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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
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  ...  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)  ...  Our results In this work, we prove the following lower bounds on the performance of online algorithms: • A lower bound of 1.2287 on the competitive ratio for deterministic algorithms for either the proportional  ... 
arXiv:2201.05999v1 fatcat:qwcbxeyrszddbhutjnzmad7oze

New Bounds for Variable-Sized Online Bin Packing

Steven S. Seiden, Rob van Stee, Leah Epstein
2003 SIAM journal on computing (Print)  
We present new algorithms for this problem and show upper bounds for them which improve on the best previous upper bounds. We also show the first general lower bounds for this problem.  ...  In the variable-sized online bin packing problem, one has to assign items to bins one by one.  ...  on the asymptotic performance ratio of any online bin packing algorithm.  ... 
doi:10.1137/s0097539702412908 fatcat:j5gd6dyce5e7fe4fczldqv3z2q

Online Bin Packing with Known T [article]

Shang Liu, Xiaocheng Li
2021 arXiv   pre-print
In the online bin packing problem, a sequence of items is revealed one at a time, and each item must be packed into an available bin instantly upon its arrival.  ...  For the latter one, our analysis provides an alternative (probably simpler) treatment and tightens the analysis of the asymptotic benchmark of the stochastic bin packing problem in Rhee and Talagrand (  ...  Another stream of literature on online bin packing takes an algorithm-centric perspective and ana- lyzes the performance of certain heuristic algorithms.  ... 
arXiv:2112.03200v1 fatcat:37nelr2365ftrkvscqaoyk5rby

Online Multidimensional Packing Problems in the Random-Order Model

David Naori, Danny Raz, Michael Wagner
2019 International Symposium on Algorithms and Computation  
Furthermore, our algorithm improves upon the best-known competitive-ratio for the online (one-dimensional) generalized assignment problem and the online knapsack problem.  ...  ACM Subject Classification Theory of computation → Packing and covering problems; Theory of computation → Online algorithms  ...  For the one-dimensional case, the best lower bound for the online GAP is derived from the lower bound for the secretary problem of e [6] .  ... 
doi:10.4230/lipics.isaac.2019.10 dblp:conf/isaac/NaoriR19 fatcat:nynljwfm7rghbd4e6umutmkz44

Seller-Focused Algorithms for Online Auctioning [chapter]

Amitabha Bagchi, Amitabh Chaudhary, Rahul Garg, Michael T. Goodrich, Vijay Kumar
2001 Lecture Notes in Computer Science  
We show that this algorithm is optimal in the worst-case and that it performs significantly better than any worst-case bounds achievable via deterministic strategies.  ...  In this paper we provide an algorithmic approach to the study of online auctioning.  ...  The authors would like to thank Leslie Hall and two anonymous referees.  ... 
doi:10.1007/3-540-44634-6_13 fatcat:dufbsprugnbfnkxmaaryucvbdi

Online bin packing with resource augmentation

Leah Epstein, Rob van Stee
2007 Discrete Optimization  
We give new algorithms for this problem that combine items in bins in an unusual way, and give bounds on their performance which improve upon the best possible bounded space algorithm.  ...  We also give general lower bounds for this problem which are nearly matching for bin sizes b ≥ 2.  ...  The second author's research was supported by the Netherlands Organization for Scientific Research (NWO), project number SION 612-061-000.  ... 
doi:10.1016/j.disopt.2007.09.004 fatcat:w2aewq4iqvhxjj7hpqofkpzw3e

Improved lower bounds for semi-online bin packing problems

János Balogh, József Békési, Gábor Galambos, Mihály Csaba Markót
2009 Computing  
In the paper we deal with lower bounds constructed for the asymptotic competitive ratio of semi-online bin packing and batched bin packing algorithms.  ...  Our results improve the lower bounds given in [10] for some special cases of the batched bin packing problem.  ...  The asymptotic performance ratio (APR) of the algorithm A is R A := lim sup m→∞ max A(L) m | OPT(L) = m . (1) The best known lower bound for the APR of any online bin packing algorithm A is 1.54014 [21  ... 
doi:10.1007/s00607-008-0023-6 fatcat:ndqd4gupdjfixeqxcl6xnenlra

Page 3916 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
In Section 4, the authors point out the lower bound of the worst-case performance ratio of RH and give the average- case performance ratio under (0, 1] uniform distribution.  ...  analysis and improvement for some linear on-line bin-packing algorithms.  ... 

