We study scheduling problems in battery-operated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadline-based settings, in this article we are interested in schedules that guarantee good response times. More specifically, our goal is to schedule a sequence of jobs on a variable-speed processor so as to minimize the total cost consisting of the energy consumption and the total flow time of all jobs. We first show that when the amount of work, for any job, may take an arbitrary value, then no online algorithm can achieve a constant competitive ratio. Therefore, most of the article is concerned with unit-size jobs. We devise a deterministic constant competitive online algorithm and show that

In this paper we fix our attention on the second step algorithms of the Burrows--Wheeler compression algorithm, which in the original version is the Move To Front transform. We discuss many of its replacements presented so far, and compare compression results obtained using them. Then we propose a new algorithm that yields a better compression ratio than the previous ones.

. 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...

We investigate ways in which an algorithm can improve its expected performance by finetuning itself automatically with respect to an arbitrary, unknown input distribution. We give such self-improving algorithms for sorting and computing Delaunay triangulations. The highlights of this work: (i) an algorithm to sort a list of numbers with optimal expected limiting complexity; and (ii) an algorithm to compute the Delaunay triangulation of a set of points with optimal expected limiting complexity. In both cases, the algorithm begins with a training phase during which it adjusts itself to the input distribution, followed by a stationary regime in which the algorithm settles to its optimized incarnation. 1

. We consider the online list accessing problem and present a new family of competitive-optimal deterministic list update algorithms which is the largest class of such algorithms known to-date. This family, called Sort-by-Rank (sbr), is parametrized with a real 0 ff 1, where sbr(0) is the Move-to-Front algorithm and sbr(1) is equivalent to the Timestamp algorithm. The behaviour of sbr(ff) mediates between the eager strategy of Move-to-Front and the more conservative behaviour of Timestamp. We also present a family of algorithms Sort-by-Delay (sbd) which is parametrized by the positive integers, where sbd(1) is Move-toFront and sbd(2) is equivalent to Timestamp. In general, sbd(k) is k-competitive for k 2. This is the first class of algorithms that is asymptotically optimal for independent, identically distributed requests while each algorithm is constant-competitive. Empirical studies with with both generated and real-world data are also included. 1 Introduction Co...

It has long been known that for the paging problem in its standard form, competitive analysis cannot adequately distinguish algorithms based on their performance: there exists a vast class of algorithms which achieve the same competitive ratio, ranging from extremely naive and inefficient strategies (such as Flush-When-Full), to strategies of excellent performance in practice (such as Least-Recently-Used and some of its variants). A similar situation arises in the list update problem: in particular, under the cost formulation studied by Martínez and Roura [TCS 2000] and Munro [ESA 2000] every list update algorithm has, asymptotically, the same competitive ratio. Several refinements of competitive analysis, as well as alternative performance measures have been introduced in the literature, with varying degrees of success in narrowing this disconnect between theoretical analysis and empirical evaluation. In this paper we study these two fundamental online problems under the framework of bijective analysis [Angelopoulos, Dorrigiv and López-Ortiz, SODA 2007 and LATIN 2008]. This is an intuitive technique which is based on pairwise comparison of the costs incurred by two algorithms on sets of request sequences of the same size. Coupled with a well-established model of locality of reference due to Albers, Favrholdt and Giel [JCSS 2005], we show that Least-Recently-Used and Move-to-Front are the unique optimal algorithms for paging and list update, respectively. Prior to this work, only measures based on average-cost analysis have separated LRU and MTF from all other algorithms. Given that bijective analysis is a fairly stringent measure (and also subsumes average-cost analysis), we prove that in a strong sense LRU and MTF stand out as the best (deterministic) algorithms.

Suppose that $S$ is a string of length $m$ drawn from an alphabet of $n$ characters, $d$ of which occur in $S$. Let $P$ be the relative frequency distribution of characters in $S$. We present a new algorithm for dynamic coding that uses at most \(\lceil \lg n \rceil 1\) bits to encode each character in $S$

this article, but rather a deep principle of on-line analysis known as Yao's minimax theorem [Yao, 1980]. This theorem is actually an adaptation of the famous minimax theorem of game theory [von Neumann and Morgenstern, 1947]. It states that the best ratio achievable by a deterministic algorithm against any distribution is exactly the same as the best ratio achievable by a randomized algorithm against a worst-case adversary. More formally, for a given on-line problem let F n denote the family of input instances of size at most n. Let D n denote the set of all probability distributions over the instances in F n . Let A n

This paper concerns the online list accessing problem. In the first part of the paper we present two new families of list accessing algorithms. The first family is of optimal, 2-competitive, deterministic online algorithms. This family, called the mri (move-to-recent-item) family, includes as members the well known move-to-front (MTF) algorithm, and the recent, more "conservative" algorithm TIMESTAMP due to Albers. So far move-to-front and TIMESTAMP were the only algorithms known to be optimal in terms of their competitive ratio. This new family contains a sequence of algorithms fA(i)g i1 where A(1) is equivalent to TIMESTAMP and the limit element A(1) is MTF. Further, in this class, for each i, the algorithm A(i) is more conservative than algorithm A(i + 1) in the sense that it is more reluctant to move an accessed item to the front, thus giving a gradual transition from the conservative TIMESTAMP to the "reckless" MTF. The second new family , called the pri (pass-recent-item) family is also infinite and contains TIMESTAMP; We show that most algorithms in this family attain a competitive ratio of 3.

Abstract. It is known that in practice, request sequences for the list update problem exhibit a certain degree of locality of reference. Motivated by this observation we apply the locality of reference model for the paging problem due to Albers et al. [STOC 2002/JCSS 2005] in conjunction with bijective analysis [SODA 2007] to list update. Using this framework, we prove that Move-to-Front (MTF) is the unique optimal algorithm for list update. This addresses the open question of defining an appropriate model for capturing locality of reference in the context of list update [Hester and Hirschberg ACM Comp. Surv. 1985]. Our results hold both for the standard cost function of Sleator and Tarjan [CACM 1985] and the improved cost function proposed independently by Martínez and Roura [TCS 2000] and Munro [ESA 2000]. This result resolves an open problem of Martínez and Roura, namely proposing a measure which can successfully separate MTF from all other list-update algorithms. 1