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38
On the Complexity of Generating Optimal LeftDeep Processing Trees with Cross Products
 In ICDT Conference
, 1995
"... . Producing optimal leftdeep trees is known to be NPcomplete for general join graphs and a quite complex cost function counting disk accesses for a special blockwise nestedloop join [2]. Independent of any cost function is the dynamic programming approach to join ordering. The number of alternat ..."
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Cited by 21 (5 self)
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. Producing optimal leftdeep trees is known to be NPcomplete for general join graphs and a quite complex cost function counting disk accesses for a special blockwise nestedloop 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 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 intermediate result sizes is a good heuristic. Then we show that summarizing the intermediate result sizes has the ASI property. It further motivates us to restri...
On the Complexity of Generating Optimal Plans with Cross Products (Extended Abstract)
 In PODS Conference
, 1997
"... In modern advanced database systems the optimizer is often faced with the problem of finding optimal evaluation strategies for queries involving a large number of joins. Examples are queries generated by deductive database systems and path expressions in objectoriented database systems. The be ..."
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Cited by 21 (1 self)
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In modern advanced database systems the optimizer is often faced with the problem of finding optimal evaluation strategies for queries involving a large number of joins. Examples are queries generated by deductive database systems and path expressions in objectoriented database systems. The best plan can be found in the very large search space of bushy trees where plans are allowed to contain cross products. A general question arises: For which (sub) problems can we expect to find polynomial algorithms generating the best plan? We attack this question from both ends of the spectrum. First, we show that we cannot expect to find any polynomial algorithm for any subproblem as long as optimal bushy trees are to be generated. More specifically, we show that the problem is NPhard independent of the query graph.
Optimal reduction of twoterminal directed acyclic graphs
 SIAM JOURNAL ON COMPUTING
, 1992
"... Algorithms for seriesparallel graphs can be extended to arbitrary twoterminal dags if node reductions are used along with series and parallel reductions. A node reduction contracts a vertex with unit indegree (outdegree) into its sole incoming (outgoing) neighbor. This paper gives an O(n2" ..."
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Cited by 14 (1 self)
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Algorithms for seriesparallel graphs can be extended to arbitrary twoterminal dags if node reductions are used along with series and parallel reductions. A node reduction contracts a vertex with unit indegree (outdegree) into its sole incoming (outgoing) neighbor. This paper gives an O(n2"5) algorithm for minimizing node reductions, based on vertex cover in a transitive auxiliary graph. Applications include the analysis of PERT networks, dynamic programming approaches to network problems, and network reliability. For NPhard problems one can obtain algorithms that are exponential only in the minimum number of node reductions rather than the number of vertices. This gives improvements if the underlying graph is nearly seriesparallel.
Bypassing Joins in Disjunctive Queries
, 1995
"... In this paper we develop a novel optimization strategy for disjunctive queries involving join predicates. This work is an extension of our previously published approach [KMPS94] for optimizing disjunctive selection predicates by generating two output streams from selection operators: a "true&qu ..."
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Cited by 12 (6 self)
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In this paper we develop a novel optimization strategy for disjunctive queries involving join predicates. This work is an extension of our previously published approach [KMPS94] for optimizing disjunctive selection predicates by generating two output streams from selection operators: a "true"stream for objects (tuples) satisfying the selection predicate and a "false"stream for those objects not satisfying the predicate. Then, each stream undergoes an individual, "customized" optimization. Here, we extend the basic idea of [KMPS94] to disjunctive queries with join operators. Analogously to selections, we propose to generate two output streams from a join operator: one "true"stream for pairs of objects (of the two input streams) that satisfy the join predicate and one "false" stream for those pairs not satisfying it. In combination with the extended selection predicate processing, this provides a large potential for efficiently evaluating disjunctive queries because it allows to "byp...
TwoDimensional Gantt Charts and a SCHEDULING ALGORITHM OF LAWLER
, 2000
"... In this note we give an alternate proof that a scheduling algorithm of Lawler [E.L. ..."
