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Alternative Models for Online Analysis

Alternative Models for Online Analysis

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Alternative Models for Online Analysis

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  1. Alternative Models for Online Analysis Alex López-Ortiz University of Waterloo joint work with Reza Dorrigiv, Spyros Angelopoulos and Ian Munro

  2. Competitive analysis drawbacks • Sometimes too pessimistic • Focus on worst case at the expense of every-day case • Uses off-line optimum concept • Perhaps one of the reasons for the theoretical vs practical motion planning divide?

  3. Paging: A case study • One of the earliest problems to be studied under the online model • Competitive analysis not always satisfactory, too pessimistic • A good starting point for considering alternatives • “Real life” inputs well understood and characterized (temporal + spatial locality)

  4. Paging Algorithms • Data brought from slower memory into cache RAM CPU

  5. Paging Algorithms • Data brought from slower memory into cache • Unit of transfer: pages of equal size • Paging algorithm ≡ Eviction policy • Commonly studied under competitive ratio framework • All lazy marking algorithms are “optimal”

  6. Theory • Commonly studied under competitive ratio framework • Worst case analysis • Marking algorithms optimal • In practice LRU is best • LFD is offline optimal • Competitive ratio is k • User is malicious adversary • Systems • Commonly studied using fault rate measure • Typical case analysis • LRU and friends is best • LRU is impractical • Huh? • Competitive ratio is 2 or 3 • User is your friend

  7. Online motion planning • Commonly studied under competitive ratio framework • Worst case analysis • Continuous curved motions • Perfect scans • Flawless detection • No error in motion • Architects are your enemy • Robotics • Commonly studied using distance & scan cost • Typical case analysis • Piecewise linear • Scanning error • High detection error • Forward & rotational lag • Architects are your friend

  8. “Architects are your friend” Most of the time, anyhow.

  9. Fix the Theory-Practice disconnect • Make both columns match How? • Fix reality or • Fix the model A more realistic theoretical model is likely to lead to practical insights

  10. Previous work (paging case) • Disconnect has been noted before. • Has been subject of intense study, viz. • Borodin et al. • Karlin et al. • Koutsoupias and Papadimitriou • Sleator and Tarjan • Denning • Young • Albers et al. • Boyar et al. + many others

  11. Theory • Commonly studied under competitive ratio framework • Worst case analysis • Marking algorithms optimal • In practice LRU is best • LFD is offline optimal • Competitive ratio is k • User is malicious adversary • Systems • Commonly studied using fault rate measure • Typical case analysis • LRU and friends is best • LRU is impractical • Huh? • Competitive ratio is 2 or 3 • User is your friend

  12. Results • competitive ratio framework/fault rate framework • new model which incorporates fault rate considerations (concave analysis) • worst case analysis/typical case analysis • model focuses on “every-case” analysis, not just worst case (bijective analysis)

  13. Results • marking algorithms optimal/LRU and friends is best • LRU is unique optimum under new model • in practice LRU is best/LRU is impractical • initiated study of computationally limited caching strategies

  14. Results • LFD is offline optimal/huh? • removed concept of offline optimum • competitive ratio is k/competitive ratio is 2 or 3 • Nothing to do!

  15. Results • user is malicious adversary/user is your friend • incorporated assumption of locality of reference in our analysis Applies to other online problems e.g. list access This leads to a new notion calledcooperative ratio

  16. Cooperative ratio • Agreement between user and algorithm about inputs which are: • likely • common • good • important

  17. Cooperative ratio • Badly written code (not cache conscious) • (Rightly) considered the programmer’s fault • Paging strategy not responsible for predicting non-standard paging behaviour • Well written code (cache conscious) • Code can rely on well defined paging behaviour to produce better code (e.g. I/O model, cache oblivious model)

  18. Cooperative ratio for motion planning • Robot must search efficiently scenes which are “reasonable” • Can perform somewhat worse in “unreasonable” scenes • Leads to adaptive-style analysis. E.g. define niceness measure of office floor plan in terms of orthogonality of scene, number of rooms/corridors, size of smallest relevant feature, etc.

  19. Cooperative ratio for motion planning • Look around the corner • Leads to “straighter” curve • Applicable to polygon recognition (work in progress)

  20. Conclusions • Improved model for paging • Bridged theory-practice disconnect • Next talk: Unique optimality of LRU under new, more realistic model • New cooperative analysis model applicable to online research