## Randomized Competitive Algorithms for the List Update Problem (1992)

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Venue: | Algorithmica |

Citations: | 39 - 2 self |

### BibTeX

@ARTICLE{Reingold92randomizedcompetitive,

author = {Nick Reingold and Jeffery Westbrook and Daniel D. Sleator},

title = {Randomized Competitive Algorithms for the List Update Problem},

journal = {Algorithmica},

year = {1992},

volume = {11},

pages = {15--32}

}

### Years of Citing Articles

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### Abstract

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...

### Citations

729 |
Tarjan. Amortized efficiency of list update and paging rules
- Sleator, E
- 1985
(Show Context)
Citation Context ...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]-=-. Roughly speaking, an on-line algorithm is c-competitive if, for any request sequence, its cost is no more than c times the cost of the optimum off-line algorithm for that sequence. In their seminal ... |

197 |
Competitive snoopy caching
- Karlin, Manasse, et al.
- 1988
(Show Context)
Citation Context ...r randomized on-line algorithms against strong adversaries. We now show that 3 is a lower bound on the competitive factor for problems in the P d models. This result generalizes that of Karlin et al. =-=[18]-=-, whose Theorem 3.3 can be interpreted as showing a lower bound of 3 on the competitive factor for lists of length 2 in the i \Gamma 1 cost model. Theorem 4.2 Let A be an on-line algorithm for list up... |

185 | An optimal on-line algorithm for metrical task system
- Borodin, Linial, et al.
- 1992
(Show Context)
Citation Context ...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]-=-. Roughly speaking, an on-line algorithm is c-competitive if, for any request sequence, its cost is no more than c times the cost of the optimum off-line algorithm for that sequence. In their seminal ... |

148 |
A locally adaptive data compression scheme
- Bentley, Sleator, et al.
- 1986
(Show Context)
Citation Context ...e, self-adjusting rules are effective because they take advantage of the locality of reference found in real systems. List update techniques have also been used to develop data compression algorithms =-=[5]-=-, as well as fast and simple algorithms for computing point maxima and convex hulls [3, 14]. For all these reasons, the list update problem has been extensively studied [4, 8, 15, 21, 24]. Sleator and... |

140 |
Competitive algorithms for on-line problems
- Manasse, McGeoch, et al.
- 1988
(Show Context)
Citation Context ...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]-=-. Roughly speaking, an on-line algorithm is c-competitive if, for any request sequence, its cost is no more than c times the cost of the optimum off-line algorithm for that sequence. In their seminal ... |

138 | On the power of randomization in on-line algorithms
- Ben-David, Borodin, et al.
- 1994
(Show Context)
Citation Context ...s good as any deterministic on-line algorithm. A great deal of recent work has focused on the use of randomization to improve --- sometimes exponentially --- the competitiveness of on-line algorithms =-=[2, 12, 13, 19]-=-. Karp and Raghavan [private communication, 1990] inaugurated the study of randomized list update algorithms by showing a lower bound of 1.18 on the competitiveness of any randomized algorithm. Irani ... |

115 | A Graph-Theoretic Game and its Application to the k-Server Problem
- Alon, Karp, et al.
- 1995
(Show Context)
Citation Context ...t provably has a better competitive ratio than any deterministic algorithm for that problem. Recently Alon et. al have given a barely random algorithm for k-servers on a circle that is 2k-competitive =-=[1]-=-. However, it is known for k = 2, and conjectured for all k, that there exists a k-competitive deterministic k-server algorithm, matching the known lower bound of k [9, 20]. We generalize the BIT algo... |

115 |
Owickiâ€śCompetitive randomized algorithms for nonuniform problems
- Karlin, Manesse, et al.
- 1994
(Show Context)
Citation Context ...s good as any deterministic on-line algorithm. A great deal of recent work has focused on the use of randomization to improve --- sometimes exponentially --- the competitiveness of on-line algorithms =-=[2, 12, 13, 19]-=-. Karp and Raghavan [private communication, 1990] inaugurated the study of randomized list update algorithms by showing a lower bound of 1.18 on the competitiveness of any randomized algorithm. Irani ... |

86 |
Memory versus randomization in on-line algorithms
- Raghavan, Snir
- 1994
(Show Context)
Citation Context |

81 |
Elementary Numerical Analysis An Algorithmic Approach
- Conte
(Show Context)
Citation Context ...atrix 16 n k Lower Bound 3 10 1.1998 4 8 1.2467 5 7 1.2728 6 5 1.268 Table 2: Lower bound results corresponding to the eigenvalue 1. We compute this eigenvector from the matrix using the power method =-=[11]-=-. Table 2 shows the best results we have obtained for n = 3; 4; 5 and 6. In all cases, the number of iterations in the power method necessary to get the distance between successive iterates less than ... |

76 | Random walks on weighted graphs and applications to on-line algorithms
- Coppersmith, Doyle, et al.
- 1993
(Show Context)
Citation Context ...s good as any deterministic on-line algorithm. A great deal of recent work has focused on the use of randomization to improve --- sometimes exponentially --- the competitiveness of on-line algorithms =-=[2, 12, 13, 19]-=-. Karp and Raghavan [private communication, 1990] inaugurated the study of randomized list update algorithms by showing a lower bound of 1.18 on the competitiveness of any randomized algorithm. Irani ... |

