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The Relative Worst Order Ratio for On-Line Algorithms [chapter]

Joan Boyar, Lene M. Favrholdt
2003 Lecture Notes in Computer Science  
Many of our results are consistent with those previously obtained with the competitive ratio or the competitive ratio on accommodating sequences, but new separations and easier proofs are found.  ...  The new ratio is used to compare on-line algorithms directly by taking the ratio of their performances on their respective worst permutations of a worst-case sequence.  ...  We would also like to thank the anonymous referees for useful comments, especially the referee who noted that the proof of Lemma 3.5 depended on Harmonic k using Next-Fit and asked about the possibility  ... 
doi:10.1007/3-540-44849-7_13 fatcat:4v4zoyyxqrdundqu7pskd5pi2a

The relative worst order ratio for online algorithms

Joan Boyar, Lene M. Favrholdt
2007 ACM Transactions on Algorithms  
Many of our results are consistent with those previously obtained with the competitive ratio or the competitive ratio on accommodating sequences, but new separations and easier proofs are found.  ...  The new ratio is used to compare on-line algorithms directly by taking the ratio of their performances on their respective worst permutations of a worst-case sequence.  ...  We would also like to thank the anonymous referees for useful comments, especially the referee who noted that the proof of Lemma 3.5 depended on Harmonic k using Next-Fit and asked about the possibility  ... 
doi:10.1145/1240233.1240245 fatcat:bfwwy6wjebhhtd5t6zjs556dmq

On-Line Maximizing the Number of Items Packed in Variable-Sized Bins [chapter]

Leah Epstein, Lene M. Favrholdt
2002 Lecture Notes in Computer Science  
We study an on-line bin packing problem. A xed number n of bins, possibly of di erent sizes, are given. The items arrive on-line, and the goal is to pack as many items as possible.  ...  It is known that there exists a legal packing of the whole sequence in the n bins. We consider fair algorithms that reject an item, only if it does not t in the empty space of any bin.  ...  Acknowledgment: We would like to thank Joan Boyar for reading and commenting on the paper. We also thank the editor Gerhard Woeginger for suggesting the title.  ... 
doi:10.1007/3-540-45655-4_50 fatcat:5c3mdkwv45depacu6gu4ae2ide

Online Bin Covering: Expectations vs. Guarantees [article]

Marie G. Christ, Lene M. Favrholdt, Kim S. Larsen
2014 arXiv   pre-print
We make the case that when guarantees are needed, even under restricted input sequences, dual Harmonic is preferable.  ...  Bin covering is a dual version of classic bin packing. Thus, the goal is to cover as many bins as possible, where covering a bin means packing items of total size at least one in the bin.  ...  Introduction Bin covering [2] is a dual version of classic bin packing. As usual, bins have size one and items with sizes between zero and one must be packed.  ... 
arXiv:1309.6477v2 fatcat:pkta4aetm5deha4wsvg6mmqcay

Page 1302 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
(DK-SU-CS; Odense) The competitive ratio for on-line dual bin packing with restricted input sequences. (English summary) Nordic J. Comput. 8 (2001), no. 4, 463-472.  ...  Summary: “We consider the on-line dual bin packing problem where we have a fixed number n of bins of equal size and a sequence of items.  ... 

Beating the Harmonic lower bound for online bin packing [article]

Sandy Heydrich, Rob van Stee
2018 arXiv   pre-print
We show that for each input, a single weighting function can be constructed to upper bound the competitive ratio on it.  ...  In this paper, we present an online bin packing algorithm with asymptotic competitive ratio of 1.5813. This is the first improvement in fifteen years and reduces the gap to the lower bound by 15%.  ...  Acknowledgements We thank the anonymous referees for their useful comments, and Leah Epstein for interesting discussions.  ... 
arXiv:1511.00876v7 fatcat:zsdb2rszbjdfblozkfrj3cpjx4

Lower bounds on the performance of online algorithms for relaxed packing problems [article]

János Balogh, György Dósa, Leah Epstein, Łukasz Jeż
2022 arXiv   pre-print
On the other hand, in the removable knapsack problem there is a fixed number of bins, and the goal of packing items, which consists in choosing a particular bin for every packed item (and nothing else)  ...  We prove new lower bounds for suitable competitive ratio measures of two relaxed online packing problems: online removable multiple knapsack, and a recently introduced online minimum peak appointment scheduling  ...  [9, 7] extended this to the sum of values of all the items packed, which is in line with dual bin packing.  ... 
arXiv:2201.05999v1 fatcat:qwcbxeyrszddbhutjnzmad7oze

Beating the Harmonic Lower Bound for Online Bin Packing

Sandy Heydrich, Rob Van Stee, Marc Herbstritt
2016 International Colloquium on Automata, Languages and Programming  
We consider the dual, eliminate all but one variable and then solve it with the ellipsoid method using a separation oracle.  ...  In particular, for item pairs where the size of one item is in (1/3, 1/2] and the other is larger than 1/2 (a large item), when deciding whether to pack such a pair together in one bin, our algorithm does  ...  Acknowledgements We thank the anonymous referees for their useful comments. S. Heydrich and R. van Stee XXX: 13  ... 
doi:10.4230/lipics.icalp.2016.41 dblp:conf/icalp/HeydrichS16 fatcat:ldwyciochzejjgt7x3oncfyqoy

