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## Alternative Models for Online Analysis

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**Alternative Models for Online Analysis**Alex López-Ortiz University of Waterloo joint work with Reza Dorrigiv, Spyros Angelopoulos and Ian Munro**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?**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)**Paging Algorithms**• Data brought from slower memory into cache RAM CPU**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”**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**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**“Architects are your friend”**Most of the time, anyhow.**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**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**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**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)**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**Results**• LFD is offline optimal/huh? • removed concept of offline optimum • competitive ratio is k/competitive ratio is 2 or 3 • Nothing to do!**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**Cooperative ratio**• Agreement between user and algorithm about inputs which are: • likely • common • good • important**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)**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.**Cooperative ratio for motion planning**• Look around the corner • Leads to “straighter” curve • Applicable to polygon recognition (work in progress)**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