U. Glaeser

increment lowestPriorityOnDisk(disk(bi))) increment blocksWithPriority(priority(bi)) increment numberOfBlocksPlaced
if (numberOfBlocksPlaced = M) then
decrement numberOfBlocksPlaced by blocksWithPriority(lowestPriority)
increment lowestPriority
By using the priority assignment described here, it has been shown that L-OPT always creates a schedule
that is within a factor Θ√(MD/L) times the length of the schedule created by the optimal offline algorithm,
and that this is the best possible ratio. In addition, L-OPT’s schedule is never more than twice the length
of that created by any online algorithm (including algorithms that consistently make fortuitously correct
guesses) that has the same amount of lookahead. Finally, note that if the entire reference string is known
in advance, then L-OPT is the optimal offline algorithm [32].
33.7 Optimal Parallel-Disk Caching
For general reference strings where blocks may be repeatedly accessed, the buffer manager must decide
which blocks to cache and which to evict. As noted earlier, the optimal single-disk caching policy
embodied in the MIN algorithm can be decidedly suboptimal in the parallel I/O case. Prefetching and
caching need to harmoniously cooperate in the multiple-disk situation. The caching problem has been
studied by several researchers in the recent past for different I/O organizations. For a distributed-buffer
configuration where each disk has its own private buffer, an algorithm P-MIN that generalizes MIN to
multiple disks was shown to be optimal [57]. P-MIN uses the furthest forward reference policy on each
disk independently to determine the eviction candidate for that disk. It initiates an I/O only on demand;
in the ensuing I/O operation it prefetches aggressively from every disk unless the reference to the block
to be prefetched is further than the references of all blocks currently in that buffer. For a shared-buffer
configuration in the stall-model of computation, a sophisticated near-optimal algorithm called Reverse-
Aggressive to minimize the stall time was proposed and analyzed in [36].
Recently, an optimal prefetching and caching algorithm, SUPERVISOR, for the parallel disk model
was presented in [34]. Like the L-OPT algorithm for prefetching, SUPERVISOR uses the general framework
of priority-controlled greedy I/O. The scheme for assigning priorities to references is, however,
considerably more complex than that used by L-OPT for read-once reference strings. Just as a low priority
with respect to prefetching indicates that an I/O for that block can be delayed, a low priority with respect
to caching indicates that the block can be evicted from the buffer.
Intuitively, SUPERVISOR assigns priorities in accordance with two principles: issue prefetches for
blocks close to their reference so that they do not wastefully occupy buffer space, and avoid caching a
block if there is any later free I/O slot available, which can be used to fetch it. Among possible candidates
for a block to cache, it is desirable to cache a block that will occupy the buffer for a smaller duration.
Hence, the question to be answered is: Given that at some time we would like two previously referenced
blocks in the buffer, which of these should have been cached and which should be fetched now? It is
preferable to cache the block whose previous reference is closer to the current time, as this reduces the
buffer pressure between the two previous accesses. SUPERVISOR uses this intuition to assign priorities
to blocks for prefetching and caching.
The formal details of the priority assignment algorithm used by SUPERVISOR are presented in [34].
The routine examines subsets of the lookahead consisting of M distinct references and then assigns priorities
to one block from each disk. The idea behind the assignment can be understood by considering the largest
subsequence of the lookahead including the last reference and having at most M distinct references. All
blocks which are assigned the smallest priority should belong to this set. Otherwise there will be some
reference such that M or more blocks referenced after it have a higher, or same priority. Which among
these blocks should have the lowest priority? The lowest priority can be assigned to, at most, one distinct
reference from each disk. Additionally, among two blocks from the same disk, this priority is assigned to
the block with the previous reference outside this subsequence is earlier, because we would rather not
© 2002 by CRC Press LLC