Amortized efficiency of list update and paging rules
Communications of the ACM
Online computation and competitive analysis
Online computation and competitive analysis
Randomized on-line algorithms and lower bounds for computing large independent sets in disk graphs
Discrete Applied Mathematics
Online Computation with Advice
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Information complexity of online problems
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Advice complexity and barely random algorithms
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
On the advice complexity of the k-server problem
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
On online algorithms with advice for the k-server problem
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Advice complexity of online coloring for paths
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
On the advice complexity of the knapsack problem
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Online graph exploration with advice
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Modeling time criticality of information
Information Processing Letters
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In this paper, we investigate to what extent the solution quality of online algorithms can be improved by allowing the algorithm to extract a given amount of information about the input. We consider the recently introduced notion of advice complexity where the algorithm, in addition to being fed the requests one by one, has access to a tape of advice bits that were computed by some oracle function from the complete input. The advice complexity is the number of advice bits read. We introduce an improved model of advice complexity and investigate the connections of advice complexity to the competitive ratio of both deterministic and randomized online algorithms using the paging problem, job shop scheduling, and the routing problem on a line as sample problems. We provide both upper and lower bounds on the advice complexity of all three problems.Our results for all of these problems show that very small advice (only three bits in the case of paging) already suffices to significantly improve over the best deterministic algorithm. Moreover, to achieve the same competitive ratio as any randomized online algorithm, a logarithmic number of advice bits is sufficient. On the other hand, to obtain optimality, much larger advice is necessary.