Relative Worst-Order Analysis: A Survey [article]

Joan Boyar, Lene M. Favrholdt, Kim S. Larsen
2018 arXiv   pre-print
Relative worst-order analysis is a technique for assessing the relative quality of online algorithms.  ...  We survey the most important results obtained with this technique and compare it with other quality measures.  ...  Acknowledgment The authors would like to thank an anonymous referee for many constructive suggestions.  ... 
arXiv:1802.07080v1 fatcat:ujbc2hdh35eqbjmh3hhmokh77m

Relative Worst-Order Analysis: A Survey [chapter]

Joan Boyar, Lene M. Favrholdt, Kim S. Larsen
2018 Lecture Notes in Computer Science  
Relative worst-order analysis is a technique for assessing the relative quality of online algorithms.  ...  We survey the most important results obtained with this technique and compare it with other quality measures.  ...  Acknowledgment The authors would like to thank an anonymous referee for many constructive suggestions.  ... 
doi:10.1007/978-3-319-98355-4_13 fatcat:4ebcicsqtjfxbnhuh5ko32skg4

Probabilistic Analysis of the Dual Next-Fit Algorithm for Bin Covering [article]

Carsten Fischer, Heiko Röglin
2015 arXiv   pre-print
We study the simplest possible online algorithm Dual Next-Fit, which packs all arriving items into the same bin until it is filled and then proceeds with the next bin in the same manner.  ...  Finally, we prove that the expected competitive ratio equals, for a large class of distributions, the random-order ratio, which is the expected competitive ratio when adversarially chosen items arrive  ...  Similarly we show that for proving a lower bound on the random order ratio of DNF it suffices to consider sequences of items that can be packed with waste zero.  ... 
arXiv:1512.04719v1 fatcat:ohtcgbgf2zdt3oxk753cqfrpve

Online Square Packing [article]

Sandor P. Fekete, Tom Kamphans, Nils Schweer
2010 arXiv   pre-print
"hang in the air") based on ideas of shelf-packing: Squares are assigned to different horizontal levels, allowing an analysis that is reminiscent of some bin-packing arguments.  ...  We analyze the problem of packing squares in an online fashion: Given a semi-infinite strip of width 1 and an unknown sequence of squares of side length in [0,1] that arrive from above, one at a time.  ...  Hence, all negative results for the bin packing problem, e.g., NP-hardness and lower bounds on the competitive ratio also hold for the strip packing problem; see [15] for a survey on (online) bin packing  ... 
arXiv:1010.4502v1 fatcat:4xpsshucc5emvhjwvc2kyzut3i

Online Knapsack Revisited [chapter]

Marek Cygan, Łukasz Jeż
2014 Lecture Notes in Computer Science  
Dual Bin Packing [1, 6] in case of the sum and Removable Knapsack [10, 11] in case of the maximum.  ...  the date of receipt and acceptance should be inserted later Keywords online algorithms · competitive analysis · online knapsack · dual bin packing CR Subject Classification Theory of computation/Design  ...  Acknowledgements We thank Monaldo Mastrolilli for suggesting the study of knapsack problems, Fabrizio Grandoni for suggesting the study of the sum objective, Yann Disser for helpful discussions, and anonymous  ... 
doi:10.1007/978-3-319-08001-7_13 fatcat:njn52trxenaj3db7qjissvrnam

Online Knapsack Revisited

Marek Cygan, Łukasz Jeż, Jiří Sgall
2014 Theory of Computing Systems  
Dual Bin Packing [1, 6] in case of the sum and Removable Knapsack [10, 11] in case of the maximum.  ...  the date of receipt and acceptance should be inserted later Keywords online algorithms · competitive analysis · online knapsack · dual bin packing CR Subject Classification Theory of computation/Design  ...  Acknowledgements We thank Monaldo Mastrolilli for suggesting the study of knapsack problems, Fabrizio Grandoni for suggesting the study of the sum objective, Yann Disser for helpful discussions, and anonymous  ... 
doi:10.1007/s00224-014-9566-4 fatcat:74zchhp7qvd5dcs6zmc7g3iwti

Fully-Dynamic Bin Packing with Limited Repacking [article]

Anupam Gupta, Guru Guruganesh, Amit Kumar, David Wajc
2018 arXiv   pre-print
We want algorithms with low asymptotic competitive ratio while repacking items sparingly between updates.  ...  We study the classic Bin Packing problem in a fully-dynamic setting, where new items can arrive and old items may depart.  ...  For any ε > 0 and 1 2 > δ > 0, for any algorithm A with a.c.r (α − ε) with additive term o(ε · n δ ), there exists an dynamic bin packing input with n items on which A uses recourse at least Ω(ε 2 · n  ... 
arXiv:1711.02078v3 fatcat:t4xpjeial5b6hjc7q5aat73xxe
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