Locality-preserving allocations problems and coloured bin packing
نویسندگان
چکیده
We study the following problem, introduced by Chung et al. in 2006. We are given, online or offline, a set of coloured items of different sizes, and wish to pack them into bins of equal size so that we use few bins in total (at most α times optimal), and that the items of each colour span few bins (at most β times optimal). We call such allocations (α, β)-approximate. As usual in bin packing problems, we allow additive constants and consider (α, β) as the asymptotic performance ratios. We prove that for ε > 0, if we desire small α, no scheme can beat (1 + ε,Ω(1/ε))-approximate allocations and similarly as we desire small β, no scheme can beat (1.69103, 1+ ε)-approximate allocations. We give offline schemes that come very close to achieving these lower bounds. For the online case, we prove that no scheme can even achieve (O(1), O(1))-approximate allocations. However, a small restriction on item sizes permits a simple online scheme that computes (2 + ε, 1.7)-approximate allocations.
منابع مشابه
Extending Two-Dimensional Bin Packing Problem: Consideration of Priority for Items
In this paper a two-dimensional non-oriented guillotine bin packing problem is studied when items have different priorities. Our objective is to maximize the total profit which is total revenues minus costs of used bins and wasted area. A genetic algorithm is developed to solve this problem where a new coding scheme is introduced. To evaluate the performance of the proposed GA, first an upper b...
متن کاملSparse, Continuous Policy Representations for Uniform Online Bin Packing via Regression of Interpolants
Online bin packing is a classic optimisation problem, widely tackled by heuristic methods. In addition to human-designed heuristic packing policies (e.g. firstor bestfit), there has been interest over the last decade in the automatic generation of policies. One of the main limitations of some previously-used policy representations is the trade-off between locality and granularity in the associa...
متن کاملDifferential Approximation Algorithms for Some Combinatorial Optimization Problems
We use a new approximation measure, the differential approximation ratio, to derive polynomial-time approximation algorithms for minimum set covering (for both weighted and unweighted cases), minimum graph coloring and bin-packing. We also propose differentialapproximation-ratio preserving reductions linking minimum coloring, minimum vertex covering by cliques, minimum edge covering by cliques ...
متن کاملAbstract: Packing rectangular shapes into a rectangular space is one of the most important discussions on Cutting & Packing problems (C;P) such as: cutting problem, bin-packing problem and distributor's pallet loading problem, etc. Assume a set of rectangular pieces with specific lengths, widths and utility values. Also assume a rectangular packing space with specific width and length. The obj...
متن کاملBin-Completion Algorithms for Multicontainer Packing and Covering Problems
Bin-completion, a bin-oriented branch-and-bound approach, was recently shown to be promising for the bin packing problem. We propose several improvements to bin-completion that significantly improves search efficiency. We also show the generality of bin-completion for packing and covering problems involving multiple containers, and present bin-completion algorithms for the multiple knapsack, 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:
- Theor. Comput. Sci.
دوره 596 شماره
صفحات -
تاریخ انتشار 2015