Caching for web searching

We study web caching when the input sequence is a depth first search traversal of some tree. There are at least two good motivations for investigating tree traversal as a search technique on the WWW: First, empirical studies of people browsing and searching the WWW have shown that user access patterns commonly are nearly depth first traversals of some tree. Secondly, (as we will show in this paper) the problem of visiting all the pages on some WWW site using anchor clicks (clicks on links) and back button clicks - by far the two most common user actions - reduces to the problem of how to best cache a tree traversal sequence (up to constant factors). We show that for tree traversal sequences the optimal offline strategy can be computed efficiently. In the bit model, where the access time of a page is proportional to its size, we show that the online algorithm LRU is (1 + 1/epsilon)-competitive against an adversary with unbounded cache as long as LRU has a cache of size at least (1 + epsilon) times the size of the largest item in the input sequence. In the general model, where pages have arbitrary access times and sizes, we show that in order to be constant competitive, any online algorithm needs a cache large enough to store Omega (log n) pages; here n is the number of distinct pages in the input sequence. We provide a matching upper bound by showing that the online algorithm Landlord is constant competitive against an adversary with an unbounded cache if Landlord has a cache large enough to store the Omega (log n) largest pages. This is further theoretical evidence that Landlord is the "right" algorithm for web caching.