Competitive algorithms for server problems

This paper updates a survey [53] written about 3 years ago. All of the results mentioned there are covered here as well. However, as a major justification for this second edition we shall be presenting many new results, some of which represent important advances. As a measure of the impressive amount of research in just 3 years, the present reference list more than doubles the list in [53].

Approximation Algorithms for Bin-Packing — An Updated Survey

An on-line problem is one in which an algorithm must handle a sequence of requests, satisfying each request without knowledge of the future requests. Examples of on-line problems include scheduling the motion of elevators, finding routes in networks, allocating cache memory, and maintaining dynamic data structures. A competitive algorithm for an on-line problem has the property that its performance on any sequence of requests is within a constant factor of the performance of any other algorithm on the same sequence. This paper presents several general results concerning competitive algorithms, as well as results on specific on-line problems.

Competitive algorithms for on-line problems

More than 400 books, articles, dissertations, and working papers are included in this bibliography on cutting and packing problems. The list of published articles and dissertations is a nearly exhaustive compilation of the English-language references on the subject. The list of working papers, although extensive, presents only a sample of the recent work in this field. All of the books and journal articles listed in the bibliography have been categorized according to the dimensionality of the problems studied and the solution methodologies employed.

https://www.jstor.org/stable/info/2583579

Cutting and Packing Problems: A Categorized, Application-Orientated Research Bibliography

In the k-server problem, one must choose how k mobile servers will serve each of a sequence of requests, making decisions in an online manner. An optimal deterministic online strategy is exhibited when the requests fall on the real line. For the weighted-cache problem, in which the cost of moving to x from any other point is $w( x )$, the weight of x, an optimal deterministic algorithm is also provided. The nonexistence of competitive algorithms for the asymmetric two-server problem and of memoryless algorithms for the weighted-cache problem is proved. A fast algorithm for oflline computing of an optimal schedule is given, and it is shown that finding an optimal offline schedule is at least as hard as the assignment problem.

New results on server problems

We analyze a service system in which two identical servers move one at a time along a linear array of N positions. Requests for service, each designating one of the N positions, join a first-in-first-out queue, where processing of the nth request does not begin until processing of the (n − 1)th requested is completed. Processing the nth request entails determining which server to move, moving this server to the requested position, and then performing the service. Several potential applications of the model are mentioned, the most notable being the design of computer storage systems with multiple access devices. Within a simple probability model we compare server-selection policies in terms of the equilibrium expected distance a server is moved in processing a request. Distance is measured under two regimes, both assigning a unit distance between adjacent positions. In the first, the positions are thought of as equally spaced along a line (interval), and in the second, equally spaced along a circle (positi...

Sequencing Problems in Two-Server Systems

Etude d'un modele mathematique de dispositifs de stockage informatique sur disque ayant deux tetes de lecture/ecriture mobiles

Optimum Head Separation in a Disk System with Two Read/Write Heads

We consider the NP-hard problem of packing into a specified rectangle a maximum number of squares from a given set. We define two related approximation algorithms and derive bounds on the worst case performance of the packings they produce.

Approximation Algorithms for Maximizing the Number of Squares Packed into a Rectangle

The authors analyze a model of a movable-head disk system with two read/write heads maintained a fixed distance d apart on each arm. Successive request-addresses are assumed to be independent random variables, uniformly distributed over the set of cylinders. The purpose of the analysis is to find that value of d which minimizes the expected seek time per request, assuming that seek time varies linearly with the distance z traveled by the heads. The authors extend an earlier analysis of this model to more general seek-time characteristics which take into account nonlinear acceleration effects. Detailed results, combining both analysis and simulation experiments, are presented for seek times linear in z/sup alpha /, 0 >

A note extending the analysis of two-head disk systems to more general seek-time characteristics

Two mathematical models dealing with optimal placement of directories on disk devices are analyzed. Storage addresses on the disk are approximated by points in the interval [0, 1]. Requests for information on the disk are represented by a sequence of file names. To process a request, a read-write head is first moved to a directory kept on the disk that specifies the address of the file, and then a head is moved to the specified address. The addresses are assumed to be independent and uniform on [0,1].In the first model we consider a system of two heads separated by a fixed distance d and a directory situated at 0 ≤ x ≤ 1. In the second model we consider a system consisting of one head and n ≥ 2 directories at 0 ≤ x1

A. R. Calderbank

Papers

Sequencing Problems in Two-Server Systems

Optimum Head Separation in a Disk System with Two Read/Write Heads

Approximation Algorithms for Maximizing the Number of Squares Packed into a Rectangle

A note extending the analysis of two-head disk systems to more general seek-time characteristics

Optimal directory placement on disk storage devices