Amortized efficiency of list update and paging rules
Communications of the ACM
Online computation and competitive analysis
Online computation and competitive analysis
On the Length of Programs for Computing Finite Binary Sequences
Journal of the ACM (JACM)
A mathematical theory of communication
ACM SIGMOBILE Mobile Computing and Communications Review
Design and Analysis of Randomized Algorithms: Introduction to Design Paradigms (Texts in Theoretical Computer Science. An EATCS Series)
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Online Computation with Advice
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
On the Advice Complexity of Online Problems
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
How much information about the future is needed?
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Information complexity of online problems
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Computer Science Review
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
A new approach to solve the k-server problem based on network flows and flow cost reduction
Computers and Operations Research
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Competitive analysis is the established tool for measuring the output quality of algorithms that work in an online environment. Recently, the model of advice complexity has been introduced as an alternative measurement which allows for a more fine-grained analysis of the hardness of online problems. In this model, one tries to measure the amount of information an online algorithm is lacking about the future parts of the input. This concept was investigated for a number of well-known online problems including the k-server problem. In this paper, we first extend the analysis of the k-server problem by giving both a lower bound on the advice needed to obtain an optimal solution, and upper bounds on algorithms for the general k-server problem on metric graphs and the special case of dealing with the Euclidean plane. In the general case, we improve the previously known results by an exponential factor, in the Euclidean case we design an algorithm which achieves a constant competitive ratio for a very small (i. e., constant) number of advice bits per request. Furthermore, we investigate the relation between advice complexity and randomized online computations by showing how lower bounds on the advice complexity can be used for proving lower bounds for the competitive ratio of randomized online algorithms.