Measuring the problem-relevant information in input

Dobrev, Štefan; Královič, Rastislav; Pardubská, Dana

doi:10.1051/ita/2009012

Cited by 59 publications

(58 citation statements)

References 31 publications

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“…How these bits of advice are given to the algorithm is the source of difference between the models. In the first model, presented in [18], an online algorithm poses a series of questions which are answered by the offline oracle in blocks of answers. The total size of the answers, measured in the number of bits, defines the advice complexity.…”

Section: Modelmentioning

confidence: 99%

Online Bin Packing with Advice

et al. 2014

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We consider the online bin packing problem under the advice complexity model where the "online constraint" is relaxed and an algorithm receives partial information about the future items. We provide tight upper and lower bounds for the amount of advice an algorithm needs to achieve an optimal packing. We also introduce an algorithm that, when provided with log n+o(log n) bits of advice, achieves a competitive ratio of 3/2 for the general problem. This algorithm is simple and is expected to find real-world applications. We introduce another algorithm that receives 2n + o(n) bits of advice and achieves a competitive ratio of 4/3 + ε. Finally, we provide a lower bound argument that implies that advice of linear size is required for an algorithm to achieve a competitive ratio better than 9/8.

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Section: Modelmentioning

confidence: 99%

Online Bin Packing with Advice

et al. 2014

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“…The idea of online algorithms with advice was proposed by Dobrev et al [11]. However, the original model used advice over a two-letter alphabet {0, 1} and an additional delimiter $.…”

Section: Definition 2 (Online Algorithm With Advicementioning

confidence: 99%

On the advice complexity of the k-server problem

Bckenhauer

Komm

Krlovi

et al. 2017

Journal of Computer and System Sciences

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The model of advice complexity offers an alternative measurement allowing for a more fine-grained analysis of the hardness of online problems than standard competitive analysis. Here, one measures the amount of information an online algorithm is lacking about the yet unrevealed parts of the input. This model was successfully used for many online problems including the k-server problem. We extend the analysis of the k-server problem by giving a lower bound on the advice necessary to obtain optimality, and upper bounds on online algorithms for the general and the Euclidean case. For the general case, we improve the previous results by an exponential factor; for the Euclidean case, we achieve a constant competitive ratio using constantly many advice bits per request. Furthermore, for many online problems, we show how lower bounds on the advice complexity can be transformed into lower bounds on the expected competitive ratio of randomized online algorithms.

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“…In contrast to problem specific approaches, advice complexity [3,9,11] is a quantitative and standardized way of relaxing the online constraint. The main idea of advice complexity is to provide an online algorithm, Alg, with some partial knowledge of the future in the form of advice bits provided by a trusted oracle which has unlimited computational power and knows the entire request sequence.…”

Section: Introductionmentioning

confidence: 99%

Weighted Online Problems with Advice

et al. 2017

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Abstract. Recently, the first online complexity class, AOC, was introduced. The class consists of many online problems where each request must be either accepted or rejected, and the aim is to either minimize or maximize the number of accepted requests, while maintaining a feasible solution. All AOC-complete problems (including Independent Set, Vertex Cover, Dominating Set, and Set Cover) have essentially the same advice complexity. In this paper, we study weighted versions of problems in AOC, i.e., each request comes with a weight and the aim is to either minimize or maximize the total weight of the accepted requests. In contrast to the unweighted versions, we show that there is a significant difference in the advice complexity of complete minimization and maximization problems. We also show that our algorithmic techniques for dealing with weighted requests can be extended to work for non-complete AOC problems such as Matching in the edge arrival model (giving better results than what follow from the general AOC results) and even non-AOC problems such as scheduling.

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Measuring the problem-relevant information in input

Cited by 59 publications

References 31 publications

Online Bin Packing with Advice

Online Bin Packing with Advice

On the advice complexity of the k-server problem

Weighted Online Problems with Advice

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