Reza Dorrigiv
Skip Abstract Section
Abstract
As computer science has progressed, numerous models and measures have been developed over the years. Among the most commonly used in theoretical computer science are the RAM model, the I/O model, worst case analysis, space (memory) usage, average case analysis, amortized analysis, adaptive analysis and the competitive ratio. New models are added to this list every few years to re ect varying constraints imposed by novel application or advances in computer architectures. Examples of alternative models are the transdichotomous RAM or word-RAM, the data stream model, the MapReduce model, the cache oblivious model and the smoothed analysis model. New models and measures, when successful expand our understanding of computation and open new avenues of inquiry. As it is to be expected relatively few models and paradigms are introduced every year, and even less are eventually proven successful. In this paper we discuss rst certain shortcomings of the online competitive analysis model particularly as it concerns paging, discuss existing solutions in the literature as well as present recent progress in developing models and measures that better re ect actual practice for the case of paging. From there we proceed to a more general discussion on how to measure and evaluate new models within theoretical computer science and how to contrast them, when appropriate, to existing models. Lastly, we highlight certain \natural" choices and assumptions of the standard worst-case model which are often unstated and rarely explicitly justied. We contrast these choices to those made in the formalization of probability theory.
- {ADLO07} S. Angelopoulos, R. Dorrigiv, and A. López-Ortiz. On the separation and equivalence of paging strategies. In Proc. SODA, pages 229-237, 2007. Google Scholar
Digital Library
- {ADLO08} S. Angelopoulos, R. Dorrigiv, and A. Lóopez-Ortiz. List update with locality of reference. In Proc. LATIN, pages 399-410, 2008. Google ScholarDigital Library
- {AFG05} S. Albers, L. M. Favrholdt, and O. Giel. On paging with locality of reference. JCSS, 70(2):145-175, 2005. Google ScholarDigital Library
- {AL08} S. Albers and S. Lauer. On list update with locality of reference. In Proc. ICALP, pages 96-107, 2008. Google ScholarDigital Library
- {ALOH08} Spyros Angelopoulos, Alejandro López-Ortiz, and Angèle M. Hamel. Optimal scheduling of contract algorithms with soft deadlines. In AAAI, 2008.Google Scholar
- {AS09} S. Angelopoulos and P. Schweitzer. Paging and list update under bijective analysis. In Proc. SODA, pages 1136-1145, 2009. Google ScholarDigital Library
- {AV88} A. Aggarwal and J. S. Vitter. The Input/Output complexity of sorting and related problems. Communications of the ACM, 31(9):1116-1127, 1988. Google ScholarDigital Library
- {BD86} G. E. P. Box and N. R. Draper. Empirical model-building and response surface. John Wiley & Sons, Inc., 1986. Google ScholarDigital Library
- {BDB94} S. Ben-David and A. Borodin. A new measure for the study of on-line algorithms. Algorithmica, 11:73-91, 1994.Google ScholarDigital Library
- {Bec04} L. Becchetti. Modeling locality: A probabilistic analysis of LRU and FWF. In Proc. ESA, pages 98-109, 2004.Google Scholar
- {BEY97} R. Bachrach and R. El-Yaniv. Online list accessing algorithms and their applications: Recent empirical evidence. In Proc. SODA, pages 53-62, 1997. Google ScholarDigital Library
- {BEY98} A. Borodin and R. El-Yaniv. Online Computation and Competitive Analysis. Cambridge University Press, 1998. Google ScholarDigital Library
- {BF03} J. Boyar and L. M. Favrholdt. The relative worst order ratio for on-line algorithms. In Proc. Italian Conf. on Algorithms and Complexity, 2003. Google ScholarDigital Library
- {BFL05} J. Boyar, L. M. Favrholdt, and K. S. Larsen. The relative worst order ratio applied to paging. In Proc. SODA, pages 718-727, 2005. Google ScholarDigital Library
- {BHH+02} Therese C. Biedl, Masud Hasan, Joseph Douglas Horton, Alejandro López-Ortiz, and Tomás Vinar. Searching for the center of a circle. In CCCG, pages 137-141, 2002.Google Scholar
- {BIRS95} A. Borodin, S. Irani, P. Raghavan, and B. Schieber. Competitive paging with locality of reference. JCSS, 50:244-258, 1995. Google ScholarDigital Library
