercer (1994) which used Smith s result. domain has the same size) p 1 is the probability that a constraint exists between two variables (also called the constraint density) and p 2 is the global conditional probability that any pair of values between the two variables is inconsistent (also called the ....

M. Dent and R. Mercer. Minimal forward checking. In Proceedings of the 6th International Conference on Tools with Artificial Intelligence, pages 432--438, 1994. IEEE Computer Society.

....the cost of a constraint check is significant then MFC is a better choice. Section 2 presents an overview and example of the FC and MFC algorithms, section 3 describes experimental results and section 4 gives conclusions and future work. A complete description of the MFC algorithm can be found in [2]. 2 Minimal Forward Checking Assume that the variable instantiation order, v 1 ; v i ; vn , is the order in which variables are chosen to be given a value. The current variable, v i , is the variable to be instantiated and d i is the current domain. The instantiated variables v ....

M. Dent and R. Mercer. Minimal Forward Checking. Technical Report UWO-CSD-374, University of Western Ontario, 1993.

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M.J. Dent and R.E. Mercer. Minimal forward checking. In Proceedings of the Sixth International Conference on Tools with Artificial Intelligence, pages 432--438, 1994.

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M.J. Dent and R.E. Mercer. Minimal forward checking. In Proceedings of the 6th International Conference on Tools with Arti cial Intelligence, pages 432-438, 1994.

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Dent M. and Mercer R. (1994). Minimal forward checking, Proceedings of TAI-94, 432-438.

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M. Dent and R. Mercer. Minimal Forward Checking. In Proc. of the 6 th IEEE International Conference on Tools with Artificial Intelligence (TAI94), pages 432--438, New Orleans, LA, 1994.

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M. J. Dent and R. E. Mercer. Minimal forward checking. In Proceedings of the Sixth IEEE International Conference on Tools with Artificial Intelligence, pages 432--438, New Orleans, LA, 1994.

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