T. Ibaraki and T. Kameda. Optimal nesting for computing n-relational joins. ACM Trans. on Database Systems, 9(3):482--502, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....we consider the problem of nding an optimal join order sequence for tree and star queries. A join between two relations is either performed using the nested loop method or the sort merge method. The problem considered in our thesis is an extension of the work studied by Ibaraki and Kameda [IK84] and Ravi Krishnamurthy, Boral and Zaniolo [KBZ86] The algorithm for obtaining an optimal join order sequence for star query has exponential time complexity [Cha00] In this thesis we present a greedy heuristic, GHGS, that outputs join sequence that is very close to the optimal solution. These ....

....optimal solution. These results are based on the experimental analysis performed on GHGS with 10000 di erent Catalogs. The greedy algorithm, GHGS, has O(m ) time complexity and O(m) space complexity where the number of relations considered are m. We have also extended the idea proposed in [IK84] and [KBZ86] to consider both, nested loop and sort merge joins to obtain an optimal join order sequence for tree queries. The time complexity of our algorithm ExIba is O(m log m2 ) and the space complexity is O(m) The time complexity of the ExKBZ algorithm is O(m ) and the space ....

[Article contains additional citation context not shown here]

T. Ibaraki and T. Kameda. Optimal Nesting for Computing N-relational Joins. ACM Tans. on Database Systems, 9(3):482-502, 1984.

....of computing optimal join order sequence for star queries, a subclass of tree queries. A join is allowed to be computed using both nested loop and sort merge join methods and the use of Cartesian products is avoided. This thesis extends the scope of the problem studied by Ibaraki and Kameda [IK84] and by Krishnamurthy, Boral and Zaniolo [KBZ86] For a star query of m 1 relations, we present O(2 ) time and O(m) space algorithms to compute the optimal join order sequence for a xed outermost relation. Under a certain restriction of the input and given any 0, we present a ....

....the high memory consumption resulting from storing all possible partial solutions. Thus, the space complexity of this algorithm is exponential in the number of relations used in the query. The running time of this algorithm is also exponential. 1.3. 2 Ibaraki Kameda Algorithm Ibaraki and Kameda [IK84] have proved that the general problem of optimizing a query is NP complete even with the restriction that the join method used is only nested loop. To compute an optimal nesting order for a general query, with some assumptions, they have given a heuristic of time complexity O(m ) where m is ....

[Article contains additional citation context not shown here]

T. Ibaraki and T. Kameda. Optimal Nesting for Computing N-relational Joins. ACM Tans. on Database Systems, 9(3):482-502, 1984.

....the database relations, attributes and access methods available and produces a precedence tree depicting an order in which the relations are joined and the join methods and access paths are used to compute each join in the tree. This problem was proved to be NP complete by Ibaraki and Kameda in [1]. The set of instances of the query optimization problem henceforth referred to as QO, considered in [1] was limited to using NL join methods only and disallowed Cartesian products between relations, between relations. Cluet and Moerkotte in [6] show that QO problem is NP complete when (a) the ....

....an order in which the relations are joined and the join methods and access paths are used to compute each join in the tree. This problem was proved to be NP complete by Ibaraki and Kameda in [1] The set of instances of the query optimization problem henceforth referred to as QO, considered in [1] was limited to using NL join methods only and disallowed Cartesian products between relations, between relations. Cluet and Moerkotte in [6] show that QO problem is NP complete when (a) the query graph is a star graph (refer to Figure 1)and (b) Cartesian products are allowed in join sequences. ....

[Article contains additional citation context not shown here]

T.Ibaraki and T.Kameda. Optimal Nesting for Computing N-relational joins. ACM Trans. on Database Systems, 9(3):482-502, 1984

....plan tree transformation would go in steps, from (R . 1 S) 2 T to (R . 2 T ) 1 S and then to (T . 2 R) 1 S. This approach treats an operator and its right hand input as a unit (e.g. the unit [ 2 T ] and swaps units; the idea has been used previously in static query optimization schemes [IK84, KBZ86, Hel98] Viewing the situation in this manner, we can naturally consider reordering multiple joins and their inputs, even if the join algorithms are different. In our query (R . 1 S) 2 T , we need [ 1 S] and [ 2 T ] to be mutually commutative, but do not require them to be the same ....

