II. Notes on Data Structuring * - Cornell University

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140 c. A, R. HOARE mark-collect garbage collection. Although it appears to relieve the pro- grammer of the responsibility of explicit control of main store allocation and deallocation, this can be dangerous in non-trivial computer applications where the responsibility is one that cannot so lightly be evaded. In the case of a deque, when reading is required in both directions, a single- linked chain is no longer adequate; and the usual solution is to adjoin two pointers to each item in the chain, one pointing to the previous item and one pointing to the following item. In fact these two pointers can be compressed into a single word containing only the difference between them. Since in the first and last items one of the pointers is a standard null value, the value of the other pointer from these items can always be obtained by subtraction. On reading or writing, the value of the link location for the new first or last item can be readily adjusted, since at this stage the address of the previous first or last item is still known. The detailed working out of this scheme is left as an exercise. An alternative method of linking the items of a chain is to collect all links together in a single contiguous table, preferably of fixed length. This giwes a form of tree representation for the sequence, and permits ready scanning in both directions. But it places an upper bound on the number of items in the sequence; and it means that the locations used for links must be per- manently allocated, even at times when the sequence is relatively short. This problem can be mitigated by the use of blocking. 8.2.3 Blocked Representation One disadvantage of chaining is the amount of extra storage required to hold the links, and the time taken to administer the free store chain on each operation. These problems are particularly severe when the size of the individual items of the sequence are small and the sequence is long. The method of solving this problem is to use blocking; that is, a combination of the contiguous and chained techniques. In this technique, a fixed-length block of storage is allocated, sufficient to hold perhaps between ten and a hundred items. When this block is filled, a new block is chained to it, using any of the methods described in the previous section. On input, a block is not released to free store until all the items it contains have been scanned. Thus the amount of store used on links can be reduced to negligible proportions. This can be of particular benefit in the tree representation of the chain. As mentioned above, the use of blocking can also avoid the problems arising from variable-length dynamic storage allocation, since the size of the block may be held constant for all sequences, independent of the size of their items. Furthermore, in cases where part or all of the sequence is to be held on backing store, the use of blocking is almost universally
NOTES ON DATA STRUCTURING 141 indicated, since backing store transfers can be very inefficient if the unit of transfer is too small. The only (dubious) disadvantage of blocking is that it inhibits effective sharing of the tails of stacks. The only remaining problem is to choose a size of block suitable for all purposes. It must obviously be large enough to accommodate the largest item of any sequence. In fact, it should be large enough to accommodate at least ten typical items; otherwise the space left over at the end of a block which is not large enough to accommodate the next item may reach significant proportions. Also, if the sequence is to be held partially or wholly on backing store, the block should be long enough to ensure that not too much space is wasted on interblock gaps, and the frequency of transfers is low enough to ensure that not too much time is spent in start-stop, latency, or head movement delays. On the other hand, if the block size is too large, the space wasted at the beginning of the first block and/or the end of the last block will become significant; thus the block size should be small enough to ensure that the typical sequence occupies at least ten blocks. In the presence of so many conflicting considerations, it is not easy to select a standard block size for sequences of differing length and item size, and all forms of backing store, with different methods of access. However, an acceptable compromise can often be made, and on present-day computer designs, a block size of between 128 and 1024 words will often be a suitable choice. Probably in most cases the size chosen is not critical within a factor of two either way. 8.2.4. Backing Store Representation In processing a sequence, a program normally requires access to one of its ends, and all the material in the middle and other end is unused for relatively long periods of time. If main storage is at all scarce, it is very profitable to transfer this material to backing store, so that the space it occupies in main store may be used for other purposes. In the case of input and output sequences, which have a lifetime greater than the program which reads or writes them, the use of backing store for long-term storage is almost obligatory. When using backing store, efficiency of processing and representation demands that transfers should occur in blocks of reasonable size. The block which contains an active end of a sequence is always held in main store; and to permit overlap of input/output with computing, the previous block (on writing) or the next block (on reading) also remains allocated during the transfer operation. 'This is known as double-buffering. It is possible to hold even more buffers in store to smooth out variations in the speed of processing and the speed of transfer; but the program designer must not fall into the
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II. Notes on Data Structuring * - Cornell University

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