Finding optimal satisficing strategies for and-or trees

Greiner, Russell; Hayward, Ryan B.; Jankowska, Magdalena; Molloy, Michael

doi:10.1016/j.artint.2005.09.002

Cited by 43 publications

(51 citation statements)

References 12 publications

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“…The complexity of this problem is unknown in the read-once case for general AND-OR trees, while optimal polynomial-time algorithms are known for AND-trees [7] and DNF trees [6]. In this work, we focus on these two types of trees in the shared case, seeking to develop optimal algorithms or to show NP-completeness.…”

Section: Problem Statement and Examplesmentioning

confidence: 99%

“…To define our problem we reuse the formalism and terminology in [6]. A query is an AND-OR tree, i.e., a rooted tree whose non-leaf nodes are AND or OR operators, and whose leaf nodes are labeled with probabilistic boolean predicates.…”

Section: Problem Statement and Examplesmentioning

confidence: 99%

“…In practice, the success probability can be estimated based on historical traces obtained from previous query evaluations. As in [6], we assume independent predicates, meaning that two predicates at two leaf nodes in a query are statistically independent. The cost is determined by the number of data items required to perform the evaluation and the evaluation cost per data item for the stream.…”

Section: Problem Statement and Examplesmentioning

confidence: 99%

“…In particular, [6] provides both a survey of known theoretical results and several new results, all assuming that each data stream occurs in at most one leaf of the query tree. This assumption is termed read-once therein.…”

Section: Introductionmentioning

confidence: 99%

“…In this case, for AND-trees (i.e., single-level trees with an AND operator at the root node) a simple O(n log n) greedy algorithm produces an optimal leaf evaluation order (n is the number of leaves in the query tree) [7]. For DNF trees (i.e., collections of AND-trees whose roots are the children of a single OR node), a O(n log n) depth-first traversal of the trees that reuses the algorithm in [7] to order leaves within each AND produces an optimal evaluation order [6]. For general AND-OR-trees the complexity of the problem is open.…”

Section: Introductionmentioning

confidence: 99%

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Cost-Optimal Execution of Boolean Query Trees with Shared Streams

Casanova

Lim

Robert

et al. 2014

2014 IEEE 28th International Parallel and Distributed Processing Symposium

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Abstract-The processing of queries expressed as trees of boolean operators applied to predicates on sensor data streams has several applications in mobile computing. Sensor data must be retrieved from the sensors, which incurs a cost, e.g., an energy expense that depletes the battery of a mobile query processing device. The objective is to determine the order in which predicates should be evaluated so as to shortcut part of the query evaluation and minimize the expected cost. This problem has been studied assuming that each data stream occurs at a single predicate. In this work we remove this assumption since it does not necessarily hold in practice. Our main results are an optimal algorithm for single-level trees and a proof of NP-completeness for DNF trees. For DNF trees, however, we show that there is an optimal predicate evaluation order that corresponds to a depth-first traversal. This result provides inspiration for a class of heuristics. We show that one of these heuristics largely outperforms other sensible heuristics, including a heuristic proposed in previous work.

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Section: Problem Statement and Examplesmentioning

confidence: 99%

Section: Problem Statement and Examplesmentioning

confidence: 99%

Section: Problem Statement and Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Cost-Optimal Execution of Boolean Query Trees with Shared Streams

Casanova

Lim

Robert

et al. 2014

2014 IEEE 28th International Parallel and Distributed Processing Symposium

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A large‐scale linear programming model for finding optimal container inspection strategies

Boros

Fedzhora

Kantor

et al. 2009

Naval Research Logistics

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Abstract:Cargo ships arriving at US ports are inspected for unauthorized materials. Because opening and manually inspecting every container is costly and time-consuming, tests are applied to decide whether a container should be opened. By utilizing a polyhedral description of decision trees, we develop a large-scale linear programming model for sequential container inspection that determines an optimal inspection strategy under various limitations, improving on earlier approaches in several ways: (a) we consider mixed strategies and multiple thresholds for each sensor, which provide more effective inspection strategies; (b) our model can accommodate realistic limitations (budget, sensor capacity, time limits, etc.), as well as multiple container types; (c) our model is computationally more tractable allowing us to solve cases that were prohibitive in preceding models, and making it possible to analyze the potential impact of new sensor technologies.

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Approximation algorithms for sequential batch‐testing of series systems

Daldal

Gamzu

Segev³

et al. 2016

Naval Research Logistics

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We introduce and study a generalization of the classic sequential testing problem, asking to identify the correct state of a given series system that consists of independent stochastic components. In this setting, costly tests are required to examine the state of individual components, which are sequentially tested until the correct system state can be uniquely identified. The goal is to propose a policy that minimizes the expected testing cost, given a‐priori probabilistic information on the stochastic nature of each individual component. Unlike the classic setting, where variables are tested one after the other, we allow multiple tests to be conducted simultaneously, at the expense of incurring an additional set‐up cost. The main contribution of this article consists in showing that the batch testing problem can be approximated in polynomial time within factor 6.829 + ε , for any fixed ε ∈ ( 0 , 1 ) . In addition, we explain how, in spite of its highly nonlinear objective function, the batch testing problem can be formulated as an approximate integer program of polynomial size, while blowing up its expected cost by a factor of at most 1 + ε . Finally, we conduct extensive computational experiments, to demonstrate the practical effectiveness of these algorithms as well as to evaluate their limitations. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 275–286, 2016

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Finding optimal satisficing strategies for and-or trees

Cited by 43 publications

References 12 publications

Cost-Optimal Execution of Boolean Query Trees with Shared Streams

Cost-Optimal Execution of Boolean Query Trees with Shared Streams

A large‐scale linear programming model for finding optimal container inspection strategies

Approximation algorithms for sequential batch‐testing of series systems

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