Online Bin Packing with Advice of Small Size

Angelopoulos, Spyros; Dürr, Christoph; Kamali, Shahin; Rosen, Alon

doi:10.1007/978-3-319-21840-3_4

Cited by 22 publications

(78 citation statements)

References 18 publications

(12 reference statements)

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“…This technique has repeatedly been applied for obtaining advice lower bounds, e.g. [1,20,10,2,11,4]. Our algorithm simulates an augmenting-paths-based algorithm by Eggert et al [14], that has originally been designed for the data streaming model, with the help of advice bits.…”

Section: Our Objective and Previous Resultsmentioning

confidence: 99%

“…Many online problems have been studied in the setting of online algorithms with advice (e.g. metrical task system [15], k-server problem [15,9,30,20], paging [13,7], bin packing problem [31,11,2], knapsack problem [8], reordering buffer management problem [1], list update problem [10], minimum spanning tree problem [4] and others). Interestingly, a variant of the algorithm with advice for list update problem of [10] was used to gain significant improvements in the compression rates for Burrows-Wheeler transform compression schemes [23].…”

Section: Models For Online Algorithms With Advicementioning

confidence: 99%

“…Throughout the paper, logarithms, where the base is omitted, are implicitly binary logarithms 2. It is straightforward to adapt the proof of Theorem 5 of[9] accordlingly.…”

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confidence: 99%

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On the Power of Advice and Randomization for Online Bipartite Matching

Dürr,

Konrad,

Renault

2016

Preprint

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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 work, we investigate the power of advice bits and random bits for online maximum bipartite matching (MBM).The well-known Karp-Vazirani-Vazirani algorithm [24] is an optimal randomized (1− 1 e )-competitive algorithm for MBM that requires access to Θ(n log n) uniform random bits. We show that Ω(log( 1 )n) advice bits are necessary and O( 15 n) sufficient in order to obtain a (1 − )-competitive deterministic advice algorithm. Furthermore, for a large natural class of deterministic advice algorithms, we prove that Ω(log log log n) advice bits are required in order to improve on the 1 2 -competitiveness of the best deterministic online algorithm, while it is known that O(log n) bits are sufficient [9].Last, we give a randomized online algorithm that uses cn random bits, for integers c ≥ 1, and a competitive ratio that approaches 1 − 1 e very quickly as c is increasing. For example if c = 10, then the difference between 1 − 1 e and the achieved competitive ratio is less than 0.0002.

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Section: Our Objective and Previous Resultsmentioning

confidence: 99%

Section: Models For Online Algorithms With Advicementioning

confidence: 99%

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On the Power of Advice and Randomization for Online Bipartite Matching

Dürr,

Konrad,

Renault

2016

Preprint

Self Cite

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“…The problem has also been studied under the advice complexity model [11,2], in which the online algorithm has access to some error-free information on the input called advice, and the objective is to quantify the tradeoffs between the performance of the algorithm and the size of the advice (in terms of bits). It should be emphasized that such studies are only of theoretical interest, not only because the advice is assumed to have no errors, but also because it may encode any information, with no learnability considerations (i.e.…”

Section: Related Workmentioning

confidence: 99%

Online Bin Packing with Predictions

Angelopoulos¹,

Kamali²,

Shadkami³

2021

Preprint

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Bin packing is a classic optimization problem with a wide range of applications from load balancing in networks to supply chain management. In this work we study the online variant of the problem, in which a sequence of items of various sizes must be placed into a minimum number of bins of uniform capacity. The online algorithm is enhanced with a (potentially erroneous) prediction concerning the frequency of item sizes in the sequence. We design and analyze online algorithms with efficient tradeoffs between their consistency (i.e., the competitive ratio assuming no prediction error) and their robustness (i.e., the competitive ratio under adversarial error), and whose performance degrades gently as a function of the error. Previous work on this problem has only addressed the extreme cases with respect to the prediction error, and has relied on overly powerful and error-free prediction oracles.

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“…Since its introduction, many online problems have been studied under the advice model. These include classical online problems such as paging [13,21,25], k-server [17,12,28,20], bin packing [15,7], and various coloring problems [10,18,29].…”

Section: Introductionmentioning

confidence: 99%

On the List Update Problem with Advice

Boyar

Kamali

Larsen

et al. 2014

Language and Automata Theory and Applications

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We study the online list update problem under the advice model of computation. Under this model, an online algorithm receives partial information about the unknown parts of the input in the form of some bits of advice generated by a benevolent offline oracle. We show that advice of linear size is required and sufficient for a deterministic algorithm to achieve an optimal solution or even a competitive ratio better than 15/14. On the other hand, we show that surprisingly two bits of advice are sufficient to break the lower bound of 2 on the competitive ratio of deterministic online algorithms and achieve a deterministic algorithm with a competitive ratio of 1.6. In this upper-bound argument, the bits of advice determine the algorithm with smaller cost among three classical online algorithms, Timestamp and two members of the Mtf2 family of algorithms. We also show that Mtf2 algorithms are 2.5-competitive.

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Online Bin Packing with Advice of Small Size

Cited by 22 publications

References 18 publications

On the Power of Advice and Randomization for Online Bipartite Matching

On the Power of Advice and Randomization for Online Bipartite Matching

Online Bin Packing with Predictions

On the List Update Problem with Advice

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