T. Ibaraki and T. Kameda. Optimal Nesting for Computing N-relational Joins. ACM Transactions on Database Systems, 9(3):482--502, October 1984.

....Therefore, the computation of an optimal join order with lowest evaluation cost by exhaustive search is perfectly feasible it takes but a few seconds CPU time. But if more than about eight relations are to be joined, the in general NP hard problem of determining the optimal order [IK84] cannot be solved exactly anymore. We have to rely on algorithms that compute (hopefully) good approximative solutions. Those algorithms fall into two classes: first, augmentation heuristics that build an evaluation plan step by step according to certain criteria, and second, randomized ....

....are: C hl (B 1 O) 7h = 8:4 C hl (O 1 B) 5h = 6:0 Thus, we get B and O as the fifth and sixth relation, respectively, and the final order is ( O 1 B) 1 W ) 1 P ) 1 A) 1 C with total cost C hl = 5 1 1 1 1) Delta h = 9h = 10:8. 4.1. 3 Krishnamurthy Boral Zaniolo Algorithm In [IK84] Ibaraki and Kameda showed that it is possible to compute the optimal nesting order in polynomial time, provided the query graph forms a tree (i.e. no cycles) and the cost function is a member of a certain class. On the basis of this result, Krishnamurthy, Boral and Zaniolo developed in [KBZ86] ....

[Article contains additional citation context not shown here]

T. Ibaraki and T. Kameda. Optimal nesting for computing N - relational joins. ACM Trans. on Database Systems, 9(3):482--502, 1984.

....tree transformation would go in steps, from (R . 1 S) 2 T to (R . 2 T ) 1 S and then to (T . 2 R) 1 S. This approach treats an operator and one of its inputs as a unit (e.g. the unit [ 2 T ] and swaps units; the idea has been used previously in static query optimization schemes [IK84, KBZ86, Hel98] Viewing the situation in this manner, we can naturally consider reordering multiple joins and their inputs, even if the join algorithms are different. In our query (R . 1 S) 2 T , we need [ 1 S] and [ 2 T ] to be mutually commutative, but do not require them to be the same ....

Toshihide Ibaraki and Tiko Kameda. Optimal Nesting for Computing N-relational Joins. ACM Transactions on Database Systems, 9(3):482--502, October 1984.

....encountered. Therefore, the computation of an optimal join order with lowest evaluation cost by exhaustive search is perfectly feasible it takes but a few seconds CPU time. But if more than about eight relations are to be joined, the generally NP hard problem of determining the optimal order [IK84] cannot be solved exactly anymore. We have to rely on algorithms that compute (hopefully) good approximate solutions. Those algorithms fall into two classes: first, augmentation heuristics that build an evaluation plan step by step according to certain criteria, and second, randomized algorithms ....

.... Minimum Selectivity is joined with the (so far) intermediate result and moved from R remaining to R used . Figure 3 shows the complete algorithm for left deep processing trees. 4.1. 3 Krishnamurthy Boral Zaniolo Algorithm On the foundation of [Law78] and [MS79] Ibaraki and Kameda showed in [IK84] that it is possible to compute the optimal nesting order in polynomial time, provided the query graph forms a tree (i.e. no cycles) and the cost function is a member of a certain class. Based on this result, Krishnamurthy, Boral and Zaniolo developed in [KBZ86] an algorithm (from now on called ....

[Article contains additional citation context not shown here]

T. Ibaraki and T. Kameda. Optimal nesting for computing N - relational joins. ACM Trans. on Database Systems, 9(3):482--502, 1984.

....78153 Le Chesnay Cedex, France 2 Lehrstuhl fur Informatik III, RWTH Aachen, 52056 Aachen, Germany Abstract. Producing optimal left deep trees is known to be NP complete for general join graphs and a quite complex cost function counting disk accesses for a special block wise nested loop join [2]. Independent of any cost function is the dynamic programming approach to join ordering. The number of alternatives this approach generates is known as well [5] Further, it is known that for some cost functions those fulfilling the ASI property [4] the problem can be solved in polynomial ....

....programming approach to join ordering. The number of alternatives this approach generates is known as well [5] Further, it is known that for some cost functions those fulfilling the ASI property [4] the problem can be solved in polynomial time for acyclic query graph, i.e. tree queries [2, 3]. Unfortunately, some cost functions like sort merge could not be treated so far. We do so by a slight detour showing that this cost function (and others too) are optimized if and only if the sum of the intermediate result sizes is minimized. This validates the database folklore that minimizing ....

