5.1 Input Problem Set 5.2 Accuracy of the Proposed Algorithm Lemma 1 Consider the Lp Problem

15] S. Jajodia and D. Mutchler. A pessimistic consistency control algorithm for replicated les which achieves high availability. A practical implementation of the factoring algorithm for network reliability. A majority consensus approach to concurrency control for multiple copy databases. Optimal Within 20% of optimal Prob 1 54 0 Prob 2 NA NA Prob 3 54 0 Prob 4 30 24 Prob 5 NA NA Note: Entries in the table represent the number of cases of each test problem that fall into the speciied category. A total of 54 cases for each test problem were run for each of the availability and the reliability problems. Results for prob3 and prob5 are NA (not available) since the CPU time requirement for exhaustive enumeration of these problem is prohibitive. meration approach. The entries in the table represent the average number of iterations required by the algorithm to solve the stated number of cases and the corresponding average eeciency of the algorithm in solving those cases. The eeciency is calculated as (1?(i=2 N))100, where i is the number of iterations. This formula is derived from the fact that if the the input problem consists of N nodes, then 2 N iterations are required for a complete enumeration. 6 Conclusion In this paper we have presented an eeective integration of the problem of optimally allocating le copies in an DCS while at the same time ensuring mutual consistency of replicated data. This yields a constrained non-linear integer programming problem. An eecient algorithm utilizing the knowledge of the special structure of the problem is proposed for consistency constraints. The proposed algorithm yielded a solution to all our sample problems quite rapidly. The CPU times (on a VAX 8550 computer) for solving problems are less than 1 second for problems with N 10, and less than 2 seconds for N 20. Thus, our algorithm is well suited for networks with up to twenty nodes even in a real-time mode of operation. Since most network reliability problems can be eeciently solved up-to about fty nodes 4], we feel that the bottleneck is in the network reliability calculation for larger networks. It is important to note that, fty nodes is about the size of a large subnet for a public data network if we consider only the gateways. Hence, the proposed algorithm is useful for modeling the subnet of modern networks, where the component computer nodes and communication links …