Results 1  10
of
49
Competitive Algorithms for Distributed Data Management
 In Proceedings of the 24th Annual ACM Symposium on Theory of Computing
"... We deal with the competitive analysis of algorithms for managing data in a distributed environment. We deal with the file allocation problem ([DF], [ML]), where copies of a file may be be stored in the local storage of some subset of processors. Copies may be replicated and discarded over time so ..."
Abstract

Cited by 101 (8 self)
 Add to MetaCart
(Show Context)
We deal with the competitive analysis of algorithms for managing data in a distributed environment. We deal with the file allocation problem ([DF], [ML]), where copies of a file may be be stored in the local storage of some subset of processors. Copies may be replicated and discarded over time so as to optimize communication costs, but multiple copies must be kept consistent and at least one copy must be stored somewhere in the network at all times. We deal with competitive algorithms for minimizing communication costs, over arbitrary sequences of reads and writes, and arbitrary network topologies. We define the constrained file allocation problem to be the solution of many individual file allocation problems simultaneously, subject to the constraints of local memory size. We give competitive algorithms for this problem on the uniform network topology. We then introduce distributed competitive algorithms for online data tracking (a generalization of mobile user tracking [AP1...
Segmentation problems
, 2004
"... We study a novel genre of optimization problems, which we call segmentation problems, motivated in part by certain aspects of clustering and data mining. For any classical optimization problem, the corresponding segmentation problem seeks to partition a set of cost vectors into several segments, s ..."
Abstract

Cited by 84 (5 self)
 Add to MetaCart
We study a novel genre of optimization problems, which we call segmentation problems, motivated in part by certain aspects of clustering and data mining. For any classical optimization problem, the corresponding segmentation problem seeks to partition a set of cost vectors into several segments, so that the overall cost is optimized. We focus on two natural and interesting (but MAXSNPcomplete) problems in this class, the HYPERCUBE SEGMENTATION PROBLEM and the CATALOG SEGMENTATION PROBLEM, and present approximation algorithms for them. We also present a general greedy scheme, which can be specialized to approximate any segmentation problem.
A polylog(n)Competitive Algorithm for Metrical Task Systems
 IN PROCEEDINGS OF THE 29TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1997
"... We present a randomized online algorithm for the Metrical Task System problem that achieves a competitive ratio of O(log 6 n) against an oblivious adversary, on any metric space. This is the first algorithm to achieve a sublinear competitive ratio for all metric spaces. Our algorithm uses a re ..."
Abstract

Cited by 50 (11 self)
 Add to MetaCart
We present a randomized online algorithm for the Metrical Task System problem that achieves a competitive ratio of O(log 6 n) against an oblivious adversary, on any metric space. This is the first algorithm to achieve a sublinear competitive ratio for all metric spaces. Our algorithm uses a recent result of Bartal [Bar96] that an arbitrary metric space can be probabilistically approximated by a set of metric spaces called "khierarchical wellseparated trees" (kHST's). Indeed, the main technical result of this paper is an O(log 2 n)competitive algorithm for \Omega\Gamma/11 2 n)HST spaces. This, combined with the result of [Bar96], yields the general bound. Note that for the kserver problem on metric spaces of k + c points our result implies a competitive ratio of O(c 6 log 6 k).
Generosity Helps, or an 11Competitive Algorithm for Three Servers
 Journal of Algorithms
, 1992
"... We propose a new algorithm called Equipoise for the kserver problem, and we prove that it is 2competitive for two servers and 11competitive for three servers. For k = 3, this is a tremendous improvement over previously known constants. The algorithm uses several techniques for designing online a ..."
Abstract

Cited by 34 (4 self)
 Add to MetaCart
We propose a new algorithm called Equipoise for the kserver problem, and we prove that it is 2competitive for two servers and 11competitive for three servers. For k = 3, this is a tremendous improvement over previously known constants. The algorithm uses several techniques for designing online algorithms  convex hulls, work functions and forgiveness. 1 Introduction The kserver problem was introduced by Manasse, McGeoch, and Sleator [13]. A given problem instance consists of a positive integer k, and a metric space M . The data consist of an initial configuration S 0 2 k M , (where k X = the set of all multisets of order k within a set X) and a sequence of requests r 1 ; r 2 ; : : : r m 2 M . We think of S 0 as the initial positions of k movable servers. After each request r t we must move one server to r t in order to "serve" the request. We are also free to move the other servers. Cost is defined as the total distance moved by all servers. More formally,...
On Online Computation
 Approximation Algorithms for NPHard Problems, chapter 13
, 1997
"... This chapter presents an introduction to the competitive analysis of online algorithms. In an online problem... ..."
Abstract

Cited by 26 (1 self)
 Add to MetaCart
(Show Context)
This chapter presents an introduction to the competitive analysis of online algorithms. In an online problem...
Distributed Computing with Advice
 Information Sensitivity of Graph Coloring, in "ICALP
"... Abstract. We consider a model for online computation in which the online algorithm receives, together with each request, some information regarding the future, referred to as advice. The advice provided to the online algorithm may allow an improvement in its performance, compared to the classical mo ..."
Abstract