Online Bin Packing with Resource Augmentation [chapter]

Leah Epstein, Rob van Stee
2005 Lecture Notes in Computer Science  
We give new algorithms for this problem that combine items in bins in an unusual way, and give bounds on their performance which improve upon the best possible bounded space algorithm.  ...  We also give general lower bounds for this problem which are nearly matching for bin sizes b ≥ 2.  ...  The second author's research was supported by the Netherlands Organization for Scientific Research (NWO), project number SION 612-061-000.  ... 
doi:10.1007/978-3-540-31833-0_4 fatcat:ipwyqwtjivgt7mqrrsnmxwnhye

Algorithms for the Relaxed Online Bin-Packing Model

Giorgio Gambosi, Alberto Postiglione, Maurizio Talamo
2000 SIAM journal on computing (Print)  
Both algorithms are below the theoretical 1.536 . . . lower bound, effective for the online binpacking algorithms without the movement of elements.  ...  In this paper, first of all, the "Relaxed" online bin-packing model will be formalized; this model allows a constant number of elements to move from one bin to another, as a consequence of the arrival  ...  We also wish to thank Lucio Bianco of CNR IASI, Rome, for suggesting the transportation applications.  ... 
doi:10.1137/s0097539799180408 fatcat:zr52f4ab65e6dejoxi5czkunfm

Two-Bounded-Space Bin Packing Revisited [chapter]

Marek Chrobak, Jiří Sgall, Gerhard J. Woeginger
2011 Lecture Notes in Computer Science  
We analyze approximation algorithms for bounded-space bin packing by comparing them against the optimal bounded-space packing (instead of comparing them against the globally optimal packing that does not  ...  For 2-boundedspace bin packing we construct a polynomial time offline approximation algorithm with asymptotic worst case ratio 3/2, and we show a lower bound of 5/4 for this scenario.  ...  An asymptotic lower bound for online algorithms Throughout this section we will consider an arbitrary online bin packing algorithm ON that uses 2-bounded space.  ... 
doi:10.1007/978-3-642-23719-5_23 fatcat:hpt4gqzaqjc6llgqpd2p4zg53m

Fast Approximation Methods for Online Scheduling of Outpatient Procedure Centers

Bjorn P. Berg, Brian T. Denton
2017 INFORMS journal on computing  
Motivated by the health care delivery application of dynamically allocating patients to procedure rooms in outpatient procedure centers, the online stochastic extensible bin packing problem is described  ...  Numerical results based on a real outpatient procedure center demonstrate the favorable results of the list-based approximations based on their average and worst case performances.  ...  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF.  ... 
doi:10.1287/ijoc.2017.0750 fatcat:bqjp3r6nxzetvh34yji6qpx434

Bounds for online bounded space hypercube packing

Leah Epstein, Rob van Stee
2007 Discrete Optimization  
We present lower and upper bounds for online bounded space hypercube packing in dimensions 2, . . . , 7.  ...  Items arrive online and each item must be placed within its bin without overlapping with other items in that bin. The goal is to minimize the total number of bins used.  ...  Let O be some class of box packing algorithms (for instance online algorithms or bounded space online algorithms).  ... 
doi:10.1016/j.disopt.2006.11.005 fatcat:h5i3n24fmzdjrg3bubn6yebfka

Scalable Relaxations of Sparse Packing Constraints: Optimal Biocontrol in Predator-Prey Network [article]

Johan Bjorck, Yiwei Bai, Xiaojian Wu, Yexiang Xue, Mark C. Whitmore, Carla Gomes
2018 arXiv   pre-print
Our algorithm outperforms competing methods in terms of scalability and solution quality, and finds near optimal strategies for the control of the HWA for fine-grained networks -- an important problem  ...  Available methods based on continuous relaxations scale poorly, to remedy this we develop a novel and scalable randomized algorithm based on a width relaxation, applicable to a broad class of combinatorial  ...  This research was supported by the National Science Foundation (CCF-1522054 and CNS-1059284), New York State Department of Environmental Conservation (Award C008698 among others) and USDA Forest Service  ... 
arXiv:1711.06800v3 fatcat:xy7lgl255zfpheekhdfbhcwzem

Chance-Constrained Binary Packing Problems

Yongjia Song, James R. Luedtke, Simge Küçükyavuz
2014 INFORMS journal on computing  
We consider a class of packing problems with uncertain data, which we refer to as the chance-constrained binary packing problem.  ...  We derive a computationally efficient coefficient strengthening procedure for this formulation, and demonstrate how the scenario variables can be efficiently projected out of the linear programming relaxation  ...  Specifically, to obtain an upper bound on ζ π j (k), for each row i = 1, 2, . . . , m we apply one step of Algorithm 1 to obtain the optimal value, ζ i π j (k), of the single-row problem (14) with a k  ... 
doi:10.1287/ijoc.2014.0595 fatcat:sugbkswexzeh3kcijyrimk3x4u
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