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Online Bin Packing with Advice
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This work considers 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 and provides tight upper and lower bounds for the amount of advice an algorithm needs to achieve an optimal packing.Abstract:
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 requests. 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 + {\epsilon}. 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.read more
Citations
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Journal ArticleDOI
The string guessing problem as a method to prove lower bounds on the advice complexity
TL;DR: This paper considers the string guessing problem as a generic online problem and shows a lower bound on the number of advice bits needed to obtain a good solution, and uses special reductions from string guessing to improve the best known lower bound for the online set cover problem and to give a lower Bound on the advice complexity of the online maximum clique problem.
Posted Content
On the List Update Problem with Advice
TL;DR: It is shown that surprisingly two bits of advice is sufficient to break the lower bound of 2 on the competitive ratio of deterministic online algorithms and achieve a deterministic algorithm with a competitive ratios better than 15/14.
Book ChapterDOI
On Advice Complexity of the k-server Problem under Sparse Metrics
TL;DR: It is shown that at least at least $\frac{n}{2}({\rm log} \alpha- 1.22)$ bits of advice is required to obtain an optimal solution for metric spaces of treewidth α, where 4 ≤ α < 2k.
Posted Content
Randomization can be as helpful as a glimpse of the future in online computation
TL;DR: In this article, it was shown that sublinear advice is sufficient to achieve a constant competitive ratio smaller than 5/4, where n is the number of requests and k is the cache size.
Book ChapterDOI
Optimal Online Edge Coloring of Planar Graphs with Advice
TL;DR: In this paper, the authors study the amount of knowledge about the future that an online algorithm needs to color the edges of a graph optimally, i.e., using as few colors as possible.
References
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Book
Approximation Algorithms
TL;DR: Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field.
Journal ArticleDOI
On the online bin packing problem
TL;DR: It is shown that a new algorithm, Harmonic++, has asymptotic performance ratio at most 1.58889, and the analysis of Harmonic+1 presented in Richey [1991] is incorrect; this is a fundamental logical flaw.
Journal ArticleDOI
Online computation with advice
TL;DR: A model for online computation in which the online algorithm receives, together with each request, some information regarding the future, referred to as advice, and its applicability is illustrated by considering two of the most extensively studied online problems, namely, metrical task systems (MTS) and the k-server problem.
Book ChapterDOI
On the Advice Complexity of Online Problems
TL;DR: The results for all of these problems show that very small advice already suffices to significantly improve over the best deterministic algorithm, and to achieve the same competitive ratio as any randomized online algorithm, a logarithmic number of advice bits is sufficient.