On the Advice Complexity of the k-Server Problem

Böckenhauer, Hans-Joachim; Komm, Dennis; Královič, Rastislav

doi:10.1007/978-3-642-22006-7_18

Cited by 60 publications

(46 citation statements)

References 15 publications

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“…Many other problems have been studied in an advice setting, including disjoint path allocation by Barhum et al [2], and job shop scheduling by Böckenhauer et al [6], as well as k-server by Böckenhauer et al [5], knapsack by Böckenhauer et al [7], set cover by Komm, Královič, and Mömke [29], metrical task systems by Emek et al [22], and buffer management by Dorrigiv, He, and Zeh [20].…”

Section: Relaxing the Online Constraintmentioning

confidence: 97%

Online multi-coloring with advice

Christ

Favrholdt

Larsen

2015

Theoretical Computer Science

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We consider the problem of online graph multi-coloring with advice. Multi-coloring is often used to model frequency allocation in cellular networks. We give several nearly tight upper and lower bounds for the most standard topologies of cellular networks, paths and hexagonal graphs. For the path, negative results trivially carry over to bipartite graphs, and our positive results are also valid for bipartite graphs. For hexagonal graphs, negative results trivially carry over to 3-colorable graphs, and most of our positive results do as well. The advice given represents information that is likely to be available, studying for instance the data from earlier similar periods of time.

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Section: Relaxing the Online Constraintmentioning

confidence: 97%

Online multi-coloring with advice

Christ

Favrholdt

Larsen

2015

Theoretical Computer Science

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“…This generality means that lower bound results under the advice model also imply strong lower bound results on semi-online algorithms, where one can infer impossibility results simply from the length of an encoding of the information a semi-online algorithm is provided with. Advice complexity is also closely related to randomization; complexity bounds from advice complexity can be transferred to the randomization case and vice versa [8,6,21,14].…”

Section: Online Algorithms With Advicementioning

confidence: 99%

Online Bin Covering with Advice

Boyar

Favrholdt

Kamali

et al. 2019

Lecture Notes in Computer Science

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The bin covering problem asks for covering a maximum number of bins with an online sequence of n items of different sizes in the range (0, 1]; a bin is said to be covered if it receives items of total size at least 1. We study this problem in the advice setting and provide tight bounds for the size of advice required to achieve optimal solutions. Moreover, we show that any algorithm with advice of size o(log log n) has a competitive ratio of at most 0.5. In other words, advice of size o(log log n) is useless for improving the competitive ratio of 0.5, attainable by an online algorithm without advice. This result highlights a difference between the bin covering and the bin packing problems in the advice model: for the bin packing problem, there are several algorithms with advice of constant size that outperform online algorithms without advice. Furthermore, we show that advice of size O(log log n) is sufficient to achieve a competitive ratio that is arbitrarily close to 0.533 and hence strictly better than the best ratio 0.5 attainable by purely online algorithms. The technicalities involved in introducing and analyzing this algorithm are quite different from the existing results for the bin packing problem and confirm the different nature of these two problems. Finally, we show that a linear number of bits of advice is necessary to achieve any competitive ratio better than 15/16 for the online bin covering problem.

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“…It is for instance analyzed in frameworks such as non-deterministic decision [36,51,52], broadcast [33], local computation of MST [35], graph coloring [34] and graph searching by a single robot [17]. Very recently, it has also been investigated in the context of online algorithms [13,24].…”

Section: Related Workmentioning

confidence: 99%

“…In addition, the authors are thankful to the anonymous reviewers for helping to improve the presentation of the paper, and for providing us with an idea that was used to prove the upper bound in Section 5.2.2. 13 The bait itself may be "imaginary" in the sense that it need not be placed physically on the terrain. Instead, a camera can just be placed filming the location, and detecting when searchers get nearby.…”

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confidence: 99%

The ANTS problem

Feinerman

Korman

2016

Distrib. Comput.

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We introduce the Ants Nearby Treasure Search (ANTS) problem, which models natural cooperative foraging behavior such as that performed by ants around their nest. In this problem, k probabilistic agents, initially placed at a central location, collectively search for a treasure on the two-dimensional grid. The treasure is placed at a target location by an adversary and the agents' goal is to find it as fast as possible as a function of both k and D, where D is the (unknown) distance between the central location and the target. We concentrate on the case in which agents cannot communicate while searching. It is straightforward to see that the time until at least one agent finds the target is at least $\Omega$(D + D 2 /k), even for very sophisticated agents, with unrestricted memory. Our algorithmic analysis aims at establishing connections between the time complexity and the initial knowledge held by agents (e.g., regarding their total number k), as they commence the search. We provide a range of both upper and lower bounds for the initial knowledge required for obtaining fast running time. For example, we prove that log log k + $\Theta$(1) bits of initial information are both necessary and sufficient to obtain asymptotically optimal running time, i.e., O(D +D 2 /k). We also we prove that for every 0 \textless{} \textless{} 1, running in time O(log 1-- k $\times$(D +D 2 /k)) requires that agents have the capacity for storing $\Omega$(log k) different states as they leave the nest to start the search. To the best of our knowledge, the lower bounds presented in this paper provide the first non-trivial lower bounds on the memory complexity of probabilistic agents in the context of search problems. We view this paper as a "proof of concept" for a new type of interdisciplinary methodology. To fully demonstrate this methodology, the theoretical tradeoff presented here (or a similar one) should be combined with measurements of the time performance of searching ants.Comment: arXiv admin note: text overlap with arXiv:1205.454

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On the Advice Complexity of the k-Server Problem

Cited by 60 publications

References 15 publications

Online multi-coloring with advice

Online multi-coloring with advice

Online Bin Covering with Advice

The ANTS problem

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