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We consider the model of online computation with advice (Emek et al., Theor. Comput. Sci. 412(24): 2642–2656, 2011). In particular, we study the k-server problem under this model. We prove three upper bounds for this problem. First, we show a $\lceil\frac{\lceil\log k\rceil}{b-2}\rceil$ -competitive online algorithm for general metric spaces with b bits of… (More)

We consider the setting of online computation with advice and study the bin packing problem and a number of scheduling problems. We show that it is possible, for any of these problems, to arbitrarily approach a competitive ratio of 1 with only a constant number of bits of advice per request. For the bin packing problem, we give an online algorithm with… (More)

In the reordering buffer management problem, a sequence of colored items arrives at a service station to be processed. Each color change between two consecutively processed items generates a cost. A reordering buffer of capacity k items can be used to preprocess the input sequence in order to decrease the number of color changes. The goal is to find a… (More)

While randomized online algorithms have access to a sequence of uniform random bits, deterministic online algorithms with advice have access to a sequence of advice bits, i.e., bits that are set by an all-powerful oracle prior to the processing of the request sequence. Advice bits are at least as helpful as random bits, but how helpful are they? In this… (More)

We consider the list update problem as defined in the seminal work on competitive analysis by Sleator and Tarjan [12]. In this problem, a sequence of requests, consisting of items to access in a linked list, is given. After an item is accessed it can be moved to any position forward in the list at no cost (free exchange), and, at any time, any two adjacent… (More)

Stochastic dominance is a technique for evaluating the performance of online algorithms that provides an intuitive, yet powerful stochastic order between the compared algorithms. Accordingly this holds for bijective analysis, which can be interpreted as stochastic dominance assuming the uniform distribution over requests. These techniques have been applied… (More)

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