- {BL99} J. Boyar and K. S. Larsen. The Seat Reservation Problem. Algorithmica, 25(4):403-417, 1999.Google ScholarCross Ref
- {BLN01} J. Boyar, K. S. Larsen, and M. N. Nielsen. The Accommodating Function: A generalization of the competitive ratio. SIAM Journal on Computing, 31(1):233-258, 2001. Google ScholarDigital Library
- {BM04} J. Boyar and P. Medvedev. The relative worst order ratio applied to seat reservation. In Proc. SWAT, pages 90-101, 2004.Google ScholarCross Ref
- {CN99} M. Chrobak and J. Noga. LRU is better than FIFO. Algorithmica, 23(2):180-185, 1999.Google ScholarCross Ref
- {DELO09} R. Dorrigiv, M. R. Ehmsen, and A. López-Ortiz. Parameterized analysis of paging and list update algorithms. In Proceedings of the 7th Workshop on Approximation and Online Algorithms (WAOA '09), 2009. to appear. Google ScholarDigital Library
- {Den68} P. J. Denning. The working set model for program behaviour. CACM, 11(5):323-333, 1968. Google ScholarDigital Library
- {Den80} P. J. Denning. Working sets past and present. IEEE Transactions on Software Engineering , SE-6(1):64-84, 1980. Google ScholarDigital Library
- {Den05} P. J. Denning. The locality principle. CACM, 48(7):19-24, 2005. Google ScholarDigital Library
- {DHS95} A. Datta, Ch. Hipke, and S. Schuierer. Competitive searching in polygons--beyond generalized streets. In Proc. 6th ISAAC, pages 32-41. LNCS 1004, 1995. Google ScholarDigital Library
- {DLO05} R. Dorrigiv and A. López-Ortiz. A survey of performance measures for on-line algorithms. SIGACT News, 36(3):67-81, September 2005.Google ScholarDigital Library
- {DLO07} R. Dorrigiv and A. López-Ortiz. The cooperative ratio of on-line algorithms. Technical Report CS-2007-39, University of Waterloo, Cheriton School of Computer science, October 2007.Google Scholar
- {DLO08} R. Dorrigiv and A. López-Ortiz. Adaptive searching in one and two dimensions. In Proc. CCCG, pages 215-218, 2008.Google Scholar
- {FW98} A. Fiat and G. J. Woeginger. Competitive odds and ends. In A. Fiat and G. J. Woeginger, editors, Online Algorithms -- The State of the Art, volume 1442 of LNCS, pages 385-394. Springer-Verlag, 1998. Google ScholarDigital Library
- {HH85} J. H. Hester and D. S. Hirschberg. Self-organizing linear search. ACM Computing Surveys, 17(3):295, September 1985. Google ScholarDigital Library
- {HIKK01} F. Hoffmann, C. Icking, R. Klein, and K. Kriegel. The polygon exploration problem. SIAM J. Comput, 31(2):577-600, 2001. Google ScholarDigital Library
- {Ick94} Ch. Icking. Motion and Visibility in Simple Polygons. Dissertation, Fernuniversität Hagen, 1994.Google Scholar
- {IKM93} Christian Icking, Rolf Klein, and Lihong Ma. How to look around a corner. In CCCG, pages 443-448, 1993.Google Scholar
- {IKP96} S. Irani, A. R. Karlin, and S. Phillips. Strongly competitive algorithms for paging with locality of reference. SIAM Journal on Computing, 25:477-497, 1996. Google ScholarDigital Library
- {Ira98} S. Irani. Competitive analysis of paging. In Amos Fiat and Gerhard J. Woeginger, editors, Online Algorithms -- The State of the Art, volume 1442 of LNCS, pages 52-73. 1998. Google ScholarDigital Library
- {Ken96} C. Kenyon. Best-fit bin-packing with random order. In Proc. SODA, pages 359-364, 1996. Google ScholarDigital Library
- {KMSY94} M.-Y. Kao, Y. Ma, M. Sipser, and Y. Yin. Optimal constructions of hybrid algorithms. In Proc. 5th SODA, pages 372-381, 1994. Google ScholarDigital Library
- {KP00} E. Koutsoupias and C. Papadimitriou. Beyond competitive analysis. SIAM Journal on Computing, 30:300-317, 2000. Google ScholarDigital Library
- {KPR00} A. R. Karlin, S. J. Phillips, and P. Raghavan. Markov paging. SIAM Journal on Computing, 30(3):906-922, 2000. Google ScholarDigital Library
- {KRT93} M.-Y. Kao, J. H. Reif, and S. R. Tate. Searching in an unknown environment: An optimal randomized algorithm for the cow-path problem. In Proc. 4th SODA, pages 441-447, 1993. Google ScholarDigital Library
- {Kru} P. Krugman. How i work. Available at: http://web.mit.edu/krugman/www/howiwork.html.Google Scholar
- {LO96} A. López-Ortiz. On-line Target Searching in Bounded and Unbounded Domains. PhD thesis, Dept. of Comp. Sci., University of Waterloo, 1996. Google ScholarDigital Library
