Advice Complexity and Barely Random Algorithms

Komm, Dennis; Královič, Rastislav

doi:10.1007/978-3-642-18381-2_28

Cited by 28 publications

(35 citation statements)

References 12 publications

(19 reference statements)

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“…There is an optimal online algorithm Alg with advice that uses at most 2 √ m − 1 4 log (m) advice bits for any instance [10]. This is due to the fact that solutions for the new measure are optimal if and only if they are optimal for the old one.…”

Section: Implications Of New Cost Measure On Former Resultsmentioning

confidence: 99%

“…Therefore, bounds on the advice complexity of optimal algorithms carry over immediately. For m large enough, any online algorithm with advice needs to use at least m/2 advice bits to be optimal [10]. Every online algorithm with advice that reads at most b advice bits has a competitive ratio of at least √ m/(3 · 2 b ) [9].…”

Section: Implications Of New Cost Measure On Former Resultsmentioning

confidence: 99%

“…Komm and Královič [10] suggested an online algorithm Alg d with advice for any odd d ∈ N that reads log d advice bits that tell the algorithm which strategy out of the diagonal strategies…”

Section: Implications Of New Cost Measure On Former Resultsmentioning

confidence: 99%

“…Maybe knowing some very simple yet crucial characteristic about the future requests helps to design online algorithms that are extremely powerful. Their model was later refined [3,6,7]; in this paper, we use the model that was introduced by Hromkovič et al [7] and analyzed among others by Komm [9,10]. Let us first describe this model on an intuitive level.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Advice Complexity of Fine-Grained Job Shop Scheduling

Wehner

2015

Lecture Notes in Computer Science

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Section: Implications Of New Cost Measure On Former Resultsmentioning

confidence: 99%

Section: Implications Of New Cost Measure On Former Resultsmentioning

confidence: 99%

Section: Implications Of New Cost Measure On Former Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Advice Complexity of Fine-Grained Job Shop Scheduling

Wehner

2015

Lecture Notes in Computer Science

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“…Note that, since its introduction, the model used in this work was applied to a large number of online problems. Among others, the job shop scheduling problem was studied by Komm and Královič [10]. They showed that this problem also allows for good algorithms with sublinear advice.…”

Section: Online Algorithms |mentioning

confidence: 99%

Online Makespan Scheduling with Sublinear Advice

Dohrau

2015

Lecture Notes in Computer Science

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Online algorithms are of importance for many practical applications. Typical examples involve scheduling and routing algorithms employed in operating systems and computer networks. Beside their practical significance, online algorithms are extensively studied from a theoretical point of view. Due to the nature of online problems, these algorithms fail to be optimal in general. The quality of their output is usually measured by the so called competitive ratio. A few years ago, another measure, the advice complexity, has been introduced to give a deeper insight into the nature of an online problem and to capture the essential information contained in the instances of the problem.The makespan scheduling problem is a generic scheduling problem where the task is to schedule jobs with different processing times on identical machines. The objective is to distribute the processing times as evenly as possible among the machines. This is why this problem is sometimes referred to as the load balancing problem. When considering the online version of the problem, the jobs arrive gradually and have to be assigned to a machine immediately at their arrival. In the work at hand, we study the advice complexity of the online makespan scheduling problem restricted to two machines.For this problem it proves to be that already little advice helps a great deal to improve the competitive ratio in comparison to purely deterministic online algorithms. Therefore, this work mainly focuses on upper bounds. First, we give linear upper and lower bounds on the advice complexity for optimal algorithms with advice, with the bounds being tight up to one bit. Afterwards, we introduce a very simple online algorithm with logarithmic advice complexity and a competitive ratio of 4 3 . We also show that with a more involved strategy an online algorithm can get arbitrarily close to this competitive ratio using only a constant number of advice bits. As the main result we prove that even a constant number of advice bits is sufficient to achieve an almost optimal solution.

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On Advice Complexity of the k-server Problem under Sparse Metrics

Gupta

Kamali

López-Ortíz

2013

Structural Information and Communication Complexity

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We consider the k-Server problem under the advice model of computation when the underlying metric space is sparse. On one side, we show that an advice of size Ω(n) is required to obtain a 1-competitive algorithm for sequences of size n, even for the 2-server problem on a path metric of size N ≥ 5. Through another lower bound argument, we show that at least n 2 (log α − 1.22) bits of advice is required to obtain an optimal solution 3 for metric spaces of treewidth α, where 4 ≤ α < 2k. On the other side, we introduce Θ(1)-competitive algorithms for a wide range of sparse graphs, which require advice of (almost) linear size. Namely, we show that for graphs of size N and treewidth α, there is an online algorithm which receives O(n(log α+log log N )) bits of advice and optimally serves a sequence of length n. With a different argument, we show that if a graph admits a system of µ collective tree (q, r)-spanners, then there is a (q + r)-competitive algorithm which receives O(n(log µ + log log N )) bits of advice. Among other results, this gives a 3-competitive algorithm for planar graphs, provided with O(n log log N ) bits of advice. 3 We use log n to denote log 2 (n). 4 In this paper we only consider deterministic algorithms.

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Advice Complexity and Barely Random Algorithms

Cited by 28 publications

References 12 publications

Advice Complexity of Fine-Grained Job Shop Scheduling

Advice Complexity of Fine-Grained Job Shop Scheduling

Online Makespan Scheduling with Sublinear Advice

On Advice Complexity of the k-server Problem under Sparse Metrics

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