# Advice Complexity and Barely Random Algorithms

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2011)

- Volume: 45, Issue: 2, page 249-267
- ISSN: 0988-3754

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topKomm, Dennis, and Královič, Richard. "Advice Complexity and Barely Random Algorithms." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 45.2 (2011): 249-267. <http://eudml.org/doc/273054>.

@article{Komm2011,

abstract = {Recently, a new measurement – the advice complexity – was introduced for measuring the information content of online problems. The aim is to measure the bitwise information that online algorithms lack, causing them to perform worse than offline algorithms. Among a large number of problems, a well-known scheduling problem, job shop scheduling with unit length tasks, and the paging problem were analyzed within this model. We observe some connections between advice complexity and randomization. Our special focus goes to barely random algorithms, i.e., randomized algorithms that use only a constant number of random bits, regardless of the input size. We adapt the results on advice complexity to obtain efficient barely random algorithms for both the job shop scheduling and the paging problem. Furthermore, so far, it has not yet been investigated for job shop scheduling how good an online algorithm may perform when only using a very small (e.g., constant) number of advice bits. In this paper, we answer this question by giving both lower and upper bounds, and also improve the best known upper bound for optimal algorithms.},

author = {Komm, Dennis, Královič, Richard},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {barely random algorithms; advice complexity; information content; online problems},

language = {eng},

number = {2},

pages = {249-267},

publisher = {EDP-Sciences},

title = {Advice Complexity and Barely Random Algorithms},

url = {http://eudml.org/doc/273054},

volume = {45},

year = {2011},

}

TY - JOUR

AU - Komm, Dennis

AU - Královič, Richard

TI - Advice Complexity and Barely Random Algorithms

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2011

PB - EDP-Sciences

VL - 45

IS - 2

SP - 249

EP - 267

AB - Recently, a new measurement – the advice complexity – was introduced for measuring the information content of online problems. The aim is to measure the bitwise information that online algorithms lack, causing them to perform worse than offline algorithms. Among a large number of problems, a well-known scheduling problem, job shop scheduling with unit length tasks, and the paging problem were analyzed within this model. We observe some connections between advice complexity and randomization. Our special focus goes to barely random algorithms, i.e., randomized algorithms that use only a constant number of random bits, regardless of the input size. We adapt the results on advice complexity to obtain efficient barely random algorithms for both the job shop scheduling and the paging problem. Furthermore, so far, it has not yet been investigated for job shop scheduling how good an online algorithm may perform when only using a very small (e.g., constant) number of advice bits. In this paper, we answer this question by giving both lower and upper bounds, and also improve the best known upper bound for optimal algorithms.

LA - eng

KW - barely random algorithms; advice complexity; information content; online problems

UR - http://eudml.org/doc/273054

ER -

## References

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- [10] J. Hromkovič, T. Mömke, K. Steinhöfel and P. Widmayer, Job shop scheduling with unit length tasks: bounds and algorithms. Algorithmic Operations Research2 (2007) 1–14. Zbl1186.90051
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