8 Conclusion and Future Work 7 Related Work

17 moves, but if the move is uphill it is accepted by a certain probability, which decreases over time. The work by Swami and Gupta 18, 17] compares various heuristics and combinatorial algorithms. Their experiments suggest that iterative improvement is the best combinatorial optimization technique. Morzy, Matysiak, and Salza 11] improved the iterative improvement algorithm by maintaining a list of constraints between iterations (called a tabu list) to avoid the repetition of non prootable moves. We have presented a polynomial-time heuristic algorithm that generates good quality plans for OODB queries. The algorithm has been tested on various random relational query graphs. Our preliminary results show that our method is clearly superior to the iterative improvement method. As a future work, we are planning to incorporate this algorithm to the experimental query optimizer for OQL being developed at the University of Texas at Arlington 4]. We are also planning to combine this algorithm with a local search technique, which improves small fragments of the query plan by performing a real cost analysis. Acknowledgements: The author is grateful to Yannis Tollis for pointers into the literature on min-cut algorithms and to Ramez Elmasri for helpful comments on the paper. 16 As another demonstration of the eeectiveness of our algorithm, we compared the quality of the produced plans with the quality of the plans produced by the iterative improvement method (II), when the latter is allowed to run 50% longer than MC (Figure 7.b). The II algorithm works as follows: a random join is selected and it is improved by the downhill improvement phase. When no improvement can be made to any node, the iterative improvement algorithm chooses another random plan and performs the same process. This task is repeated until the total running time of II exceeds the speciied time limit (1:5 times the running time of MC). At the end, the best plan found during all iterations is returned. The values in Figure 7.b represent scaled costs: if t 1 is the cost of the plan produced by MC and t 2 is the cost of the plan produced by II, then the table entry is (t 2 ? t 1)=t 1. Like before, each value is the average value of ten experiments. We can see that min-cut clearly beats iterative improvement despite the time advantage given to II. Figure 7.c compares IMC with II, when II is allowed to run …