Fully-Dynamic Bin Packing with Little Repacking

Feldkord, Björn; Feldotto, Matthias; Gupta, Anupam; Guruganesh, Guru; Kumar, Amit; Riechers, Sören; Wajc, David

doi:10.4230/lipics.icalp.2018.51

Cited by 3 publications

(9 citation statements)

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“…They also showed that a non-amortized migration factor of Ω(1/ε) is needed for this. A generalized model, where an item i has arbitrary movement costs c i -not necessarily linked to the size of an item -was studied by Feldkord et al [14]. They showed that for α ≈ 1.387 and every ε > 0, a competitive ratio of α + ε is achievable with migration O(1/ε 2 ), but no algorithm with migration o(n) and ratio α − ε exists.…”

Section: Makespan Minimization and Santa Clausmentioning

confidence: 99%

“…In contrast to the dynamic case, where amortized migration does not help to improve upon the lower bound of 3/2 on the competitive ratio, amortization allows to design a simple algorithm for the static case, achieving a competitive ratio of 1 + ε with amortized migration of O(1/ε). Some of the ideas applied here were used for bin packing [14] in the past. The small value ε will again satisfy 0 < ε ≤ 0.5.…”

Section: Static Casementioning

confidence: 99%

“…A number of different scenarios to loosen the strict requirement of irreversibilitycalled semi-online scenarios -have been developed over time in order to find algorithms that achieve good competitive ratios for some of the scenarios bounded reversibility. In the last few years, the concept of the migration factor has been studied intensively [4,11,12,13,14,17,20,22,23]. Roughly speaking, a migration factor of β allows to reverse a total size of β • s(o) decisions, where s(o) denotes the size of the newly arrived object o.…”

Section: Introductionmentioning

confidence: 99%

“…This notion of reversibility is very natural, as it guarantees that a small object can only lead to small changes in the solution structure. Furthermore, algorithms with bounded migration factor often show a very clear-cut tradeoff between their migration and the competitive ratio: Many algorithms in this setting have a bounded migration factor which can be defined as a function f (ε) (growing with 1 ε ) and a small competitive ratio g(ε) (growing with ε), where the functions f and g can be defined for all ε > 0 [4,11,14,17,20,22,23]. Such algorithms are called robust, as the amount of reversibility allowed only depends on the solution guarantee that one wants to achieve.…”

Section: Introductionmentioning

confidence: 99%

“…Many different problems have been studied in online and semi-online scenarios, but two problems that have been considered in nearly every scenario are classic scheduling problems: The bin packing problem and the makespan minimization problem. Both of these problems have been studied intensively in the migration model [4,11,13,14,20,22,23]. Both of these problems also have corresponding dual maximization variants.…”

Section: Introductionmentioning

confidence: 99%

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Online Bin Covering with Limited Migration

Berndt¹,

Epstein²,

Jansen³

et al. 2019

Preprint

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Semi-online models where decisions may be revoked in a limited way have been studied extensively in the last years. This is motivated by the fact that the pure online model is often too restrictive to model real-world applications, where some changes might be allowed. A well-studied measure of the amount of decisions that can be revoked is the migration factor β: When an object o of size s(o) arrives, the decisions for objects of total size at most β • s(o) may be revoked. Usually β should be a constant. This means that a small object only leads to small changes. This measure has been successfully investigated for different, classic problems such as bin packing or makespan minimization. The dual of makespan minimization -the Santa Claus or machine covering problem -has also been studied, whereas the dual of bin packing -the bin covering problem -has not been looked at from such a perspective.In this work, we extensively study the bin covering problem with migration in different scenarios. We develop algorithms both for the static case -where only insertions are allowed -and for the dynamic case, where items may also depart. We also develop lower bounds for these scenarios both for amortized migration and for worst-case migration showing that our algorithms have nearly optimal migration factor and asymptotic competitive ratio (up to an arbitrary small ε). We therefore resolve the competitiveness of the bin covering problem with migration.

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Section: Makespan Minimization and Santa Clausmentioning

confidence: 99%

Section: Static Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Online Bin Covering with Limited Migration

Berndt¹,

Epstein²,

Jansen³

et al. 2019

Preprint

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Online bin covering with limited migration

Berndt

Epstein

Jansen

et al. 2023

Journal of Computer and System Sciences

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PERMUTATION Strikes Back: The Power of Recourse in Online Metric Matching

Gupta¹,

Krishnaswamy²,

Sandeep³

2019

Preprint

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In the classical ONLINE-METRIC-MATCHING problem, we are given a metric space with k servers. A collection of clients arrive in an online fashion, and upon arrival, a client should irrevocably be matched to an as-yet-unmatched server. The goal is to find an online matching which minimizes the total cost, i.e., the sum of distances between each client and the server it is matched to. We know deterministic algorithms [KP93, KMV94] that achieve a competitive ratio of 2k−1, and this bound is tight for deterministic algorithms. Randomization can be used to overcome this lower bound, and we know O(log 2 k) competitive algorithms [BBGN07] and an Ω(log k) lower bound. The problem has also long been considered in specialized metrics such as the line metric or metrics of bounded doubling dimension, with the current best result on a line metric being a deterministic O(log k) competitive algorithm [Rag18]. Obtaining (or refuting) O(log k)-competitive algorithms in general metrics and constant-competitive algorithms on the line metric have been long-standing open questions in this area.In this paper, we investigate the robustness of these lower bounds by considering the Online Metric Matching with Recourse problem where we are allowed to change a small number of previous assignments upon arrival of a new client. Indeed, we show that a small logarithmic amount of recourse can significantly improve the quality of matchings we can maintain. For general metrics, we show a simple deterministic O(log k)-competitive algorithm with O(log k)-amortized recourse, an exponential improvement over the 2k − 1 lower bound when no recourse is allowed. We next consider the line metric, and present a deterministic algorithm which is 3-competitive and has O(log k)-recourse, again a substantial improvement over the best known O(log k)-competitive algorithm when no recourse is allowed. We finally illustrate another benefit of allowing limited recourse: we can extend the Online Metric Matching model to handle arrivals and departures of both clients and servers (as opposed to just handling arrivals of clients) and still maintain competitive solutions. Indeed, we show a simple randomized O(log n)-competitive algorithm with O(log ∆)-recourse in this fully online setting, where n is the number of points in the metric space and ∆ is the aspect ratio of the underlying metric. Perhaps the most important technical contribution of this work is in showing that these improved results can, in fact, be achieved by suitably equipping a two-decades-old algorithm PERMUTATION for online metric matching with limited recourse.

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Fully-Dynamic Bin Packing with Little Repacking

Cited by 3 publications

References 0 publications

Online Bin Covering with Limited Migration

Online Bin Covering with Limited Migration

Online bin covering with limited migration

PERMUTATION Strikes Back: The Power of Recourse in Online Metric Matching

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