A data structure is described which can be used for representing a collection of priority queues. The primitive operations are insertion, deletion, union, update, and search for an item of earliest priority.

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A data structure for manipulating priority queues

We tackle the problem of maintaining materialized top-k views. Top-k queries, including MIN and MAX as important special cases, occur frequently in common database workloads. A top-k view can be materialized to improve query performance, but in general it is not self-maintainable unless it contains all tuples in the base table. Deletions and updates on the base table may cause tuples to leave the top-k view, resulting in expensive queries over the base table to "refill" the view. We propose an algorithm that reduces the frequency of refills by maintaining a top-k' view instead of a top-k view, where k' changes at runtime between k and some k/sub max//spl ges/k. We show that in most practical cases, our algorithm can reduce the expected amortized cost of refill queries to O(1) while still keeping the view small. The optimal value of k/sub max/ depends on the update pattern and the costs of querying the base table and updating the view. Compared with the simple approach of maintaining either the top-k view itself or a copy of the base table, our algorithm can provide orders-of-magnitude improvements in performance with appropriate k/sub max/ values. We show how to choose k/sub max/ dynamically to adapt to the actual system workload and performance at runtime, without requiring accurate prior knowledge.

/pdf/efficient-maintenance-of-materialized-top-k-views-25j82fe5o7.pdf

Efficient maintenance of materialized top-k views

New analytical and empirical results for the performance of future event set algorithms in discrete event simulation are presented. These results provide a clear insight to the factors affecting algorithm performance, permit evaluation of the hold model, and determine the best algorithm(s) to use. The analytical results include a classification of distributions for efficient insertion scanning of a linear structure. In addition, it is shown that when more than one distribution is present, there is generally an increase in the probability that new insertions will have smaller times than those in the future event set. Twelve algorithms, including most of those recently proposed, were empirically evaluated using primarily simulation models. Of the twelve tested, four performed well, three performed fairly, and five performed poorly.

/pdf/analysis-of-future-event-set-algorithms-for-discrete-event-1b4m0w56sa.pdf

Analysis of future event set algorithms for discrete event simulation

Building heaps fast

We introduce a new representation of a priority queue in an array such that the operation of insert can be performed in constant time and minimum extraction in logarithmic time. In developing this structure we first introduce a very simple scheme permitting insertions in constant amortized time. This is modified to achieve the worst-case behavior using roughly lg*n pairs of pointers, and finally this pointer requirement is removed.

An implicit binomial queue with constant insertion time

The average number of levels that a new element moves up when inserted into a heap is investigated. Two probabilistic models under which such an average might be computed are proposed. A `Lemma of Conservation of Ignorance' is formulated and used in the derivation of an exact formula for the average in one of these models. It is shown that this average is bounded by a constant and its asymptotic behaviour is discussed. Numerical data for the second model are also provided and analyzed.

Random insertion into a priority queue structure

The average number of levels that a new element moves up when inserted into a heap is investigated. Two probabilistic models, under which such an average might be computed are proposed. A "lemma of conservation of ignorance" is formulated and used in the derivation of an exact formula for the average in one of these models. It is shown that this average is bounded by a constant and its asymptotic behavior is discussed. Numerical data for the second model is also provided and analyzed.

Thomas Porter

Papers

Random insertion into a priority queue structure

Random insertion into a priority queue structure.