A Memory-Efficient Doubly Linked List

The current delete implementation erases the whole list. For this article, our objective is to show the dynamic memory usage and execution times for the implemented primitives. It should not be difficult to come up with a canonical set of primitive operations for all the known operations of a doubly linked list.

Because our traversal depends on having pointers to two nodes, we cannot delete the current node as soon as we find the next node. Instead, we always delete the previous node once the next node is found. Moreover, if the current node is the end, when we free the current node, we are done. A node is considered to be an end node if the NextNode() function applied to it returns a null node.

A sample program to test the implementation discussed here is available as Listing 2 from the Linux Journal FTP site (ftp.linuxjournal.com/pub/lj/listings/issue129/6828.tgz). On my Pentium II (349MHz, 32MB of RAM and 512KB of level 2 cache), when I run the pointer distance implementation, it takes 15 seconds to create 20,000 nodes. This is the time needed for the insertion of 20,000 nodes. Traversal and deletion of the whole list does not take even a second, hence the profiling at that granularity is not helpful. For system-level implementation, one might want to measure timings in terms of milliseconds.

When we run the same pointer distance implementation on 10,000 nodes, insertion takes only three seconds. Traversal through the list and deletion of the entire list both take less than a second. For 20,000 nodes the memory being used for the whole list is 160,000 bytes, and for 10,000 nodes it is 80,000 bytes. On 30,000 nodes it takes 37 seconds to run the insertion. Again it takes less than a second to finish either the traversal or the deletion of the whole list. It is somewhat predictable that we would see this kind of timing, as the dynamic memory (heap) used here is being used more and more as the number of nodes increases. Hence, finding a memory slot from the dynamic memory takes longer and longer in a nonlinear, rather hyperlinear fashion.

For the conventional implementation, the insertion of 10,000 nodes takes the same three seconds. Traversal takes less than a second for both forward and backward traversal. Total memory taken for 10,000 nodes is 120,000 bytes. For 20,000 nodes, the insertion takes 13 seconds. The traversal and deletion individually takes less than a second. Total memory taken for 20,000 nodes is 240,000 bytes. On 30,000 nodes it takes 33 seconds to run the insertion and less than a second to run the traversal and the deletion. Total memory taken by 30,000 nodes is 360,000 bytes.

A memory-efficient implementation of a doubly linked list is possible to have without compromising much timing efficiency. A clever design would give us a canonical set of primitive operations for both implementations, but the time consumptions would not be significantly different for those comparable primitives.