Cited by 26 (3 self)
 Add to MetaCart
(Show Context)
Abstract. We consider a model for online computation in which the online algorithm receives, together with each request, some information regarding the future, referred to as advice. The advice provided to the online algorithm may allow an improvement in its performance, compared to the classical model of complete lack of information regarding the future. We are interested in the impact of such advice on the competitive ratio, and in particular, in the relation between the size b of the advice, measured in terms of bits of information per request, and the (improved) competitive ratio. Since b = 0 corresponds to the classical online model, and b = ⌈log A⌉, where A is the algorithm’s action space, corresponds to the optimal (offline) one, our model spans a spectrum of settings ranging from classical online algorithms to offline ones. In this paper we propose the above model and illustrate its applicability by considering two of the most extensively studied online problems, namely, metrical task systems (MTS) and the kserver problem. For MTS we establish tight (up to constant factors) upper and lower bounds on the competitive ratio of deterministic and randomized online algorithms with advice for any choice of 1 ≤ b ≤ Θ(log n), where n is the number of states in the system: we prove that any randomized online algorithm for MTS has competitive ratio Ω(log(n)/b) and we present a deterministic online algorithm for MTS with competitive ratio O(log(n)/b). For the kserver problem we construct a deterministic online algorithm for general metric spaces with competitive ratio k O(1/b) for any choice of Θ(1) ≤ b ≤ log k. 1
Randomized Algorithms for Metrical Task Systems
 Theoretical Computer Science
, 1995
"... Borodin, Linial, and Saks introduce a general model for online systems in [BLS92] called task systems and show a deterministic algorithm which achieves a competitive ratio of 2n \Gamma 1 for any metrical task system with n states. We present a randomized algorithm which achieves a competitive ratio ..."
Abstract

Cited by 21 (2 self)
 Add to MetaCart
(Show Context)
Borodin, Linial, and Saks introduce a general model for online systems in [BLS92] called task systems and show a deterministic algorithm which achieves a competitive ratio of 2n \Gamma 1 for any metrical task system with n states. We present a randomized algorithm which achieves a competitive ratio of e=(e\Gamma1)n\Gamma1=(e\Gamma1) ß 1:5820n\Gamma0:5820 for this same problem. For the uniform metric space, Borodin, Linial, and Saks present an algorithm which achieves a competitive ratio of 2Hn , and they show a lower bound of Hn for any randomized algorithm. We improve their upper bound for the uniform metric space by showing a randomized algorithm which is \Gamma Hn +O( p log n) \Delta competitive. 1 Introduction In computer systems, it is often necessary to solve problems with incomplete information. The input evolves with time, and incremental computational decisions must be made based on only part of the input. A typical situation is where a sequence of tasks must be perfo...
A Randomized Algorithm for Two Servers on the Line
 Information and Computation
, 1998
"... In the kserver problem we wish to minimize, in an online fashion, the movement cost of k servers in response to a sequence of requests. For 2 servers, it is known that the optimal deterministic algorithm has competitive ratio 2, and it has been a longstanding open problem whether it is possible t ..."
Abstract

Cited by 19 (5 self)
 Add to MetaCart
(Show Context)
In the kserver problem we wish to minimize, in an online fashion, the movement cost of k servers in response to a sequence of requests. For 2 servers, it is known that the optimal deterministic algorithm has competitive ratio 2, and it has been a longstanding open problem whether it is possible to improve this ratio using randomization. We give a positive answer to this problem when the underlying metric space is a real line, by providing a randomized online algorithm for this case with competitive ratio at most 155 78 ß 1:987. This is the first algorithm for 2 servers that achieves a competitive ratio smaller than 2 in a nonuniform metric space with more than three points. We consider a more general problem called the (k; l)server problem, in which a request is served using l out of k available servers. We show that the randomized 2server problem can be reduced to the deterministic (2l; l)server problem. We prove a lower bound of 2 on the competitive ratio of the (4; 2)server...
Page Migration Algorithms Using Work Functions
 In Proc. of the 4th Int. Symp. on Algorithms and Computation (ISAAC
, 1994
"... The page migration problem occurs in managing a globally addressed shared memory in a multiprocessor system. Each physical page of memory is located at a given processor, and memory references to that page by other processors are charged a cost equal to the network distance. At times the page may mi ..."
Abstract

Cited by 15 (1 self)
 Add to MetaCart
The page migration problem occurs in managing a globally addressed shared memory in a multiprocessor system. Each physical page of memory is located at a given processor, and memory references to that page by other processors are charged a cost equal to the network distance. At times the page may migrate between processors, at a cost equal to the distance times a page size factor, D. The problem is to schedule movements online so as to minimize the total cost of memory references. Page migration can also be viewed as a restriction of the 1server with excursions problem. This paper presents a collection of algorithms and lower bounds for the page migration problem in various settings. Competitive analysis is used. The competitiveness of an online algorithm is the worstcase ratio of its cost to the optimum cost on any sequence of requests. Randomized (2 + 1 2D )competitive online algorithms are given for trees and products of trees, including the mesh and the hypercube, and for un...
Unfair Problems and Randomized Algorithms for Metrical Task Systems
, 1998
"... Borodin, Linial, and Saks introduce a general model for online systems in [Borodin et al. 1992] called metrical task systems. In this paper, the unfair two state problem, a natural generalization of the two state metrical task system problem, is studied. A randomized algorithm for this problem is pr ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
Borodin, Linial, and Saks introduce a general model for online systems in [Borodin et al. 1992] called metrical task systems. In this paper, the unfair two state problem, a natural generalization of the two state metrical task system problem, is studied. A randomized algorithm for this problem is presented, and it is shown that this algorithm is optimal. Using the analysis of unfair two state problem, a proof of a decomposition theorem similar to that of Blum, Karloff, Rabani and Saks [Blum et al. 1992] is presented. This theorem allows one to design divide and conquer algorithms for specific metrical task systems. Our theorem gives the same bounds asymptotically, but has less restrictive boundary conditions. 1 Introduction In computer systems, it is often necessary to solve problems with incomplete information. The input evolves with time, and incremental computational decisions must be made based on only part of the input. A typical situation is where a sequence of tasks must be pe...