Variable-Sized Bin Packing: Tight Absolute Worst-Case Performance Ratios for Four Approximation Algorithms

2001 ◽  
Vol 30 (6) ◽  
pp. 2069-2083 ◽  
Author(s):  
Chengbin Chu ◽  
Rémy La
Keyword(s):  
Approximation Algorithms ◽  
Bin Packing ◽  
Worst Case

scholarly journals Worst case bin packing for OTN electrical layer networks dimensioning

2011 ◽  
Author(s):  
Tamas Kiraly ◽  
Attila Bernath ◽  
Laszlo Vegh ◽  
Lajos Bajzik ◽  
Erika Kovacs ◽  
...  
Keyword(s):  
Bin Packing ◽  
Worst Case ◽  
Electrical Layer

APPROXIMATION ALGORITHMS FOR A VARIANT OF DISCRETE PIERCING SET PROBLEM FOR UNIT DISKS

2013 ◽  
Vol 23 (06) ◽  
pp. 461-477 ◽  
Author(s):  
MINATI DE ◽  
GAUTAM K. DAS ◽  
PAZ CARMI ◽  
SUBHAS C. NANDY
Keyword(s):  
Approximation Algorithms ◽  
Simple Algorithm ◽  
Constant Factor ◽  
Performance Ratio ◽  
Approximation Result ◽  
Worst Case ◽  
Approximation Factor ◽  
Minimum Number ◽  
Unit Disks ◽  
Set Of Points

In this paper, we consider constant factor approximation algorithms for a variant of the discrete piercing set problem for unit disks. Here a set of points P is given; the objective is to choose minimum number of points in P to pierce the unit disks centered at all the points in P. We first propose a very simple algorithm that produces 12-approximation result in O(n log n) time. Next, we improve the approximation factor to 4 and then to 3. The worst case running time of these algorithms are O(n8 log n) and O(n15 log n) respectively. Apart from the space required for storing the input, the extra work-space requirement for each of these algorithms is O(1). Finally, we propose a PTAS for the same problem. Given a positive integer k, it can produce a solution with performance ratio [Formula: see text] in nO(k) time.

scholarly journals A-shaped bin packing: Worst case analysis via simulation

2005 ◽  
Vol 1 (3) ◽  
pp. 323-335
Author(s):  
Wenxun Xing ◽  
◽  
Feng Chen ◽  
Keyword(s):  
Bin Packing ◽  
Case Analysis ◽  
Worst Case Analysis ◽  
Worst Case

Alleviating the Thrashing by Adding Medium- Term Scheduler

2010 ◽  
pp. 118-136
Author(s):  
Moses Reuven ◽  
Yair Wiseman
Keyword(s):  
Operating System ◽  
Approximation Algorithms ◽  
Shared Memory ◽  
Bin Packing ◽  
Memory Capacity ◽  
Substantial Improvement ◽  
Experimental Results ◽  
Memory Usage ◽  
Medium Term ◽  
Short Term

A technique for minimizing the paging on a system with a very heavy memory usage is proposed. When there are processes with active memory allocations that should be in the physical memory, but their accumulated size exceeds the physical memory capacity. In such cases, the operating system begins swapping pages in and out the memory on every context switch. The authors lessen this thrashing by placing the processes into several bins, using Bin Packing approximation algorithms. They amend the scheduler to maintain two levels of scheduling - medium-term scheduling and short-term scheduling. The mediumterm scheduler switches the bins in a Round-Robin manner, whereas the short-term scheduler uses the standard Linux scheduler to schedule the processes in each bin. The authors prove that this feature does not necessitate adjustments in the shared memory maintenance. In addition, they explain how to modify the new scheduler to be compatible with some elements of the original scheduler like priority and realtime privileges. Experimental results show substantial improvement on very loaded memories.

GENERALIZED FIRST-FIT ALGORITHMS IN TWO AND THREE DIMENSIONS

1990 ◽  
Vol 01 (02) ◽  
pp. 131-150 ◽  
Author(s):  
KEQIN LI ◽  
KAM-HOI CHENG
Keyword(s):  
Bin Packing ◽  
Three Dimensional ◽  
Packing Problem ◽  
Three Dimensions ◽  
Performance Ratio ◽  
Dimensional Case ◽  
Performance Bound ◽  
Worst Case ◽  
Packing Problems ◽  
The One

We investigate the two and three dimensional bin packing problems, i.e., packing a list of rectangles (boxes) into unit square (cube) bins so that the number of bins used is a minimum. A simple on-line packing algorithm for the one dimensional bin packing problem, the First-Fit algorithm, is generalized to two and three dimensions. We first give an algorithm for the two dimensional case and show that its asymptotic worse case performance ratio is [Formula: see text]. The algorithm is then generalized to the three dimensional case and its performance ratio [Formula: see text]. The second algorithm takes a parameter and we prove that by choosing the parameter properly, it has an asymptotic worst case performance bound which can be made as close as desired to 1.72=2.89 and 1.73=4.913 respectively in two and three dimensions.

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