Improved lower bounds for the online bin stretching problem
نویسندگان
چکیده
We use game theory techniques to automatically compute improved lower bounds on the competitive ratio for the bin stretching problem. Using these techniques, we improve the best lower bound for this problem to 19/14. We explain the technique and show that it can be generalized to compute lower bounds for any online or semi-online packing or scheduling problem. We also present a lower bound, with value 7/6, on the expected competitive ratio of randomized algorithms for the bin stretching problem.
منابع مشابه
Lower Bounds for Online Bin Stretching with Several Bins
Online Bin Stretching is a semi-online variant of Bin Packing with a set number of m bins, where all bins can be overpacked to capacity S ≥ 1, which is to be minimized. There is also a guarantee that an offline algorithm can pack the input to m bins of unit size. We focus on the problem of Online Bin Stretching for small m, namely 3 ≤ m ≤ 5. Recent progress on this problem has led into a lower ...
متن کاملImproved Lower Bounds for the Online Bin Packing Problem with Cardinality Constraints
The bin packing problem has been extensively studied and numerous variants have been considered. The k-item bin packing problem is one of the variants introduced by Krause et al. in Journal of the ACM 22(4). In addition to the formulation of the classical bin packing problem, this problem imposes a cardinality constraint that the number of items packed into each bin must be at most k. For the o...
متن کاملLower bounds for several online variants of bin packing
We consider several previously studied online variants of bin packing and prove new and improved lower bounds on the asymptotic competitive ratios for them. For that, we use a method of fully adaptive constructions. In particular, we improve the lower bound for the asymptotic competitive ratio of online square packing significantly, raising it from roughly 1.68 to above 1.75.
متن کاملThe Best Two-Phase Algorithm for Bin Stretching
Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin. We give an algorithm for Online Bin Stretching with a stretching factor of 1.5 for any number of bins. We build o...
متن کاملOn-Line Bin-Stretching
We are given a sequence of items that can be packed into m unit size bins. In the classical bin packing problem we x the size of the bins and try to pack the items in the minimum number of such bins. In contrast, in the bin-stretching problem we x the number of bins and try to pack the items while stretching the size of the bins as least as possible. We present two on-line algorithms for the bi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- 4OR
دوره 15 شماره
صفحات -
تاریخ انتشار 2017