11,193 research outputs found
Vector Bin Packing with Multiple-Choice
We consider a variant of bin packing called multiple-choice vector bin
packing. In this problem we are given a set of items, where each item can be
selected in one of several -dimensional incarnations. We are also given
bin types, each with its own cost and -dimensional size. Our goal is to pack
the items in a set of bins of minimum overall cost. The problem is motivated by
scheduling in networks with guaranteed quality of service (QoS), but due to its
general formulation it has many other applications as well. We present an
approximation algorithm that is guaranteed to produce a solution whose cost is
about times the optimum. For the running time to be polynomial we
require and . This extends previous results for vector
bin packing, in which each item has a single incarnation and there is only one
bin type. To obtain our result we also present a PTAS for the multiple-choice
version of multidimensional knapsack, where we are given only one bin and the
goal is to pack a maximum weight set of (incarnations of) items in that bin
Safety-Level Aware Bin-Packing Approach for Control Functions Assignment
International audienceThe assignment of functions to controllers is a crucial step when building an operational control system architecture. We identified this problem as a Multiple Choice Vector Bin-Packing with Conflicts that is a generalization of the one-dimensional Bin-Packing problem. Such problems are known to be strongly NP-Hard and exact techniques to solve them are too time and/or space consuming because of the combinatorial explosion. Therefore, in this paper, we propose a fast First-Fit Decreasing based heuristic that derives an optimized number of controllers in polynomial time. The objective is to minimize the global cost of controllers while satisfying safety constraints. We show through experiments that the adopted approach allows us to obtain values that are in average very close to the optimum
Optimal Placement Algorithms for Virtual Machines
Cloud computing provides a computing platform for the users to meet their
demands in an efficient, cost-effective way. Virtualization technologies are
used in the clouds to aid the efficient usage of hardware. Virtual machines
(VMs) are utilized to satisfy the user needs and are placed on physical
machines (PMs) of the cloud for effective usage of hardware resources and
electricity in the cloud. Optimizing the number of PMs used helps in cutting
down the power consumption by a substantial amount.
In this paper, we present an optimal technique to map virtual machines to
physical machines (nodes) such that the number of required nodes is minimized.
We provide two approaches based on linear programming and quadratic programming
techniques that significantly improve over the existing theoretical bounds and
efficiently solve the problem of virtual machine (VM) placement in data
centers
Improved approximation bounds for Vector Bin Packing
In this paper we propose an improved approximation scheme for the Vector Bin
Packing problem (VBP), based on the combination of (near-)optimal solution of
the Linear Programming (LP) relaxation and a greedy (modified first-fit)
heuristic. The Vector Bin Packing problem of higher dimension (d \geq 2) is not
known to have asymptotic polynomial-time approximation schemes (unless P = NP).
Our algorithm improves over the previously-known guarantee of (ln d + 1 +
epsilon) by Bansal et al. [1] for higher dimensions (d > 2). We provide a
{\theta}(1) approximation scheme for certain set of inputs for any dimension d.
More precisely, we provide a 2-OPT algorithm, a result which is irrespective of
the number of dimensions d.Comment: 15 pages, 3 algorithm
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