We prove upper and lower bounds on the competitiveness of randomized algorithms for the list update problem of Sleator and Tarjan. We give a simple and elegant randomized algorithm that is more competitive than the best previous randomized algorithm due to Irani. Our algorithm uses randomness only during an initialization phase, and from then on runs completely deterministically. It is the first randomized competitive algorithm with this property to beat the deterministic lower bound. We generalize our approach to a model in which access costs are fixed but update costs are scaled by an arbitrary constant d. We prove lower bounds for deterministic list update algorithms and for randomized algorithms against oblivious and adaptive on-line adversaries. In particular, we show that for this problem adaptive on-line and adaptive off-line adversaries are equally powerful. 1 Introduction Recently much attention has been given to competitive analysis of on-line algorithms [7, 20, 22, 25]. Ro...

this article. Two examples of simple permutation algorithms are move-to-front, which moves the accessed record to the front of the list, shifting all records previously ahead of it back one position; and transpose, which merely exchanges the accessed record with the one immediately ahead of it in the list. These will be described in more detail later. Knuth [1973] describes several search methods that are usually more efficient than linear search. Bentley and McGeoch [1985] justify the use of self-organizing linear search in the following three contexts:

. 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...

Optimum off-line algorithms for the list update problem are investigated. The list update problem involves implementing a dictionary of items as a linear list. Several characterizations of optimum algorithms are given; these lead to optimum algorithm which runs in time \Theta2 n (n \Gamma 1)!m, where n is the length of the list and m is the number of requests. The previous best algorithm, an adaptation of a more general algorithm due to Manasse et al. [9], runs in time \Theta(n!) 2 m. 1 Introduction A dictionary is an abstract data type that stores a collection of keyed items and supports the operations access, insert, and delete. In the sequential search or list update problem, a dictionary is implemented as simple linear list, either stored as a linked collection of items or as an array. An access is done by starting at the front of the list and examining each succeeding item until either finding the item desired or reaching the end of the list and reporting the item not present...

This thesis presents research done by the author on competitive analysis of on-line problems. An on-line problem is a problem that is given and solved one piece at a time. An on-line strategy for solving such a problem must give the solution to each piece knowing only the current piece and preceding pieces, in ignorance of the pieces to be given in the future. We consider on-line strategies that are competitive (guaranteeing solutions whose costs are within a constant factor of optimal) for several combinatorial optimization problems: paging, weighted caching, the k-server problem, and weighted matching. We introduce variations on the standard model of competitive analysis for paging: allowing randomization, allowing resource-bounded lookahead, and loose competitiveness, in which performance over a range of fast memory sizes is considered and noncompetitiveness is allowed provided the fault rate is insignificant. Each variation leads to substantially better competitive ratios. We prese...

The list update problem is studied in a distributed environment where the set of items is partitioned across two processors and in which the cost of accessing an item is a combination of a list searching cost and a communication cost. A natural generalization of the Move-To-Front (MTF) algorithm, called Distributed Move-To-Front (DMTF), is analyzed under two models of information available to the algorithm. In the global knowledge model (DLU[GK]), the algorithm knows the partition of items in advance, while in the local knowledge model (DLU[LK]), this information is unknown to the algorithm. Both competitive and expected value analyses are given. It is shown that for an n-item set, the performance of DMTF is a factor of O(n) worse in the local knowledge model than in the global knowledge model. 1 Introduction The list update problem, the problem of rearranging a singly-linked list to improve average access times, has been subject to considerable analysis in the literature. Each ana...

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...

Weintroduce and analyze new randomized policies for the managementofweb caches. The proposed policies are fully scalable, that is, handling a hit or an eviction requires only O(1) time. Our analysis is probabilistic, in nature, and based on an extended version of the IR model. The extension is needed in order to deal with the varying-cost and varying-size features of web documents. Under this assumption, we derive closed-form expressions for the stationary probabilities of finding each possible arrangement of the documents within the cache. Our analysis shows that the performance of the proposed algorithms are close to that of the optimal off-line algorithm. Using simulations and real traces, we also show that the new algorithms perform at least as well as existing algorithms of higher complexity. Variations on the algorithms, aimed at increasing their responsiveness to non-stationary trends, are also investigated. This researchwas partially supported by NSF grant ANI-9872764. y Corresponding author. The research of this author was performed at the University of California Berkeley, under a fellowship for prospective researchers from the Swiss National Science Foundation. 1