A Robust AFPTAS for Online Bin Packing with Polynomial Migration,

نویسندگان

  • Klaus Jansen
  • Kim-Manuel Klein
چکیده

In this paper we develop general LP and ILP techniques to find an approximate solution with improved objective value close to an existing solution. The task of improving an approximate solution is closely related to a classical theorem of Cook et al. [7] in the sensitivity analysis for LPs and ILPs. This result is often applied in designing robust algorithms for online problems. We apply our new techniques to the online bin packing problem, where it is allowed to reassign a certain number of items, measured by the migration factor. The migration factor is defined by the total size of reassigned items divided by the size of the arriving item. We obtain a robust asymptotic fully polynomial time approximation scheme (AFPTAS) for the online bin packing problem with migration factor bounded by a polynomial in 1 . This answers an open question stated by Epstein and Levin [10] in the affirmative. As a byproduct we prove an approximate variant of the sensitivity theorem by Cook at el. [7] for linear programs.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Bin packing with general cost structures

Following the work of Anily et al., we consider a variant of bin packing, called BIN PACKING WITH GENERAL COST STRUCTURES (GCBP) and design an asymptotic fully polynomial time approximation scheme (AFPTAS) for this problem. In the classic bin packing problem, a set of one-dimensional items is to be assigned to subsets of total size at most 1, that is, to be packed into unit sized bins. However,...

متن کامل

AFPTAS results for common variants of bin packing: A new method to handle the small items

We consider two well-known natural variants of bin packing, and show that these packing problemsadmit asymptotic fully polynomial time approximation schemes (AFPTAS). In bin packing problems,a set of one-dimensional items of size at most 1 is to be assigned (packed) to subsets of sum at most1 (bins). It has been known for a while that the most basic problem admits an AFPTAS. In this...

متن کامل

Online Strip Packing with Polynomial Migration

We consider the relaxed online strip packing problem, where rectangular items arrive online and have to be packed into a strip of fixed width such that the packing height is minimized. Thereby, repacking of previously packed items is allowed. The amount of repacking is measured by the migration factor, defined as the total size of repacked items divided by the size of the arriving item. First, ...

متن کامل

Fully Dynamic Bin Packing Revisited

We consider the fully dynamic bin packing problem, where items arrive and depart in an online fashion. The goal is to minimize the number of used bins at every timestep while repacking of already packed items is allowed. Ivković and Lloyd [IL98] have developed an algorithm with asymptotic competitive ratio of 5/4 using O(log n) (amortized) shifting moves whenever an item is inserted or removed ...

متن کامل

Asymptotic fully polynomial approximation schemes for variants of open-end bin packing

We consider three variants of the open-end bin packing problem. Such variants of bin packing allow the total size of items packed into a bin to exceed the capacity of a bin, provided that a removal of the last item assigned to a bin would bring the contents of the bin below the capacity. In the first variant, this last item is the minimum sized item in the bin, that is, each bin must satisfy th...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013