. We survey results on self-organizing data structures for the search problem and concentrate on two very popular structures: the unsorted linear list, and the binary search tree. For the problem of maintaining unsorted lists, also known as the list update problem, we present results on the competitiveness achieved by deterministic and randomized on-line algorithms. For binary search trees, we present results for both on-line and off-line algorithms. Self-organizing data structures can be used to build very effective data compression schemes. We summarize theoretical and experimental results. 1 Introduction This paper surveys results in the design and analysis of self-organizing data structures for the search problem. The general search problem in pointer data structures can be phrased as follows. The elements of a set are stored in a collection of nodes. Each node also contains O(1) pointers to other nodes and additional state data which can be used for navigation and self-organizati...

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We consider self-organizing data structures in the case where the sequence of accesses can be modeled by a first order Markov chain. For the simple-k- and batched-k--move-to-front schemes, explicit formulae for the expected search costs are derived and compared. We use a new approach that employs the technique of expanding a Markov chain. This approach generalizes the results of Gonnet/Munro/Suwanda. In order to analyze arbitrary memory-free move-forward heuristics for linear lists, we restrict our attention to a special access sequence, thereby reducing the state space of the chain governing the behaviour of the data structure. In the case of accesses with locality (inert transition behaviour), we find that the hierarchies of self-organizing data structures with respect to the expected search time are reversed, compared with independent accesses. Finally we look at self-organizing binary trees with the move-to-root rule and compare the expected search cost with the entropy of the Markov chain of accesses.

this paper we assume that the sequence of required keys is a Markov chain with transition kernel P, and we consider the class f* of stochastic matrices P such that move-to-front is optimal among on-line rules, with respect to the stationary search cost. We give properties of f* that bear out the usual explanation of optimality of move-to-front by a locality phenomenon exhibited by the sequence of required keys. We produce explicitly a large subclass of f*. We also show that in some cases move-to-front is optimal with respect to the speed of convergence toward stationary search cost. 1. Introduction. Let us describe a simple example of a self-organizing sequential search data structure. Let S = {1,2, ... ,M} be a set of items ; assume that these items are stored in places, and that the set p of places is {1,2, ... ,M}. When an item is required, it is searched for in place 1, then, if not found, in place 2, and so on, and a cost p is incurred if the item is finally found in place p. Once the item has been found, a control is taken on the search process by replacing the item in a wisely chosen place : for instance, closer to American Mathematical Society 1980 subject classification. Primary 68P05, 90C40 ; secondary 60J10. Key words and phrases. Controlled Markov chain, Bellman optimality condition, self organizing data structure, sequential search, locality. Abbreviated title (running head). Optimality of move-to-front rule. 2 place 1, in such a way that the most frequently accessed items spend most of their time near place 1. When doing this, we must free the new position h of the accessed item by pushing the items remaining between the old position k and the new position h, the notaccessed items retaining their relative order, as in figure 1. Let F = (F n ) n1 be the s...

www.elsevier.com/locate/comnet Modeling correlations in web traces and implications for designing replacement policies Konstantinos Psounis a,*

The transposition rule is an algorithm for self-organizing linear lists. Upon a request for a given item, the item is transposed with the preceding one. The cost of a request is the distance of the requested item from the beginning of the list. An asymptotic optimality of the rule with the respect to the optimal static arrangement is demonstrated for two families of request distributions. The result is established by considering an associated constrained asymmetric exclusion process.