[Article contains additional citation context not shown here]

Ibaraki, T., Kameda, T.: Optimal Nesting for computing n-Relational Joins. ACM. Trans. on Database Systems, 9(3) (1984) 482---502

....Therefore, the computation of an optimal join order with lowest evaluation cost by exhaustive search is perfectly feasible it takes but a few seconds CPU time. But if more than about eight relations are to be joined, the in its general form NP hard problem of determining the optimal order [IK84] cannot be solved exactly anymore. We have to rely on algorithms that compute (hopefully) good approximative solutions. Those algorithms fall into two classes: first, augmentation heuristics that build an evaluation plan step by step according to certain criteria, and second, randomized ....

....selects the relation from the set that can be joined with lowest cost with the remaining relations. This strategy is applied repeatedly until no relations are left (Figure 4) 4.1. 4 Krishnamurthy Boral Zaniolo Algorithm On the foundation of [Law78] and [MS79] Ibaraki and Kameda showed in [IK84] that it is possible to compute the optimal nesting order in polynomial time, provided the query graph forms a tree (i.e. no cycles) and the cost function is a member of a certain class. Based on this result, Krishnamurthy, Boral and Zaniolo developed in [KBZ86] an algorithm (from now on called ....

[Article contains additional citation context not shown here]

T. Ibaraki and T. Kameda. Optimal nesting for computing N - relational joins. ACM Trans. on Database Systems, 9(3):482--502, 1984.

....optimizer to plan the rewritten query. This does not integrate well with a System R style optimization algorithm, however, since LDL increases the number of joins to order, and System R s complexity is exponential in the number of joins. Thus [KZ88] proposes using the polynomialtime IK KBZ [IK84, KBZ86] approach for optimizing the join order. Unfortunately, both the System R and IK KBZ optimization algorithms consider only left deep plan trees, and no left deep plan tree can model the optimal plan tree of Figure 1. That is because the plan tree of Figure 1, with selections p and q ....

Toshihide Ibaraki and Tiko Kameda. Optimal Nesting for Computing N-relational Joins. ACM Transactions on Database Systems, 9(3):482--502, October 1984.

....predicates occur due to subqueries which can not be unnested. Several researchers have proposed algorithms for the optimal ordering of expensive joins and selections. All these algorithms bear exponential worst case complexity. In this paper we generalize the approaches of Ibaraki, Kameda [6] and Krishnamurthy, Boral, Zaniolo [10] for ordering joins to capture joins and selections both with expensive predicates. We use a refined version of the standard cost function given in [10] to account for expensive join and selection predicates. Concerning the search space and the class of ....

....the complexity of dynamic programming algorithms for the join ordering problem. They also gave the first real world examples to show that abandoning cross products can lead to more expensive plans. An NP hardness result for the join ordering problem for general query graphs was established in 1984 [6]. Later on, a further results showed that even the problem of determining optimal left deep trees with cross products for star queries is NP complete [1] The first polynomial time optimization algorithm was devised by Ibaraki and Kameda [6] in 1984. Their IK algorithm solved the join ordering ....

[Article contains additional citation context not shown here]

T. Ibaraki and T. Kameda. Optimal nesting for computing n-relational joins. ACM Trans. on Database Systems, 9(3):482--502, 1984.

.... shapes, their proposed dynamic algorithm becomes exponential (O(2 n ) The only heuristic join ordering algorithm for general (cyclic) graphs that we are aware of is the KBZ algorithm by Krishnamurthy, Boral, and Zaniolo [10] which in turn is based on the IK algorithm of Ibaraki and Kameda [7]. The IK algorithm finds the optimal deep left tree of an acyclic graph under certain cost functions in polynomial time by assigning ranks to relations and ordering the relations according to rank. The KBZ algorithm is an O(n 2 ) heuristic that finds the minimum spanning tree of a cyclic graph ....

T. Ibaraki and T. Kameda. Optimal Nesting for Computing N-Relational Joins. ACM Transactions on Database Systems, 9(3):482--502, September 1984.

