49,784 research outputs found
Two simple algorithms for bin covering
We define two simple algorithms for the bin covering problem and give their asymptotic performance
Online Bin Covering with Limited Migration
Semi-online models where decisions may be revoked in a limited way have been studied extensively in the last years.
This is motivated by the fact that the pure online model is often too restrictive to model real-world applications, where some changes might be allowed. A well-studied measure of the amount of decisions that can be revoked is the migration factor beta: When an object o of size s(o) arrives, the decisions for objects of total size at most beta * s(o) may be revoked. Usually beta should be a constant. This means that a small object only leads to small changes. This measure has been successfully investigated for different, classical problems such as bin packing or makespan minimization. The dual of makespan minimization - the Santa Claus or machine covering problem - has also been studied, whereas the dual of bin packing - the bin covering problem - has not been looked at from such a perspective.
In this work, we extensively study the bin covering problem with migration in different scenarios. We develop algorithms both for the static case - where only insertions are allowed - and for the dynamic case, where items may also depart. We also develop lower bounds for these scenarios both for amortized migration and for worst-case migration showing that our algorithms have nearly optimal migration factor and asymptotic competitive ratio (up to an arbitrary small epsilon). We therefore resolve the competitiveness of the bin covering problem with migration
Online Bin Covering: Expectations vs. Guarantees
Bin covering is a dual version of classic bin packing. Thus, the goal is to
cover as many bins as possible, where covering a bin means packing items of
total size at least one in the bin.
For online bin covering, competitive analysis fails to distinguish between
most algorithms of interest; all "reasonable" algorithms have a competitive
ratio of 1/2. Thus, in order to get a better understanding of the combinatorial
difficulties in solving this problem, we turn to other performance measures,
namely relative worst order, random order, and max/max analysis, as well as
analyzing input with restricted or uniformly distributed item sizes. In this
way, our study also supplements the ongoing systematic studies of the relative
strengths of various performance measures.
Two classic algorithms for online bin packing that have natural dual versions
are Harmonic and Next-Fit. Even though the algorithms are quite different in
nature, the dual versions are not separated by competitive analysis. We make
the case that when guarantees are needed, even under restricted input
sequences, dual Harmonic is preferable. In addition, we establish quite robust
theoretical results showing that if items come from a uniform distribution or
even if just the ordering of items is uniformly random, then dual Next-Fit is
the right choice.Comment: IMADA-preprint-c
A study on exponential-size neighborhoods for the bin packing problem with conflicts
We propose an iterated local search based on several classes of local and
large neighborhoods for the bin packing problem with conflicts. This problem,
which combines the characteristics of both bin packing and vertex coloring,
arises in various application contexts such as logistics and transportation,
timetabling, and resource allocation for cloud computing. We introduce
evaluation procedures for classical local-search moves, polynomial variants of
ejection chains and assignment neighborhoods, an adaptive set covering-based
neighborhood, and finally a controlled use of 0-cost moves to further diversify
the search. The overall method produces solutions of good quality on the
classical benchmark instances and scales very well with an increase of problem
size. Extensive computational experiments are conducted to measure the
respective contribution of each proposed neighborhood. In particular, the
0-cost moves and the large neighborhood based on set covering contribute very
significantly to the search. Several research perspectives are open in relation
to possible hybridizations with other state-of-the-art mathematical programming
heuristics for this problem.Comment: 26 pages, 8 figure
Selfish Bin Covering
In this paper, we address the selfish bin covering problem, which is greatly
related both to the bin covering problem, and to the weighted majority game.
What we mainly concern is how much the lack of coordination harms the social
welfare. Besides the standard PoA and PoS, which are based on Nash equilibrium,
we also take into account the strong Nash equilibrium, and several other new
equilibria. For each equilibrium, the corresponding PoA and PoS are given, and
the problems of computing an arbitrary equilibrium, as well as approximating
the best one, are also considered.Comment: 16 page
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