The relative worst order ratio applied to paging

The relative worst order ratio, a new measure for the quality of on-line algorithms, was recently defined and applied to two bin packing problems. Here, we apply it to the paging problem and obtain the following results: We devise a new deterministic paging algorithm, Retrospective-LRU, and show that it performs better than LRU. This is supported by experimental results, but contrasts with the competitive ratio. All deterministic marking algorithms have the same competitive ratio, but here we find that LRU is better than FWF. According to the relative worst order ratio, no deterministic marking algorithm can be significantly better than LRU, but the randomized algorithm MARK is better than LRU. Finally, look-ahead is shown to be a significant advantage, in contrast to the competitive ratio, which does not reflect that look-ahead can be helpful.

[1]  Marek Chrobak,et al.  Competitive analysis of randomized paging algorithms , 2000, Theor. Comput. Sci..

[2]  Leen Stougie,et al.  Online Bin Coloring , 2001, ESA.

[3]  Luca Becchetti,et al.  Modeling Locality: A Probabilistic Analysis of LRU and FWF , 2004, ESA.

[4]  Allan Borodin,et al.  Competitive paging with locality of reference , 1991, STOC '91.

[5]  Allan Borodin,et al.  On randomization in online computation , 1997, Proceedings of Computational Complexity. Twelfth Annual IEEE Conference.

[6]  Prabhakar Raghavan,et al.  A Statistical Adversary for On-line Algorithms , 1991, On-Line Algorithms.

[7]  Jeffrey R. Spirn,et al.  Program Behavior: Models and Measurements , 1977 .

[8]  Susanne Albers,et al.  On the Influence of Lookahead in Competitive Paging Algorithms , 1997, Algorithmica.

[9]  Leah Epstein,et al.  Separating online scheduling algorithms with the relative worst order ratio , 2006, J. Comb. Optim..

[10]  Neal E. Young,et al.  On-Line File Caching , 2002, SODA '98.

[11]  Robert E. Tarjan,et al.  Amortized efficiency of list update and paging rules , 1985, CACM.

[12]  David S. Johnson,et al.  Fast Algorithms for Bin Packing , 1974, J. Comput. Syst. Sci..

[13]  Dany Breslauer,et al.  On Competitive On-Line Paging with Lookahead , 1995, Theor. Comput. Sci..

[14]  Kim S. Larsen,et al.  On-line seat reservations via off-line seating arrangements , 2005, Int. J. Found. Comput. Sci..

[15]  Bala Kalyanasundaram,et al.  Speed is as powerful as clairvoyance , 2000, JACM.

[16]  Neal E. Young,et al.  On-line caching as cache size varies , 1991, SODA '91.

[17]  Allan Borodin,et al.  A new measure for the study of on-line algorithms , 2005, Algorithmica.

[18]  Neal E. Young,et al.  Competitive paging and dual-guided on-line weighted caching and watching algorithms , 1992 .

[19]  Neal E. Young,et al.  Competitive paging and dual-guided algorithms for weighted caching and matching (Thesis) , 1991 .

[20]  Mark H. Overmars,et al.  Union-copy structures and dynamic segment trees , 1993, JACM.

[21]  Marek Chrobak,et al.  LRU Is Better than FIFO , 1999, SODA '98.

[22]  Eric Torng.  A Unified Analysis of Paging and Caching , 1998, Algorithmica.

[23]  Lyle A. McGeoch,et al.  Competitive algorithms for on-line problems , 1988, STOC '88.

[24]  Anna R. Karlin,et al.  Markov Paging , 2000, SIAM J. Comput..

[25]  Laszlo A. Belady,et al.  A Study of Replacement Algorithms for Virtual-Storage Computer , 1966, IBM Syst. J..

[26]  Ronald L. Graham,et al.  Bounds for certain multiprocessing anomalies , 1966 .

[27]  Marek Chrobak,et al.  New results on server problems , 1991, SODA '90.

[28]  Joan Boyar,et al.  The Accommodating Function: A Generalization of the Competitive Ratio , 2001, SIAM J. Comput..

[29]  Amos Fiat,et al.  Experimental Studies of Access Graph Based Heuristics: Beating the LRU Standard? , 1997, SODA.

[30]  Joan Boyar,et al.  The Seat Reservation Problem , 1999, Algorithmica.

[31]  Susanne Albers,et al.  On paging with locality of reference , 2002, STOC '02.

[32]  Christos H. Papadimitriou,et al.  Beyond competitive analysis [on-line algorithms] , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[33]  Joan Boyar,et al.  The Relative Worst Order Ratio for On-Line Algorithms , 2003, CIAC.

[34]  Lyle A. McGeoch,et al.  A strongly competitive randomized paging algorithm , 1991, Algorithmica.

[35]  Anna R. Karlin,et al.  Competitive snoopy caching , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[36]  Neal Young,et al.  The K-Server Dual and Loose Competitiveness for Paging , 1991, On-Line Algorithms.

[37]  Amos Fiat,et al.  Competitive Paging Algorithms , 1991, J. Algorithms.

[38]  Joan Boyar,et al.  The relative worst order ratio for online algorithms , 2007, TALG.

[39]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[40]  C. Kenyon.  Best-fit bin-packing with random order , 1996, SODA '96.