- {LOAH06} Alejandro López-Ortiz, Spyros Angelopoulos, and Angèle M. Hamel. Optimal scheduling of contract algorithms for anytime problems. In AAAI, 2006.Google Scholar
- {LOS96} A. López-Ortiz and S. Schuierer. Walking streets faster. In Proc. 5th SWAT, pages 345-356. LNCS 1097, 1996. Google ScholarDigital Library
- {LOS01a} A. López-Ortiz and S. Schuierer. The ultimate strategy to search on m rays? Theoretical Computer Science, 261(2):267-295, 2001. Google ScholarDigital Library
- {LOS01b} Alejandro López-Ortiz and Graeme Sweet. Parallel searching on a lattice. In CCCG, pages 125-128, 2001.Google Scholar
- {LOS02} Alejandro López-Ortiz and Sven Schuierer. Online parallel heuristics and robot searching under the competitive framework. In SWAT, pages 260-269, 2002. Google ScholarDigital Library
- {LOS04} A. López-Ortiz and S. Schuierer. On-line parallel heuristics, processor scheduling and robot searching under the competitive framework. Theoretical Computer Science, 310(1- 3):527-537, 2004. Google ScholarDigital Library
- {PAZ09} Chris Hamilton Peyman Afshani and Norbert Zeh. Cache-oblivious range reporting with optimal queries requires superlinear space. In SCG '09: Proceedings of the 25th annual symposium on Computational geometry, pages 277-286. ACM, 2009. Google ScholarDigital Library
- {Pro99} H. Prokop. Cache-oblivious algorithms. Master's thesis, Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999.Google Scholar
- {PS06} K. Panagiotou and A. Souza. On adequate performance measures for paging. In Proc. STOC, pages 487-496, 2006. Google ScholarDigital Library
- {RS71} Henry R. Richardson and Lawrence D. Stone. Operations analysis during the under-water search for scorpions. Naval Research Logistics Quarterly, 18(2):141-157, 1971.Google ScholarCross Ref
- {RWS94} N. Reingold, J. Westbrook, and D. D. Sleator. Randomized competitive algorithms for the list update problem. Algorithmica, 11:15-32, 1994.Google ScholarDigital Library
- {Sch98} F. Schulz. Two new families of list update algorithms. In Proc. ISAAC, pages 99-108, 1998. Google ScholarDigital Library
- {ST85a} D. D. Sleator and R. E. Tarjan. Amortized efficiency of list update and paging rules. CACM, 28:202-208, 1985. Google ScholarDigital Library
- {ST85b} D. D. Sleator and R. E. Tarjan. Self-adjusting binary search trees. JACM, 32(3):652- 686, 1985. Google ScholarDigital Library
- {Tor98} E. Torng. A unified analysis of paging and caching. Algorithmica, 20(2):175-200, 1998.Google ScholarCross Ref
- {Uni} New Mexico State University. Homepage of new mexico state university tracebase (online). Available at: http://tracebase.nmsu.edu/tracebase.html.Google Scholar
- {You94} N. E. Young. The k-server dual and loose competitiveness for paging. Algorithmica, 11(6):525-541, 1994.Google ScholarDigital Library
- {You98} N. E. Young. Bounding the diffuse adversary. In Proc. SODA, pages 420-425, 1998. Google ScholarDigital Library
- {You00} N. E. Young. On-line paging against adversarially biased random inputs. Journal of Algorithms, 37(1):218-235, 2000. Google ScholarDigital Library
- {You02} N. E. Young. On-line file caching. Algorithmica, 33(3):371-383, 2002.Google ScholarCross Ref
Recommendations
A simple linear model of demand paging performance
Predicting the performance of a proposed automatically managed multilevel memory system requires a model of the patterns by which programs refer to the information stored in the memory. Some recent experimental measurements on the Multics virtual memory ...
Energy and Performance Optimization of Demand Paging With OneNAND Flash
New fusion memory devices consisting of multiple heterogeneous memory components in a single die or package offer efficient ways to optimize embedded systems in terms of energy, performance, and cost. Samsung Electronics recently announced the OneNAND ...
A Case for Alternative Nested Paging Models for Virtualized Systems
Address translation often emerges as a critical performance bottleneck for virtualized systems and has recently been the impetus for hardware paging mechanisms. These mechanisms apply similar translation models for both guest and host address ...
Comments