3,878 research outputs found
Bounded space on-line variable-sized bin packing
In this paper we consider the fc-bounded space on-line bin packing problem. Some efficient approximation algorithms are described and analyzed. Selecting either the smallest or the largest available bin size to start a new bin as items arrive turns out to yield a worst-case performance bound of 2. By packing large items into appropriate bins, an efficient approximation algorithm is derived from fc-bounded space on-line bin packing algorithms and its worst-case performance bounds is 1.7 for k > 3
A tight lower bound for an online hypercube packing problem and bounds for prices of anarchy of a related game
We prove a tight lower bound on the asymptotic performance ratio of
the bounded space online -hypercube bin packing problem, solving an open
question raised in 2005. In the classic -hypercube bin packing problem, we
are given a sequence of -dimensional hypercubes and we have an unlimited
number of bins, each of which is a -dimensional unit hypercube. The goal is
to pack (orthogonally) the given hypercubes into the minimum possible number of
bins, in such a way that no two hypercubes in the same bin overlap. The bounded
space online -hypercube bin packing problem is a variant of the
-hypercube bin packing problem, in which the hypercubes arrive online and
each one must be packed in an open bin without the knowledge of the next
hypercubes. Moreover, at each moment, only a constant number of open bins are
allowed (whenever a new bin is used, it is considered open, and it remains so
until it is considered closed, in which case, it is not allowed to accept new
hypercubes). Epstein and van Stee [SIAM J. Comput. 35 (2005), no. 2, 431-448]
showed that is and , and conjectured that
it is . We show that is in fact . To
obtain this result, we elaborate on some ideas presented by those authors, and
go one step further showing how to obtain better (offline) packings of certain
special instances for which one knows how many bins any bounded space algorithm
has to use. Our main contribution establishes the existence of such packings,
for large enough , using probabilistic arguments. Such packings also lead to
lower bounds for the prices of anarchy of the selfish -hypercube bin packing
game. We present a lower bound of for the pure price of
anarchy of this game, and we also give a lower bound of for
its strong price of anarchy
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn
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
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