منابع مشابه
A note on the lower bound for online strip packing
This note presents a lower bound of 3/2+ √ 33/6 ≈ 2.457 on the competitive ratio for online strip packing. The instance construction we use to obtain the lower bound was first coined by Brown, Baker and Katseff [2]. Recently this instance construction is used to improve the lower bound in computer aided proofs. We derive the best possible lower bound that can be obtained with this instance cons...
متن کاملAn 8/3 Lower Bound for Online Dynamic Bin Packing
We study the dynamic bin packing problem introduced by Coffman, Garey and Johnson. This problem is a generalization of the bin packing problem in which items may arrive and depart dynamically. The objective is to minimize the maximum number of bins used over all time. The main result is a lower bound of 8/3 ∼ 2.666 on the achievable competitive ratio, improving the best known 2.5 lower bound. T...
متن کاملLNCS 7164 - Improved Lower Bound for Online Strip Packing
In the two-dimensional strip packing problem a number of rectangles have to be packed without rotation or overlap into a strip such that the height of the strip used is minimal. The width of the rectangles is bounded by 1 and the strip has width 1 and infinite height. We study the online version of this packing problem. In the online version the rectangles are given to the online algorithm one ...
متن کاملBeating the Harmonic Lower Bound for Online Bin Packing
In the online bin packing problem, items of sizes in (0, 1] arrive online to be packed into bins of size 1. The goal is to minimize the number of used bins. In this paper, we present an online bin packing algorithm with asymptotic performance ratio of 1.5815, which constitutes the first improvement over the algorithm HARMONIC++ in fifteen years and reduces the gap to the lower bound by roughly ...
متن کامل4/3 Rectangle Tiling lower bound
The problem that we consider is the following: given an n × n array A of positive numbers, find a tiling using at most p rectangles (which means that each array element must be covered by some rectangle and no two rectangles must overlap) that minimizes the maximum weight of any rectangle (the weight of a rectangle is the sum of elements which are covered by it). We prove that it is NP-hard to ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Optimization
سال: 2019
ISSN: 1382-6905,1573-2886
DOI: 10.1007/s10878-019-00423-z