## Competitive Analysis of Randomized Paging Algorithms (2000)

### Cached

### Download Links

- [www.research.microsoft.com]
- [research.microsoft.com]
- [www.cs.ucr.edu]
- [131.107.65.21]
- [www.cs.ucr.edu]
- DBLP

### Other Repositories/Bibliography

Citations: | 62 - 9 self |

### BibTeX

@MISC{Achlioptas00competitiveanalysis,

author = {Dimitris Achlioptas and Marek Chrobak and John Noga},

title = {Competitive Analysis of Randomized Paging Algorithms},

year = {2000}

}

### OpenURL

### Abstract

The paging problem is defined as follows: we are given a two-level memory system, in which one level is a fast memory, called cache, capable of holding k items, and the second level is an unbounded but slow memory. At each given time step, a request to an item is issued. Given a request to an item p,amiss occurs if p is not present in the fast memory. In response to a miss, we need to choose an item q in the cache and replace it by p. The choice of q needs to be made on-line, without the knowledge of future requests. The objective is to design a replacement strategy with a small number of misses. In this paper we use competitive analysis to study the performance of randomized on-line paging algorithms. Our goal is to show how the concept of work functions, used previously mostly for the analysis of deterministic algorithms, can also be applied, in a systematic fashion, to the randomized case. We present two results: we first show that the competitive ratio of the marking algorithm is ex...

### Citations

728 |
Amortized efficiency of list update and paging rules
- Sleator, Tarjan
- 1985
(Show Context)
Citation Context ...ich all distances are equal to one. In the deterministic case, it is known that the well-known Lru (least recently used) strategy is k-competitive, and that no better competitiveness is possible (see =-=[15]-=-). In this paper we concentrate on the randomized version of this problem. It is quite easy to show (see [6]) that no randomized online algorithm can be better than H k -competitive, where H k is the ... |

164 | Competitive paging algorithms
- Fiat, Karp, et al.
- 1991
(Show Context)
Citation Context ...ently used) strategy is k-competitive, and that no better competitiveness is possible (see [15]). In this paper we concentrate on the randomized version of this problem. It is quite easy to show (see =-=[6]-=-) that no randomized online algorithm can be better than H k -competitive, where H k is the k-th harmonic number. Two algorithms have been proposed for this problem in the past. Fiat et al [6] gave a ... |

164 |
Extensive games and the problem of information
- Kuhn
- 1953
(Show Context)
Citation Context ...lity distribution on the set of possible moves. In the theory of multi-stage games these two approaches are sometimes called, respectively, mixed strategies and behavior strategies (see, for example, =-=[11]-=-). The definitions of cost and competitiveness extend naturally to randomized algorithms, independently of which of the two above definitions is being used. If A is a randomized algorithm then cost A ... |

138 |
Competitive algorithms for server problems
- Manasse, McGeoch, et al.
- 1990
(Show Context)
Citation Context ...aging is a classical online problem and has been extensively studied in the literature on competitive on-line algorithms. It can be viewed as a special case of the k-server problem (see, for example, =-=[10, 12, 2]-=-), in which all distances are equal to one. In the deterministic case, it is known that the well-known Lru (least recently used) strategy is k-competitive, and that no better competitiveness is possib... |

120 | Competitive Paging with Locality of Reference
- Borodin, Irani, et al.
- 1995
(Show Context)
Citation Context ...cache problems are considered as linear programming problems and the resulting dual problem is investigated. Several results about the so-called loose competitiveness of these problems are proven. In =-=[1]-=- and [7] the paging problem is addressed with the assumption that after any particular request the next request is likely to be from a small set of nearby items. We believe that the work function appr... |

118 | Beyond competitive analysis
- Koutsoupias, Papadimitriou
(Show Context)
Citation Context ...ually starts with some characterization of work functions for a given problem. Then, the properties of work functions are used to design and analyze an online algorithm. Koutsoupias and Papadimitriou =-=[9]-=- presented a simple, elegant characterization of work functions for paging. In an earlier work, McGeoch and Sleator in [13] gave an equivalent characterization of the behavior of an optimal algorithm,... |

112 |
A strongly competitive randomized paging algorithm
- McGeoch, Sleator
- 1991
(Show Context)
Citation Context ...Two algorithms have been proposed for this problem in the past. Fiat et al [6] gave a simple marking algorithm (called Mark) and proved that it is 2H k -competitive. Subsequently, McGeoch and Sleator =-=[13]-=- presented another algorithm, called Partition, and proved that it is H k -competitive, and thus optimal. Work functions have played an important role in the analysis of online problems. However, up u... |

