Alternative models for online analysis
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Alternative Models for Online Analysis. Alex L ó pez-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

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Alternative Models for Online Analysis

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Alternative models for online analysis

Alternative Models for Online Analysis

Alex López-Ortiz

University of Waterloo

joint work with Reza Dorrigiv,

Spyros Angelopoulos and Ian Munro


Alternative models for online analysis

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?


Alternative models for online analysis

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

Paging Algorithms

  • Data brought from slower memory into cache

RAM

CPU


Alternative models for online analysis

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”


Alternative models for online analysis

  • 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


Alternative models for online analysis

  • 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


Alternative models for online analysis

“Architects are your friend”

Most of the time, anyhow.


Fix the theory practice disconnect

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

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


Alternative models for online analysis

  • 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

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)


Results1

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


Results2

Results

  • LFD is offline optimal/huh?

    • removed concept of offline optimum

  • competitive ratio is k/competitive ratio is 2 or 3

    • Nothing to do!


Results3

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

Cooperative ratio

  • Agreement between user and algorithm about inputs which are:

    • likely

    • common

    • good

    • important


Cooperative ratio1

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

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 planning1

Cooperative ratio for motion planning

  • Look around the corner

  • Leads to “straighter” curve

  • Applicable to polygon recognition (work in progress)


Conclusions

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


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