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2054 Cost of Parallel Evaluation of Operations
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We achieve parallelism by partitioning the I/O among multiple disks, and partitioning the CPU work among multiple processors If such a split is achieved without any overhead, and if there is no skew in the splitting of work, a parallel operation using n processors will take 1/n times as long as the same operation on a single processor We already know how to estimate the cost of an operation such as a join or a selection The time cost of parallel processing would then be 1/n of the time cost of sequential processing of the operation We must also account for the following costs: Startup costs for initiating the operation at multiple processors Skew in the distribution of work among the processors, with some processors getting a larger number of tuples than others Contention for resources such as memory, disk, and the communication network resulting in delays Cost of assembling the nal result by transmitting partial results from each processor The time taken by a parallel operation can be estimated as Tpart + Tasm + max(T0 , T1 , , Tn 1 ) where Tpart is the time for partitioning the relations, Tasm is the time for assembling the results and Ti the time taken for the operation at processor Pi Assuming that the tuples are distributed without any skew, the number of tuples sent to each processor
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can be estimated as 1/n of the total number of tuples Ignoring contention, the cost Ti of the operations at each processor Pi can then be estimated by the techniques in 13 The preceding estimate will be an optimistic estimate, since skew is common Even though breaking down a single query into a number of parallel steps reduces the size of the average step, it is the time for processing the single slowest step that determines the time taken for processing the query as a whole A partitioned parallel evaluation, for instance, is only as fast as the slowest of the parallel executions Thus, any skew in the distribution of the work across processors greatly affects performance The problem of skew in partitioning is closely related to the problem of partition over ow in sequential hash joins ( 13) We can use over ow resolution and avoidance techniques developed for hash joins to handle skew when hash partitioning is used We can use balanced range partitioning and virtual processor partitioning to minimize skew due to range partitioning, as in Section 2023
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206 Interoperation Parallelism
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There are two forms of interoperation parallelism: pipelined parallelism, and independent parallelism
2061 Pipelined Parallelism
As discussed in 13, pipelining forms an important source of economy of computation for database query processing Recall that, in pipelining, the output tuples of one operation, A, are consumed by a second operation, B, even before the rst operation has produced the entire set of tuples in its output The major advantage of pipelined execution in a sequential evaluation is that we can carry out a sequence of such operations without writing any of the intermediate results to disk Parallel systems use pipelining primarily for the same reason that sequential systems do However, pipelines are a source of parallelism as well, in the same way that instruction pipelines are a source of parallelism in hardware design It is possible to run operations A and B simultaneously on different processors, so that B consumes tuples in parallel with A producing them This form of parallelism is called pipelined parallelism Consider a join of four relations: r1
We can set up a pipeline that allows the three joins to be computed in parallel Suppose processor P1 is assigned the computation of temp1 r1 1 r2 , and P2 is assigned the computation of r3 1 temp1 As P1 computes tuples in r1 1 r2 , it makes these tuples available to processor P2 Thus, P2 has available to it some of the tuples in r1 1 r2 before P1 has nished its computation P2 can use those tuples that are available to begin computation of temp1 1 r3 , even before r1 1 r2 is fully computed by P1 Likewise, as P2 computes tuples in (r1 1 r2 ) 1 r3 , it makes these tuples available to P3 , which computes the join of these tuples with r4
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