Online View Maintenance Under a Response-Time Constraint
A materialized view is a certain synopsis structure precomputed from one or more data sets (called base tables) in order to facilitate various queries on the data. When the underlying base tables change, the materialized view also needs to be updated accordingly to reflect those changes. We consider the problem of batch-incrementally maintaining a materialized view under a response-time constraint. We propose techniques for selectively processing updates to some base tables while keeping others batched, with the goal of minimizing the total maintenance cost while meeting the response-time constraint. We reduce this to a generalized paging problem, where the cost of evicting a page is a concave non-decreasing function of the number of continuous requests seen since the last time it was evicted. Our main result is an online algorithm that achieves a constant competitive ratio for all concave cost functions while relaxing the response-time constraint by a constant factor. For several special classes of cost functions, the competitive ratio can be improved with simpler, more intuitive algorithms. Our algorithms are based on emulating the behavior of an online paging algorithm on a page request sequence carefully designed from the cost function. The key novel technical ideas are twofold. The first involves discretizing the cost function, so that there is a collection of periodic paging sequences, with page sizes decreasing geometrically, which approximates the behavior of the original function. The second involves designing an online view maintenance algorithm based on the paging process, by emulating the behavior of the paging scheme in recursively defined phases.
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