An Optimal Online Algorithm for Bounded Space Variable-Sized Bin Packing

2000 ◽  
pp. 283-295 ◽  
Author(s):  
Steven S. Seiden
Keyword(s):  
Online Algorithm ◽  
Bin Packing ◽  
Space Variable ◽  
Bounded Space

Which Algorithm for Scheduling Add-on Elective Cases Maximizes Operating Room Utilization? 

1999 ◽  
Vol 91 (5) ◽  
pp. 1491-1491 ◽  
Author(s):  
Franklin Dexter ◽  
Alex Macario ◽  
Rodney D. Traub
Keyword(s):  
Information System ◽  
Operating Room ◽  
Bin Packing ◽  
Space Variable ◽  
Fuzzy Constraints ◽  
Surgical Services ◽  
Open Time ◽  
Bounded Space ◽  
Utilization Time ◽  
Best Fit

Background The algorithm to schedule add-on elective cases that maximizes operating room (OR) suite utilization is unknown. The goal of this study was to use computer simulation to evaluate 10 scheduling algorithms described in the management sciences literature to determine their relative performance at scheduling as many hours of add-on elective cases as possible into open OR time. Methods From a surgical services information system for two separate surgical suites, the authors collected these data: (1) hours of open OR time available for add-on cases in each OR each day and (2) duration of each add-on case. These empirical data were used in computer simulations of case scheduling to compare algorithms appropriate for "variable-sized bin packing with bounded space." "Variable size" refers to differing amounts of open time in each "bin," or OR. The end point of the simulations was OR utilization (time an OR was used divided by the time the OR was available). Results Each day there were 0.24 +/- 0.11 and 0.28 +/- 0.23 simulated cases (mean +/- SD) scheduled to each OR in each of the two surgical suites. The algorithm that maximized OR utilization, Best Fit Descending with fuzzy constraints, achieved OR utilizations 4% larger than the algorithm with poorest performance. Conclusions We identified the algorithm for scheduling add-on elective cases that maximizes OR utilization for surgical suites that usually have zero or one add-on elective case in each OR. The ease of implementation of the algorithm, either manually or in an OR information system, needs to be studied.

ONE-SPACE BOUNDED ALGORITHMS FOR TWO-DIMENSIONAL BIN PACKING

2010 ◽  
Vol 21 (06) ◽  
pp. 875-891 ◽  
Author(s):  
FRANCIS Y. L. CHIN ◽  
HING-FUNG TING ◽  
YONG ZHANG
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Bin Packing ◽  
Two Dimensional ◽  
Unit Square ◽  
Competitive Algorithm ◽  
Previous Time ◽  
Bounded Space ◽  
Over Time

In this paper, we study the bounded space variation, especially one-space bounded, of two-dimensional bin packing. A sequence of rectangular items arrive over time, and the following item arrives after the packing of the previous one. The height and width of each item are no more than 1, we need to pack these items into unit square bins of size 1 × 1 where rotation of 90° is allowed and our objective is to minimize the number of used bins. Once an item is packed into a square bin, the position of this item is fixed and it cannot be shifted within this bin. At any time, there is at most one active bin; the current unpacked item can be only packed into the active bin and the inactive bins (closed at some previous time) cannot be used for any future items. We first propose an online algorithm with a constant competitive ratio 12, then improve the competitive ratio to 8.84 by the some complicated analysis. Our results significantly improve the previous best known O(( log log m)2)-competitive algorithm [10], where m is the width of the square bin and the size of each item is a × b, where a, b are integers no more than m. Furthermore, the lower bound for the competitive ratio is also improved to 2.5.

Resource augmentation for online bounded space bin packing

2002 ◽  
Vol 44 (2) ◽  
pp. 308-320 ◽  
Author(s):  
János Csirik ◽  
Gerhard J. Woeginger
Keyword(s):  
Bin Packing ◽  
Resource Augmentation ◽  
Bounded Space

scholarly journals Improved Space for Bounded-Space, On-Line Bin-Packing

1993 ◽  
Vol 6 (4) ◽  
pp. 575-581 ◽  
Author(s):  
Gerhard Woeginger
Keyword(s):  
Bin Packing ◽  
On Line ◽  
Bounded Space

Two-Bounded-Space Bin Packing Revisited

2011 ◽  
pp. 263-274 ◽  
Author(s):  
Marek Chrobak ◽  
Jiří Sgall ◽  
Gerhard J. Woeginger
Keyword(s):  
Bin Packing ◽  
Bounded Space

scholarly journals Resource augmented semi-online bounded space bin packing

2009 ◽  
Vol 157 (13) ◽  
pp. 2785-2798 ◽  
Author(s):  
Leah Epstein ◽  
Elena Kleiman
Keyword(s):  
Bin Packing ◽  
Bounded Space

Tight bounds for NF-based bounded-space online bin packing algorithms

2017 ◽  
Vol 35 (2) ◽  
pp. 350-364
Author(s):  
József Békési ◽  
Gábor Galambos
Keyword(s):  
Bin Packing ◽  
Bounded Space

scholarly journals A tight lower bound for the online bounded space hypercube bin packing problem

2021 ◽  
Vol vol. 23, no. 3 (Discrete Algorithms) ◽  
Author(s):  
Yoshiharu Kohayakawa ◽  
Flávio Keidi Miyazawa ◽  
Yoshiko Wakabayashi
Keyword(s):  
Lower Bound ◽  
Bin Packing ◽  
Packing Problem ◽  
Performance Ratio ◽  
Asymptotic Performance ◽  
Bin Packing Problem ◽  
Bounded Space ◽  
Space Variant

In the $d$-dimensional hypercube bin packing problem, a given list of $d$-dimensional hypercubes must be packed into the smallest number of hypercube bins. Epstein and van Stee [SIAM J. Comput. 35 (2005)] showed that the asymptotic performance ratio $\rho$ of the online bounded space variant is $\Omega(\log d)$ and $O(d/\log d)$, and conjectured that it is $\Theta(\log d)$. We show that $\rho$ is in fact $\Theta(d/\log d)$, using probabilistic arguments.

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