Advice Complexity and Barely Random Algorithms

Dennis Komm; Richard Královič

RAIRO - Theoretical Informatics and Applications (2011)

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

Abstract

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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.

How to cite

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Komm, Dennis, and Královič, Richard. "Advice Complexity and Barely Random Algorithms." RAIRO - Theoretical Informatics and Applications 45.2 (2011): 249-267. <http://eudml.org/doc/222011>.

@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},
keywords = {Barely random algorithms; advice complexity; information content; online problems; barely random algorithms},
language = {eng},
month = {6},
number = {2},
pages = {249-267},
publisher = {EDP Sciences},
title = {Advice Complexity and Barely Random Algorithms},
url = {http://eudml.org/doc/222011},
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
DA - 2011/6//
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; barely random algorithms
UR - http://eudml.org/doc/222011
ER -

References

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  2. H.-J. Böckenhauer, D. Komm, R. Královič, R. Královič and T. Mömke, On the advice complexity of online problems, in 20th International Symposium on Algorithms and Computation (ISAAC 2009) Lect. Notes Comput. Sci.5878 (2009) 331–340.  
  3. H.-J. Böckenhauer, D. Komm, R. Královič, R. Královič and T. Mömke, Online algorithms with advice. To appear.  
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  9. J. Hromkovič, R. Královič and R. Královič, Information complexity of online problems, in 35th International Symposium on Mathematical Foundations of Computer Science (MFCS 2010). Lect. Notes Comput. Sci.6281 (2010) 24–36.  
  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.  
  11. D. Komm and R. Královič, Advice complexity and barely random algorithms, in 37th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2011). Lect. Notes Comput. Sci.6543 (2011) 332–343.  
  12. T. Mömke, On the power of randomization for job shop scheduling with k -units length tasks. RAIRO-Theor. Inf. Appl.43 (2009) 189–207.  
  13. N. Reingold, J. Westbrook and D. Sleator, Randomized competitive algorithms for the list update problem. Algorithmica11 (1994) 15–32.  

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