Je#rey Ullman. The complexity of ordering subgoals. In PODS, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the two algorithms, we observe that PARTITION consistently outperforms CHAIN in finding near optimal plans. The central problem we have discussed in this chapter, namely the problem of ordering subgoals to find the best feasible sequence, can be viewed as the well known join order problem [76]. More precisely, we can assign infinite cost to infeasible sequences of subgoals and proceed to find the best join order. The join order problem has been extensively studied in the literature, and many solutions have been proposed. Some solutions perform a rather exhaustive enumeration of plans, ....

J. Ullman, M. Vardi. The Complexity of Ordering Subgoals. In Proc. PODS Conference, 1988.

....this subgoal. Mor88] gave an algorithm for testing the existence of a feasible RGG given a set of rules and a query goal. The algorithm is inherently exponential in time. However, if there is a bound on the arity of predicates, then the algorithm with this heuristic takes polynomial time [UV88] 6.2 Undecidability Result In some cases, even though a set of rules does not has a feasible RGG with respect to a query goal, the query may still be stable, since we may rewrite the rules to obtain a new set of rules that has a feasible RGG with respect to the query goal. For example, if we ....

Je#rey D. Ullman and Moshe Y. Vardi. The complexity of ordering subgoals. In PODS, pages 74--81, 1988.

....this subgoal. Mor88] gave an algorithm for testing the existence of a feasible RGG given a set of rules and a query goal. The algorithm is inherently exponential in time. However, if there is a bound on the arity of predicates, then the algorithm with this heuristic takes polynomial time [UV88] 7.3 What If a Feasible RGG Does not Exist In some cases, even though a set of rules do not has a feasible RGG with respect to a query goal, the query may still be stable, since we may rewrite the rules to obtain a new set of rules that has a feasible RGG with respect to the query goal. The ....

Jeffrey D. Ullman and Moshe Y. Vardi. The complexity of ordering subgoals. In Proc. of ACM Symposium on Principles of Database Systems (PODS), pages 74--81. ACM Press, 1988.

....successfully. This assumption is not so realistic. The construction may be imprecise since we do not consider the problems with respect to aliased variables. These problems can be resolved by the groundness analysis presented in Chapter 5. The complexity of rule goal graphs was studied in [UV88] Theoretically, its size is exponential of input programs, but is known to be practically linear. 25 perm bf Gamma Gamma Gamma Gamma r [j] 1:0 r [P jE;X;F;P1;L] 2:0 Gamma Gamma Gamma Gamma append ffb Gamma Gamma Gamma Gamma r [Lj] 3:0 r ....

J. D. Ullman and M. Y. Vardi. The complexity of ordering subgoals. In Proceedings of Principles of Database Systems, pages 74--81, 1988.

....of subgoal sequences. Several researchers have explored the problem of automatic reordering of subgoals in logic programs (Warren, 1981; Naish, 1985b; Smith Genesereth, 1985; Natarajan, 1987; Markovitch Scott, 1989) The general subgoal ordering problem is known to be NP hard (Ullman, 1982; Ullman Vardi, 1988). Smith and Genesereth (1985) and Markovitch and Scott (1989) present search algorithms for finding optimal orderings. These algorithms are general and carry exponential costs for non trivial sets of subgoals. Natarajan (1987) describes an efficient algorithm for the special case where subgoals in ....

....moment that there exists a mechanism that returns the average cost and number of solutions of a subgoal in time . In Section 5 we show how this control knowledge can be obtained by inductive learning. 3. 2 Ordering of Independent Sets of Subgoals The general subgoal ordering problem is NP hard (Ullman Vardi, 1988). However, there is a special case where ordering can be performed efficiently: if all the subgoals in the Ledeniov Markovitch given set are independent, i.e. do not share free variables. This section begins with the definition of subgoal dependence and related concepts. We then show an ....

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Ullman, J. D., & Vardi, M. Y. (1988). The complexity of ordering subgoals. In Proceedings of the Seventh ACM SIGACT-SIGMOD Symposium on Principles of Database Systems, pp. 74--81, Austin, TX. ACM Press, New York.

....leftdeep tree executions of the subgoals. Proof. For any feasible execution of the logical plan based on a bushy tree of subgoals, we can construct another feasible execution based on a left deep tree of subgoals (with the same leaf order) This is similar to the bound is easier assumption of [28]. See the full version of our paper [32] for a detailed proof. 2.4 The Formal Cost Model Our cost model is defined as follows: 1. The cost of a subgoal in the feasible plan is the number of source queries needed to answer this subgoal. 2. The cost of a feasible plan is the sum of the costs of all ....

J. Ullman, M. Vardi. The Complexity of Ordering Subgoals. In ACM PODS, 1988.

....by parameterized queries in P 0 . Note that this is always possible because the left deep tree execution keeps the cumulative bindings of all the variables of all the subgoals to the left of the subgoal under consideration. This observation is similar to the bound is easier assumption of [28]. Thus, we conclude that if a bushy tree of subgoals has a feasible plan, we are guaranteed to find a feasible plan by considering only left deep tree executions. 2.4 The Formal Cost Model Our cost model is defined as follows: 1. The cost of a subgoal in a feasible plan is the number of source ....

J. Ullman, M. Vardi. The Complexity of Ordering Subgoals. In ACM PODS, 1988.

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Je#rey Ullman. The complexity of ordering subgoals. In PODS, 1988.

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Je#rey Ullman. The complexity of ordering subgoals. In PODS, 1988.

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J. Ullman. The Complexity of Ordering Subgoals. In ACM Symposium on Principles of Database Systems (PODS), 1988.

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