We propose a new way of characterizing the complexity of online problems. Instead of measuring the degradation of the output quality caused by the ignorance of the future we choose to quantify the amount of additional global information needed for an online algorithm to solve the problem optimally. In our model, the algorithm cooperates with an oracle that can see the whole input. We define the advice complexity of the problem to be the minimal number of bits (normalized per input request, and minimized over all algorithm-oracle pairs) communicated by the algorithm to the oracle in order to solve the problem optimally. Hence, the advice complexity measures the amount of problem-relevant information contained in the input. We introduce two modes of communication between the algorithm and the oracle based on whether the oracle offers an advice spontaneously (helper) or on request (answerer). We analyze the Paging and DiffServ problems in terms of advice complexity and deliver upper and lower bounds in both communication modes; in the case of DiffServ problem in helper mode the bounds are tight.

Keywords: online algorithms, communication complexity, advice complexity, paging

@article{ITA_2009__43_3_585_0, author = {Dobrev, Stefan and Kr\'alovi\v{c}, Rastislav and Pardubsk\'a, Dana}, title = {Measuring the problem-relevant information in input}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {585--613}, publisher = {EDP-Sciences}, volume = {43}, number = {3}, year = {2009}, doi = {10.1051/ita/2009012}, zbl = {1176.68089}, mrnumber = {2541132}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ita/2009012/} }

TY - JOUR AU - Dobrev, Stefan AU - Královič, Rastislav AU - Pardubská, Dana TI - Measuring the problem-relevant information in input JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2009 DA - 2009/// SP - 585 EP - 613 VL - 43 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita/2009012/ UR - https://zbmath.org/?q=an%3A1176.68089 UR - https://www.ams.org/mathscinet-getitem?mr=2541132 UR - https://doi.org/10.1051/ita/2009012 DO - 10.1051/ita/2009012 LA - en ID - ITA_2009__43_3_585_0 ER -

%0 Journal Article %A Dobrev, Stefan %A Královič, Rastislav %A Pardubská, Dana %T Measuring the problem-relevant information in input %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2009 %P 585-613 %V 43 %N 3 %I EDP-Sciences %U https://doi.org/10.1051/ita/2009012 %R 10.1051/ita/2009012 %G en %F ITA_2009__43_3_585_0

Dobrev, Stefan; Královič, Rastislav; Pardubská, Dana. Measuring the problem-relevant information in input. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 43 (2009) no. 3, pp. 585-613. doi : 10.1051/ita/2009012. http://www.numdam.org/articles/10.1051/ita/2009012/

[1] Competitive analysis of randomized paging algorithms. Theoret. Comput. Sci. 234 (2000) 203-218. | MR | Zbl

, and ,[2] On the influence of lookahead in competitive paging algorithms. Algorithmica 18 (1997) 283-305. | MR | Zbl

,[3] Online algorithms: A survey. Math. Prog. 97 (2003) 3-26. | MR | Zbl

,[4] A study of replacement algorithms for virtual storage computers. IBM Systems Journal 5 (1966) 78-101.

,[5] A new measure for the study of on-line algorithms. Algorithmica 11 (1994) 73-91. | MR | Zbl

and ,[6] Online Computation and Competitive Analysis. Cambridge University Press (1998). | MR | Zbl

and ,[7] Competitive paging with locality of reference. In Proc. 23rd Annual ACM Symposium on Theory of Computing (1991) 249-259. | Zbl

, , and ,[8] Theoretical Evidence for the superiority of LRU-2 over LRU for the paging problem. In Fourth Workshop on Approximation on Online Algorithms. Lecture Notes Comput. Sci. 4368 (2006) 95-107. | MR | Zbl

, and ,[9] The accommodating function: a generalization of the competitive ratio. SIAM J. Comput. 31 (2001) 233-258. | MR | Zbl

, and ,[10] The relative worst order ratio for online algorithms, Algorithms and Complexity, 5th Italian Conference, CIAC 2003, Rome, Italy. Lect. Notes Comput. Sci. 2653 (2003) 58-69. | MR | Zbl

and ,[11] lower and upper bounds on FIFO buffer management in QoS switches, In Proc. ESA 2006. Lect. Notes Comput. Sci. 4168 (2006) 352-363. | MR | Zbl

and ,[12] Competitive paging algorithms. J. Algorithms 12 (1991) 685-699. | Zbl

, , , , and ,[13] Distributed computing with advice: information sensitivity of graph coloring. In Proc. 34th International Colloquium on Automata, Languages and Programming (ICALP 2007) (2007). | MR | Zbl

, , and ,[14] Tree exploration with an oracle. In Proc. 31st International Symposium on Mathematical Foundations of Computer Science (MFCS 2006). Lect. Notes Comput. Sci. 4162 (2006) 24-37. | MR | Zbl

, and ,[15] Oracle size: a new measure of difficulty for communication problems. In Proc. 25th Ann. ACM Symposium on Principles of Distributed Computing (PODC 2006) (2006) 179-187.

, and ,[16] Bounds for certain multiprocessing anomalies. Bell Systems Technical Journal 45 (1966) 1563-1581. | Zbl

,[17] Online computation. In Approximation Algorithms for NP-Hard Problems, D.S. Hochbaum, Ed. PWS Publishing Company (1997) 521-564.

and ,[18] Strongly competitive algorithms for paging with locality of reference. In Proc. 3rd Annual ACM-SIAM Symposium on Discrete Algorithms (1992) 228-236. | MR | Zbl

, and ,[19] Speed is as Powerful as Clairvoyance. IEEE Symposium on Foundations of Computer Science (1995) 214-221. | Zbl

and ,[20] Competitive Snoopy Caching. Algorithmica 3 (1988) 79-119. | MR | Zbl

, , and ,[21] On-line algorithms versus off-line algorithms: how much is it worth to know the future? Proc. IFIP 12th World Computer Congress 1 (1992) 416-429.

,[22] Beyond competitive analysis. In Proc. 34th Annual Symposium on Foundations of Computer Science (1994) 394-400.

and ,[23] Nearly optimal FIFO buffer management for DiffServ. PODC 2002 (2002) 134-143.

and ,[24] Competitive Algorithms for Online Problems. In Proc. 20th Annual Symposium on the Theory of Computing (1988) 322-333. | Zbl

, and ,[25] Optimal time-critical scheduling via resource augmentation. In Proc. 29th Annual ACM Symposium on the Theory of Computing (1997) 140-149. | Zbl

, , and ,[26] The expressiveness of silence: tight bounds for synchronous communication of information using bits and silence. In Proc. 18th International Workshop on Graph-Theoretic Concepts in Computer Science (1992) 321-332. | MR | Zbl

and ,[27] A statistical adversary for on-line algorithms. In On-Line Algorithms, DIMACS Series in Discrete Mathematics and Theoretical Computer Science (1991) 79-83. | Zbl

,[28] A Remark of Stirling's Formula. Amer. Math. Month. 62 (1955) 26-29. | MR | Zbl

,[29] Amortized efficiency of update and paging rules. Commun. ACM 28 (1985) 202-208. | MR

and ,[30] A Unified Analysis of Paging and Caching. Algorithmica 20 (1998) 175-200. | MR | Zbl

,[31] On-line paging against adversially biased random inputs. J. Algorithms 37 (2000) 218-235. | MR | Zbl

,[32] The $k$-server dual and loose competitiveness for paging. Algorithmica 11 (1994) 525-541. | MR

,*Cited by Sources: *