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 SP - 585 EP - 613 VL - 43 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/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 http://www.numdam.org/articles/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/

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