5,267 research outputs found
Fully Dynamic Bin Packing Revisited
We consider the fully dynamic bin packing problem, where items arrive and
depart in an online fashion and repacking of previously packed items is
allowed. The goal is, of course, to minimize both the number of bins used as
well as the amount of repacking. A recently introduced way of measuring the
repacking costs at each timestep is the migration factor, defined as the total
size of repacked items divided by the size of an arriving or departing item.
Concerning the trade-off between number of bins and migration factor, if we
wish to achieve an asymptotic competitive ration of for the
number of bins, a relatively simple argument proves a lower bound of
for the migration factor. We establish a nearly
matching upper bound of using
a new dynamic rounding technique and new ideas to handle small items in a
dynamic setting such that no amortization is needed. The running time of our
algorithm is polynomial in the number of items and in .
The previous best trade-off was for an asymptotic competitive ratio of
for the bins (rather than ) and needed an amortized
number of repackings (while in our scheme the number of repackings
is independent of and non-amortized)
Dynamic Windows Scheduling with Reallocation
We consider the Windows Scheduling problem. The problem is a restricted
version of Unit-Fractions Bin Packing, and it is also called Inventory
Replenishment in the context of Supply Chain. In brief, the problem is to
schedule the use of communication channels to clients. Each client ci is
characterized by an active cycle and a window wi. During the period of time
that any given client ci is active, there must be at least one transmission
from ci scheduled in any wi consecutive time slots, but at most one
transmission can be carried out in each channel per time slot. The goal is to
minimize the number of channels used. We extend previous online models, where
decisions are permanent, assuming that clients may be reallocated at some cost.
We assume that such cost is a constant amount paid per reallocation. That is,
we aim to minimize also the number of reallocations. We present three online
reallocation algorithms for Windows Scheduling. We evaluate experimentally
these protocols showing that, in practice, all three achieve constant amortized
reallocations with close to optimal channel usage. Our simulations also expose
interesting trade-offs between reallocations and channel usage. We introduce a
new objective function for WS with reallocations, that can be also applied to
models where reallocations are not possible. We analyze this metric for one of
the algorithms which, to the best of our knowledge, is the first online WS
protocol with theoretical guarantees that applies to scenarios where clients
may leave and the analysis is against current load rather than peak load. Using
previous results, we also observe bounds on channel usage for one of the
algorithms.Comment: 6 figure
Online Bin Stretching with Three Bins
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
for three bins. Additionally, we present a lower bound of for Online Bin Stretching on three bins and a lower bound of
for four and five bins that were discovered using a computer search.Comment: Preprint of a journal version. See version 2 for the conference
paper. Conference paper split into two journal submissions; see
arXiv:1601.0811
Analysis of Granular Flow in a Pebble-Bed Nuclear Reactor
Pebble-bed nuclear reactor technology, which is currently being revived
around the world, raises fundamental questions about dense granular flow in
silos. A typical reactor core is composed of graphite fuel pebbles, which drain
very slowly in a continuous refueling process. Pebble flow is poorly understood
and not easily accessible to experiments, and yet it has a major impact on
reactor physics. To address this problem, we perform full-scale,
discrete-element simulations in realistic geometries, with up to 440,000
frictional, viscoelastic 6cm-diameter spheres draining in a cylindrical vessel
of diameter 3.5m and height 10m with bottom funnels angled at 30 degrees or 60
degrees. We also simulate a bidisperse core with a dynamic central column of
smaller graphite moderator pebbles and show that little mixing occurs down to a
1:2 diameter ratio. We analyze the mean velocity, diffusion and mixing, local
ordering and porosity (from Voronoi volumes), the residence-time distribution,
and the effects of wall friction and discuss implications for reactor design
and the basic physics of granular flow.Comment: 18 pages, 21 figure
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
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