On-line packing and covering problems

Csirik, János; Woeginger, Gerhard J.

doi:10.1007/bfb0029568

Cited by 122 publications

(86 citation statements)

References 80 publications

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“…In the first case, minimizing D w is equivalent to maximizing the number of bins H, such that in each bin h, ∑ i∈B h (r −U i ) ≥ r. This is the classic bin covering problem, or the dual bin packing problem [3,2,7], which is known to be strongly-NP hard [12]. There are polynomial time approximation algorithms [8,9,10].…”

Section: Lemma 4 the Necessary And Sufficient Condition For An Isolamentioning

confidence: 99%

Performance bounds for peer-assisted live streaming

LiuShao

Zhang-ShenRui

JiangWenjie

et al. 2008

SIGMETRICS Perform. Eval. Rev.

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Peer-assisted streaming is a promising way for service providers to offer high-quality IPTV to consumers at reasonable cost. In peerassisted streaming, the peers exchange video chunks with one another, and receive additional data from the central server as needed.In this paper, we analyze how to provision resources for the streaming system, in terms of the server capacity, the video quality, and the depth of the distribution trees that deliver the content. We derive the performance bounds for minimum server load, maximum streaming rate, and minimum tree depth under different peer selection constraints. Furthermore, we show that our performance bounds are actually tight, by presenting algorithms for constructing trees that achieve our bounds.

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Section: Lemma 4 the Necessary And Sufficient Condition For An Isolamentioning

confidence: 99%

Performance bounds for peer-assisted live streaming

LiuShao

Zhang-ShenRui

JiangWenjie

et al. 2008

SIGMETRICS Perform. Eval. Rev.

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“…Bin packing is a classical combinatorial optimization problem that has been studied since the early 70's and different variants continue to attract researchers' attention (see [7,10,12]). It is well known that the problem is NP-hard [14].…”

Section: Introductionmentioning

confidence: 99%

“…Extensive work (see [7,10,12]) has been done in the offline and online settings. In the offline setting, all the items and their sizes are known in advance.…”

Section: Introductionmentioning

confidence: 99%

Online Multi-dimensional Dynamic Bin Packing of Unit-Fraction Items

Burcea

Wong

Yung

2013

Lecture Notes in Computer Science

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Abstract. We study the 2-D and 3-D dynamic bin packing problem, in which items arrive and depart at arbitrary times. The 1-D problem was first studied by Coffman, Garey, and Johnson motivated by the dynamic storage problem. Bar-Noy et al. have studied packing of unit fraction items (i.e., items with length 1/k for some integer k ≥ 1), motivated by the window scheduling problem. In this paper, we extend the study of 2-D and 3-D dynamic bin packing problem to unit fractions items. The objective is to pack the items into unit-sized bins such that the maximum number of bins ever used over all time is minimized. We give a scheme that divides the items into classes and show that applying the First-Fit algorithm to each class is 6.7850-and 21.6108-competitive for 2-D and 3-D, respectively, unit fraction items. This is in contrast to the 7.4842 and 22.4842 competitive ratios for 2-D and 3-D, respectively, that would be obtained using only existing results for unit fraction items.

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“…Bin packing problem has been studied since the early 70's and different variants of the problem continue to attract researchers' attention (see the survey [7,10,11]). In the classical bin packing problem, we want to pack a sequence of items each with size in the range (0, 1] into a minimum number of unit-size bins.…”

Section: Introductionmentioning

confidence: 99%

“…There is a long history of results for the classical bin packing problem and its variants [7,10,11]. Most of the previous works considered "static" bin packing in the sense that items do not depart.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Bin Packing of Unit Fractions Items

Chan¹,

Tak-Wah²,

Wong

2005

Automata, Languages and Programming

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This paper studies the dynamic bin packing problem, in which items arrive and depart at arbitrary time. We want to pack a sequence of unit fractions items (i.e., items with sizes 1/w for some integer w ≥ 1) into unit-size bins such that the maximum number of bins ever used over all time is minimized. Tight and almosttight performance bounds are found for the family of any-fit algorithms, including first-fit, best-fit, and worst-fit. In particular, we show that the competitive ratio of best-fit and worst-fit is 3, which is tight, and the competitive ratio of first-fit lies between 2.45 and 2.4942. We also show that no on-line algorithm is better than 2.428-competitive.

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On-line packing and covering problems

Cited by 122 publications

References 80 publications

Performance bounds for peer-assisted live streaming

Performance bounds for peer-assisted live streaming

Online Multi-dimensional Dynamic Bin Packing of Unit-Fraction Items

Dynamic Bin Packing of Unit Fractions Items

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