.... throughout the entire execution of the query, it is possible to efficiently generate an optimal plan over the desired execution space [CS96] Another line of research refines query optimization by focusing on join reordering where an important working assumption is that predicates are zero cost [IK84, KBZ86, SI92]. A general formulation of query optimization for various buffer sizes can be found in [INS 92] This runtime parameter is typically unknown before the actual query execution. By constructing various plans in advance, the most appropriate one can be chosen at run time just before the query is ....

T. Ibaraki, T. Kameda. Optimal Nesting for Computing N-Relational Joins. ACM Transactions on Database Systems, October 1984.

....10 nodes, using a hash function on attribute R1:A. c The number of distinct values in the relation. Table 1: Contents of the metabase for the relations of the sample query. The crucial issue in terms of search strategy is the join ordering problem, that is NP complete on the number of relations [14]. A typical approach to solve the problem [26] is to use dynamic programming, which is a standard optimization technique. It is almost exhaustive and assures that the best of all plans is found. It incurs an acceptable optimization cost (time and space) when the number of relations in the query is ....

T. Ibaraki and T. Kameda. Optimal nesting for computing n-relational joins. ACM Transactions on Database Systems, 9(3):482--502, 1984.

....that will manage terabytes of Geographic Information System (GIS) data, to support global change researchers. It is expected that these researchers will be writing queries with expensive functions to analyze this data. A benchmark of such queries is presented in [SFGM93] Ibaraki and Kameda [IK84] Krishnamurthy, Boral and Zaniolo [KBZ86] and Swami and Iyer [SI92] have developed and refined a query optimization scheme that is built on the notion of rank that we will use below. However, their scheme uses rank to reorder joins rather than restrictions. Their techniques do not consider the ....

....optimizes all paths in an arbitrary tree. Furthermore, their schemes are a proposal for a completely new method for query optimization, while ours is an extension that can be applied to the plans of any query optimizer. It is possible to fuse the technique we develop in this paper with those of [IK84, KBZ86, SI92] but we do not focus on that issue here since their schemes are not widely in use. The notion of expensive restrictions was considered in the context of the LDL logic programming system [CGK89] Their solution was to model a restriction on relation R as a join between R and a ....

[Article contains additional citation context not shown here]

Toshihide Ibaraki and Tiko Kameda. Optimal Nesting for Computing N-relational Joins. ACM Transactions on Database Systems, 9(3):482--502, October 1984.

....v defined by j v (R)j is assigned to each IU v in a relation R. The bottom up calculation of the e values is performed as follows: The initialization is done by the basic numbers of the building blocks. The further calculation is mainly based on a formula also used for generating join orderings [8]. For example, let an expansion v 0 :v:a be applied on a relation R where the e values are known. Let c Tv ;a be the cardinality of the range of the attribute type associated function a and e v be equal to j v (R)j. Then, the following formula determines the number e 0 v of values being ....

T. Ibaraki and T. Kameda. Optimal nesting for computing N-relational joins. ACM Trans. on Database Systems, 9(3):482--502, 1984.

No context found.

T. Ibaraki and T. Kameda. Optimal nesting for computing n-relational joins. ACM Trans. on Database Systems, 9(3):482--502, 1984.

No context found.

T. Ibaraki and T. Kameda. Optimal nesting for computing n-relational joins. ACM Trans. on Database Systems, 9(3):482--502, 1984.

No context found.

T. Ibaraki and T. Kameda. Optimal nesting for computing n-relational joins. ACM Trans. on Database Systems, 9(3):482--502, 1984.

No context found.

T. Ibaraki and T. Kameda. Optimal nesting for computing n-relational joins. ACM Trans. on Database Systems, 9(3):482--502, 1984.

No context found.

T. Ibaraki and T. Kameda. Optimal nesting for computing n-relational joins. ACM Trans. on Database Systems, 9(3):482--502, 1984.

No context found.

T. Ibaraki and T. Kameda. Optimal nesting for computing N-relational joins. TODS, 9(3), 1984.

No context found.

T. Ibaraki and T. Kameda. Optimal nesting for computing N-relational joins. TODS, 9(3), 1984.

No context found.

Ibaraki, T., Kameda, T. Optimal nesting for computing N--relational joins. ACM Trans. on Database systems, 9(3): 482--502. 1984.

No context found.

T. Ibaraki and T. Kameda. Optimal nesting for computing N-relational joins. ACM Trans. on Database Systems, 9(3):482--502, 1984.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC