Competitive Parallel Disk Prefetching and Buffer Management

We provide a competitive analysis framework for online prefetching and buffer management algorithms in parallel I/O systems, using a read-once model of block references. This has widespread applicability to key I/O-bound applications such as external merging and concurrent playback of multiple video streams. Two realistic lookahead models, global lookahead and local lookahead, are defined. Algorithms NOM and GREED based on these two forms of lookahead are analyzed for shared buffer and distributed buffer configurations, both of which occur frequently in existing systems. An important aspect of our work is that we show how to implement both the models of lookahead in practice using the simple techniques of forecasting and flushing. Given a -disk parallel I/O system and a globally shared I/O buffer that can hold upto disk blocks, we derive a lower bound of on the competitive ratio of any deterministic online prefetching algorithm with lookahead. NOM is shown to match the lower bound using global -block lookahead. In contrast, using only local lookahead results in an competitive ratio. When the buffer is distributed into portions of blocks each, the algorithm GREED based on local lookahead is shown to be optimal, and NOM is within a constant factor of optimal. Thus we provide a theoretical basis for the intuition that global lookahead is more valuable for prefetching in the case of a shared buffer configuration whereas it is enough to provide local lookahead in case of the distributed configuration. Finally, we analyze the performance of these algorithms for reference strings generated by a uniformly-random stochastic process and we show that they achieve the minimal expected number of I/Os. These results also give bounds on the worst-case expected performance of algorithms which employ randomization in the data layout

Online Assignment Algorithms for Dynamic Bipartite Graphs

This paper analyzes the problem of assigning weights to edges incrementally in a dynamic complete bipartite graph consisting of producer and consumer nodes. The objective is to minimize the overall cost while satisfying certain constraints. The cost and constraints are functions of attributes of the edges, nodes and online service requests. Novelty of this work is that it models real-time distributed resource allocation using an approach to solve this theoretical problem. This paper studies variants of this assignment problem where the edges, producers and consumers can disappear and reappear or their attributes can change over time. Primal-Dual algorithms are used for solving these problems and their competitive ratios are evaluated

Derandomization of Online Assignment Algorithms for Dynamic Graphs

This paper analyzes different online algorithms for the problem of assigning weights to edges in a fully-connected bipartite graph that minimizes the overall cost while satisfying constraints. Edges in this graph may disappear and reappear over time. Performance of these algorithms is measured using simulations. This paper also attempts to derandomize the randomized online algorithm for this problem