1,619 research outputs found
Locality-preserving allocations Problems and coloured Bin Packing
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
times optimal), and that the items of each colour span few bins (at
most times optimal). We call such allocations -approximate. As usual in bin packing problems, we allow additive
constants and consider as the asymptotic performance ratios.
We prove that for \eps>0, if we desire small , no scheme can beat
(1+\eps, \Omega(1/\eps))-approximate allocations and similarly as we desire
small , no scheme can beat (1.69103, 1+\eps)-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
-approximate allocations. However, a small restriction on item
sizes permits a simple online scheme that computes (2+\eps, 1.7)-approximate
allocations
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
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
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 Simple PTAS for the Dual Bin Packing Problem and Advice Complexity of Its Online Version
Recently, Renault (2016) studied the dual bin packing problem in the per-request advice model of online algorithms. He showed that given O(1/eps) advice bits for each input item allows approximating the dual bin packing problem online to within a factor of 1+eps. Renault asked about the advice complexity of dual bin packing in the tape-advice model of online algorithms. We make progress on this question. Let s be the maximum bit size of an input item weight. We present a conceptually simple online algorithm that with total advice O((s + log n)/eps^2) approximates the dual bin packing to within a 1+eps factor. To this end, we describe and analyze a simple offline PTAS for the dual bin packing problem. Although a PTAS for a more general problem was known prior to our work (Kellerer 1999, Chekuri and Khanna 2006), our PTAS is arguably simpler to state and analyze. As a result, we could easily adapt our PTAS to obtain the advice-complexity result.
We also consider whether the dependence on s is necessary in our algorithm. We show that if s is unrestricted then for small enough eps > 0 obtaining a 1+eps approximation to the dual bin packing requires Omega_eps(n) bits of advice. To establish this lower bound we analyze an online reduction that preserves the advice complexity and approximation ratio from the binary separation problem due to Boyar et al. (2016). We define two natural advice complexity classes that capture the distinction similar to the Turing machine world distinction between pseudo polynomial time algorithms and polynomial time algorithms. Our results on the dual bin packing problem imply the separation of the two classes in the advice complexity world
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