DeepAI
Log In Sign Up

Parallel Online Algorithms for the Bin Packing Problem

10/08/2019
by   Sandor P. Fekete, et al.
0

We study parallel online algorithms: For some fixed integer k, a collective of k parallel processes that perform online decisions on the same sequence of events forms a k-copy algorithm. For any given time and input sequence, the overall performance is determined by the best of the k individual total results. Problems of this type have been considered for online makespan minimization; they are also related to optimization with advice on future events, i.e., a number of bits available in advance. We develop Predictive Harmonic_3 (PH3), a relatively simple family of k-copy algorithms for the online Bin Packing Problem, whose joint competitive factor converges to 1.5 for increasing k. In particular, we show that k=6 suffices to guarantee a factor of 1.5714 for PH3, which is better than 1.57829, the performance of the best known 1-copy algorithm Advanced Harmonic, while k=11 suffices to achieve a factor of 1.5406, beating the known lower bound of 1.54278 for a single online algorithm. In the context of online optimization with advice, our approach implies that 4 bits suffice to achieve a factor better than this bound of 1.54278, which is considerably less than the previous bound of 15 bits.

READ FULL TEXT

page 1

page 2

page 3

page 4

04/30/2019

Online Bin Covering with Advice

The bin covering problem asks for covering a maximum number of bins with...
05/20/2019

Robust Online Algorithms for Dynamic Problems

Online algorithms that allow a small amount of migration or recourse hav...
12/07/2021

Online Sorting and Translational Packing of Convex Polygons

We investigate various online packing problems in which convex polygons ...
12/06/2021

Online Bin Packing with Known T

In the online bin packing problem, a sequence of items is revealed one a...
02/13/2018

Quantum Online Streaming Algorithms with Constant Number of Advice Bits

Online algorithms are known model that is investigated with respect to a...
10/08/2020

Isometric and affine copies of a set in volumetric Helly results

We show that for any compact convex set K in ℝ^d and any finite family ℱ...