4 research outputs found
Improved online hypercube packing
In this paper, we study online multidimensional bin packing problem when all
items are hypercubes.
Based on the techniques in one dimensional bin packing algorithm Super
Harmonic by Seiden, we give a framework for online hypercube packing problem
and obtain new upper bounds of asymptotic competitive ratios.
For square packing, we get an upper bound of 2.1439, which is better than
2.24437.
For cube packing, we also give a new upper bound 2.6852 which is better than
2.9421 by Epstein and van Stee.Comment: 13 pages, one figure, accepted in WAOA'0
On Two Dimensional Orthogonal Knapsack Problem
In this paper, we study the following knapsack problem: Given a list of
squares with profits, we are requested to pack a sublist of them into a
rectangular bin (not a unit square bin) to make profits in the bin as large as
possible. We first observe there is a Polynomial Time Approximation Scheme
(PTAS) for the problem of packing weighted squares into rectangular bins with
large resources, then apply the PTAS to the problem of packing squares with
profits into a rectangular bin and get a approximation
algorithm
A New Upper Bound on 2D Online Bin Packing
The 2D Online Bin Packing is a fundamental problem in Computer Science and
the determination of its asymptotic competitive ratio has attracted great
research attention. In a long series of papers, the lower bound of this ratio
has been improved from 1.808, 1.856 to 1.907 and its upper bound reduced from
3.25, 3.0625, 2.8596, 2.7834 to 2.66013. In this paper, we rewrite the upper
bound record to 2.5545. Our idea for the improvement is as follows. In SODA
2002 \cite{SS03}, Seiden and van Stee proposed an elegant algorithm called , comprised of the {\em Harmonic algorithm} and the {\em Improved
Harmonic algorithm} , for the two-dimensional online bin packing problem and
proved that the algorithm has an asymptotic competitive ratio of at most
2.66013. Since the best known online algorithm for one-dimensional bin packing
is the {\em Super Harmonic algorithm} \cite{S02}, a natural question to ask is:
could a better upper bound be achieved by using the Super Harmonic algorithm
instead of the Improved Harmonic algorithm? However, as mentioned in
\cite{SS03}, the previous analysis framework does not work. In this paper, we
give a positive answer for the above question. A new upper bound of 2.5545 is
obtained for 2-dimensional online bin packing. The main idea is to develop new
weighting functions for the Super Harmonic algorithm and propose new techniques
to bound the total weight in a rectangular bin
Improved Online Hypercube Packing
Abstract. In this paper, we study online multidimensional bin packing problem when all items are hypercubes. Based on the techniques in one dimensional bin packing algorithm Super Harmonic by Seiden, we give a framework for online hypercube packing problem and obtain new upper bounds of asymptotic competitive ratios. For square packing, we get an upper bound of 2.1439, which is better than 2.24437. For cube packing, we also give a new upper bound 2.6852 which is better than 2.9421 by Epstein and van Stee