A direct extension to the counting method is presented which can deal efficiently with both acyclic and cyclic relations. The extension to cycle cases, called the synchronized counting method, is simulated and studied using a Petri net model. Worst-case analysis shows that n/sup 2/ semijoin operations are required, where n is the number of nodes in the graph representing the relevant part of the input relations. The algorithm is shown to be sound and complete, and a comparison with other methods in the literature is included. >

Synchronized counting method

Counting method is an efficient algorithm in the processing of linear recursive queries in acyclic databases. Level-Cycle Merging (LCM) method is an extension of the counting method to process linear recursive queries in both cyclic and acyclic databases. The method precompiles databases to extract self level-cycle information, uses level-cycle sets to register level recurrence sequences in both up-chain and down-chain processing, and extracts answers by level matching analysis. To improve performance, golden cycle optimization is also proposed. Our analysis shows that the method has the same asymptotic running time as the counting method and a reasonable cost on EDB compilation and updates. Our study shows that Level-Cycle Merging compares favorably with other recently developed cyclic counting techniques.

The Level-Cycle Merging Method.

The Level-Cycle Merging Method

We present a general solution to the problem of optimized execution of logic programs containing linear recursive rules. Our solution is based on extensions of the classical counting method, which is known to be efficient but of limited applicability. In fact, the range of applicability of the counting method, and its variants proposed by previous researchers, suffer from one or more of the following limitations: the method can be applied only when (1) the adorned program contains one recursive rule, (2) the ‘left part’ and the ‘right part’ of the recursive rule do not have any common variable and (3) the relation associated with the left part of the recursive rule is ‘acyclic’. In this paper, a simple and unified framework is presented, where those limitations are removed, and the counting method thus become applicable to all programs with linear rules. This framework also allows a simple treatment of programs factorizable into segments, which can be computed separately yielding a much faster execution. A simple factorization technique based on argument reduction is presented that produces optimizations similar to those defined in the literature for RLC-linear programs (i.e., programs with right- linear rules, left-linear rules and a combination of the two).

Optimization of Linear Logic Programs Using Counting Methods

Grahne et al. have presented a graph algorithm for evaluating a subset of recursive queries. This method consists of two phases. In the first phase, the method transforms a linear binary-chain program into a set of equations over expressions containing predicate symbols. In the second phase, a graph is constructed from the equations and the answers are produced by traversing the relevant paths. In this paper, we describe a new algorithm which requires less time than Grahne's. The key idea of the improvement is to reduce the search space that will be traversed when a query is invoked. Furthermore, we speed up the evaluation of cyclic data by generating most answers directly in terms of the answers already found and the associated "path information" instead of traversing the corresponding paths as usual. In this way, our algorithm achieves a linear time complexity for both acyclic and cyclic data.

/pdf/on-the-graph-traversal-and-linear-binary-chain-programs-4lu5bz2ac0.pdf

On the graph traversal and linear binary-chain programs

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Synchronized counting method