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Cited by 12 (0 self)
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In this note we give an alternate proof that a scheduling algorithm of Lawler [E.L.
Optimization and Evaluation of Disjunctive Queries
 IEEE Trans. on Knowledge and Data Engineering
, 2000
"... this paper, we propose a novel technique, called ###### ##########, for evaluating such disjunctive queries. The bypass processing technique is based on new selection and join operators that produce two output streams: the ####stream with tuples satisfying the selection (join) predicate and the # ..."
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Cited by 6 (3 self)
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this paper, we propose a novel technique, called ###### ##########, for evaluating such disjunctive queries. The bypass processing technique is based on new selection and join operators that produce two output streams: the ####stream with tuples satisfying the selection (join) predicate and the #####stream with tuples not satisfying the corresponding predicate. Splitting the tuple streams in this way enables us to bypass costly predicates whenever the fate of the corresponding tuple (stream) can be determined without evaluating this predicate. In the paper, we show how to systematically generate bypass evaluation plans utilizing a bottomup building block approach. We show that our evaluation technique allows to incorporate the standard SQL semantics of null values. For this, we devise two different approaches: One is based on explicitly incorporating threevalued logic into the evaluation plans; the other one relies on twovalued logic by moving all negations to atomic conditions of the selection predicate. We describe how to extend an iteratorbased query engine to support bypass evaluation with little extra overhead. This query engine was used to quantitatively evaluate the bypass evaluation plans against the traditional evaluation techniques utilizing a CNF or DNFbased query predicate
On Expressing Value Externalities in Position Auctions
"... Externalities are recognized to exist in the sponsored search market, where two colocated ads compete for user attention. Existing work focuses on the effect of another ad on the quantity of clicks received. We focus instead on the negative effect of another ad on the value per click, and propose a ..."
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Cited by 4 (0 self)
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Externalities are recognized to exist in the sponsored search market, where two colocated ads compete for user attention. Existing work focuses on the effect of another ad on the quantity of clicks received. We focus instead on the negative effect of another ad on the value per click, and propose a general model of externalities, in which a bidder has no value for a slot under a set of certain conditions, each on one other bidder’s allocated slot. We provide a generic greedy algorithm for the winner determination problem (WDP) in this model together with a pricing scheme that closely follow the Generalized Second Price (GSP) auction used in practice. For value externalities that satisfy a property of downwardmonotonicity, these mechanisms provide no new opportunities for manipulation beyond the ones already available via untruthful claims about bid value in GSP under the standard slot auction model. Our main instantiation of downwardmonotonic constraints is an identityspecific language, in which a bidder can require that it precedes some subset of other bidders. For this language’s WDP, we establish worstcase complexity and inapproximability results. This motivates the choice of approximations, e.g. via the greedy algorithm. As another way of circumventing the hardness results, we present fixedparameter algorithms for the WDPs of two sublanguages of the identityspecific model. 1.
Optimal Ordering of Selections and Joins in Acyclic Queries with Expensive Predicates
 Lehrstuhl für Praktische Informatik III, RWTH
, 1996
"... The generally accepted optimization heuristics of pushing selections down does not yield optimal plans in the presence of expensive predicates. Therefore, several researchers have proposed algorithms for the optimal ordering of expensive joins and selections in a query evaluation plan. All of these ..."
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Cited by 4 (4 self)
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The generally accepted optimization heuristics of pushing selections down does not yield optimal plans in the presence of expensive predicates. Therefore, several researchers have proposed algorithms for the optimal ordering of expensive joins and selections in a query evaluation plan. All of these algorithms have an exponential run time. For a special case, we propose a polynomial algorithm which  in one integrated step  computes the optimal join order and places expensive predicates optimally within the join tree. The special case is characterized by the following statements: 1. only leftdeep trees are considered, 2. no crossproducts are considered, 3. the cost function has to exhibit the ASI property, and 4. cheap selections are pushed beforehand. 1 Introduction Traditional work on algebraic query optimization has mainly focused on the problem of ordering joins in a query. Restrictions like selections and projections are generally treated by "pushdown rules". According to t...