71 |
On self-organizing sequential search heuristics
- Rivest
- 1976
(Show Context)
Citation Context ...data compression algorithms [5], as well as fast and simple algorithms for computing point maxima and convex hulls [3, 14]. For all these reasons, the list update problem has been extensively studied =-=[4, 8, 15, 21, 24]-=-. Sleator and Tarjan [25] demonstrated that the move-to-front algorithm, which uses the simple rule of moving an item to the front of the list each time it is accessed, is 2-competitive. Subsequently ... |

62 |
Competitive algorithms for replication and migration poblems
- Black, Sleator
- 1989
(Show Context)
Citation Context ...he scaling conjecture of Manasse et. al. [20] may apply to randomized algorithms. This version of the list update problem is similar to the replication/migration problems studied by Black and Sleator =-=[6]-=-. We also show a lower bound of 3 on the competitiveness of any deterministic algorithm in this model, so again our randomized algorithms beat the deterministic lower bound. An important question in t... |

41 |
Amortized analyses of self-organizing sequential search heuristics
- Bentley, McGeoch
- 1985
(Show Context)
Citation Context ...data compression algorithms [5], as well as fast and simple algorithms for computing point maxima and convex hulls [3, 14]. For all these reasons, the list update problem has been extensively studied =-=[4, 8, 15, 21, 24]-=-. Sleator and Tarjan [25] demonstrated that the move-to-front algorithm, which uses the simple rule of moving an item to the front of the list each time it is accessed, is 2-competitive. Subsequently ... |

41 | Sleator D. Competitive snoopy caching. Algorithmica - Karlin, Manasse, et al. - 1988 |

40 |
Fast linear expected-time algorithms for computing maxima and convex hulls
- Bentley, Clarkson, et al.
- 1993
(Show Context)
Citation Context ...ference found in real systems. List update techniques have also been used to develop data compression algorithms [5], as well as fast and simple algorithms for computing point maxima and convex hulls =-=[3, 14]-=-. For all these reasons, the list update problem has been extensively studied [4, 8, 15, 21, 24]. Sleator and Tarjan [25] demonstrated that the move-to-front algorithm, which uses the simple rule of m... |

39 | On Serial Files with Relocatable Records - McCabe - 1965 |

29 | Randomized algorithms for multiprocessor page migration
- Westbrook
- 1992
(Show Context)
Citation Context ... number of random bits regardless of the number of requests serviced, yet still beat the deterministic lower 17 bound. Recently barely random algorithms have also been found for the migration problem =-=[10, 26]-=-. Open Question #3: For which other on-line problems do such algorithms exist? Our results in Section 4 give evidence for the conjecture that for a large class of applications, adaptive on-line and ad... |

24 |
On competitive algorithms for paging problems
- Fiat, Karp, et al.
- 1991
(Show Context)
Citation Context |

23 |
Two results on the list update problem
- IRANI
- 1991
(Show Context)
Citation Context ...augurated the study of randomized list update algorithms by showing a lower bound of 1.18 on the competitiveness of any randomized algorithm. Irani discovered a 1:875-competitive randomized algorithm =-=[16]-=-, thus exhibiting the first randomized algorithm to beat the deterministic lower bound. In this paper we examine the effect of randomization in greater depth. We present a very simple randomized algor... |

22 | On fast algorithms for two servers
- Chrobak, Larmore
- 1991
(Show Context)
Citation Context ...a circle that is 2k-competitive [1]. However, it is known for k = 2, and conjectured for all k, that there exists a k-competitive deterministic k-server algorithm, matching the known lower bound of k =-=[9, 20]-=-. We generalize the BIT algorithm to a family of COUNTER algorithms. Using a COUNTER algorithm, we are able to achieve our best result, a p 3-competitive 2 algorithm. We also consider a generalized li... |

14 | Randomized algorithms for the list update problem
- Reingold, Westbrook
- 1990
(Show Context)
Citation Context ...tics commonly used in system software to maintain 1 A preliminary version of these results appeared in a joint paper with S. Irani in the proceedings of the 2nd Symposium on Discrete Algorithms, 1991 =-=[17]-=-. 2 Department of Computer Science, Yale University, New Haven, CT 06520-2158. Research partially supported by NSF grants CCR-8808949 and CCR-8958528. 3 Department of Computer Science, Yale University... |

12 |
On a model for storage and search
- Burville, Kingman
- 1973
(Show Context)
Citation Context ...data compression algorithms [5], as well as fast and simple algorithms for computing point maxima and convex hulls [3, 14]. For all these reasons, the list update problem has been extensively studied =-=[4, 8, 15, 21, 24]-=-. Sleator and Tarjan [25] demonstrated that the move-to-front algorithm, which uses the simple rule of moving an item to the front of the list each time it is accessed, is 2-competitive. Subsequently ... |

12 | On a model for storage and - Burville, Kingman - 1973 |

10 |
An Account of Self-Organizing Systems
- Hendricks
- 1976
(Show Context)
Citation Context |

9 |
Optimal Multiprocessor Migration Algorithms Using Work Functions
- Chrobak, Larmore, et al.
- 1989
(Show Context)
Citation Context ... number of random bits regardless of the number of requests serviced, yet still beat the deterministic lower 17 bound. Recently barely random algorithms have also been found for the migration problem =-=[10, 26]-=-. Open Question #3: For which other on-line problems do such algorithms exist? Our results in Section 4 give evidence for the conjecture that for a large class of applications, adaptive on-line and ad... |