96 | On the k-Server Conjecture
- Iioutsoupias, Papadimitriou
- 1995
(Show Context)
Citation Context ...aging is a classical online problem and has been extensively studied in the literature on competitive on-line algorithms. It can be viewed as a special case of the k-server problem (see, for example, =-=[10, 12, 2]-=-), in which all distances are equal to one. In the deterministic case, it is known that the well-known Lru (least recently used) strategy is k-competitive, and that no better competitiveness is possib... |

86 |
Memory versus randomization in on-line algorithms
- Raghavan, Snir
- 1994
(Show Context)
Citation Context ...nd O(1) time for each request. One problem that we leave open is whether there is a simple H k -competitive algorithm for paging that uses only with the same performance as Mark. Raghavan and Snir in =-=[14]-=- investigated a memory versus randomization trade-off in online algorithms. Is there also a trade-off between memory and competitiveness? It would also be interesting to extend the applications of wor... |

73 | Strongly competitive algorithms for paging with locality of reference
- Irani, Karlin, et al.
- 1996
(Show Context)
Citation Context ...oblems are considered as linear programming problems and the resulting dual problem is investigated. Several results about the so-called loose competitiveness of these problems are proven. In [1] and =-=[7]-=- the paging problem is addressed with the assumption that after any particular request the next request is likely to be from a small set of nearby items. We believe that the work function approach can... |

61 | The k-Server Dual and Loose Competitiveness for Paging - Young - 1994 |

60 | P.: Markov paging
- Karlin, Phillips, et al.
- 2000
(Show Context)
Citation Context ...se an algorithm from the second set, and considering the worst case ratio of costs of the two algorithms. There is also some recent research in this direction that does not involve work functions. In =-=[8]-=- the paging problem is considered in the case where the requests come from a Markov process. In [16] both the paging and weighted cache problems are considered as linear programming problems and the r... |

45 | On-line caching as cache size varies - Young - 1991 |

37 | An Optimal On-line Algorithm for R Servers on Trees
- Chrobak, Larmore
- 1991
(Show Context)
Citation Context ...aging is a classical online problem and has been extensively studied in the literature on competitive on-line algorithms. It can be viewed as a special case of the k-server problem (see, for example, =-=[10, 12, 2]-=-), in which all distances are equal to one. In the deterministic case, it is known that the well-known Lru (least recently used) strategy is k-competitive, and that no better competitiveness is possib... |

35 | Amortized e - ciency of list update and paging rules - Sleator, Tarjan - 1985 |

33 | On-line distributed data management - Lund, Reingold, et al. - 1994 |

29 | Generosity helps or an 11-competitive algorithm for three servers
- Chrobak, Larmore
- 1994
(Show Context)
Citation Context ...s jS(!)j = M , and if X is B's configuration, then B executes the following forgiveness step: it replaces the offset function ! by the work function ��X \Gamma k + 1, where ��X is the cone on =-=X. (See [5, 4] for oth-=-er examples of the forgiveness method.) Note that ��X \Gamma k + 1s!, so B cannot benefit from this action. B does not incur any cost, but the new offset function is ��X , which means that the... |

20 | Randomized Algorithms for Metrical Task Systems - Irani, Seiden - 1998 |

16 |
The k-server dual and loose competitiveness for paging, Algorithmica 11
- Young
- 1994
(Show Context)
Citation Context ...ithms. There is also some recent research in this direction that does not involve work functions. In [8] the paging problem is considered in the case where the requests come from a Markov process. In =-=[16]-=- both the paging and weighted cache problems are considered as linear programming problems and the resulting dual problem is investigated. Several results about the so-called loose competitiveness of ... |

13 | Page migration algorithms using work functions - Chrobak, Larmore, et al. - 1992 |

11 |
migration algorithms using work functions
- Chrobak, Larmore, et al.
- 1997
(Show Context)
Citation Context ...ntil recently, this technique has been used mostly in the analysis of deterministic algorithms. The only example that we are aware of, where work functions have been applied to the randomized case is =-=[5]-=-, where some optimal randomized algorithms for the page migration problem were developed based on this technique. One of our goals was to show how work functions can also be applied in the competitive... |

8 | Linear programs for randomized on-line algorithms - Lund, Reingold - 1994 |

3 |
Metrical service systems: Randomized strategies
- Larmore
- 1992
(Show Context)
Citation Context ...t a distribution-based algorithm. The cost of a move can be defined by a so-called transport distance between the distributions. It can be shown that this approach is equivalent to the other two (see =-=[3, 5]-=-). Algorithm Mark is defined as a behavior algorithm, while our H k -competitive algorithm Equitable is easier to define using the distribution-based approach. However, for the sake of completeness an... |