11,125 research outputs found
Algorithms for Constructing Overlay Networks For Live Streaming
We present a polynomial time approximation algorithm for constructing an
overlay multicast network for streaming live media events over the Internet.
The class of overlay networks constructed by our algorithm include networks
used by Akamai Technologies to deliver live media events to a global audience
with high fidelity. We construct networks consisting of three stages of nodes.
The nodes in the first stage are the entry points that act as sources for the
live streams. Each source forwards each of its streams to one or more nodes in
the second stage that are called reflectors. A reflector can split an incoming
stream into multiple identical outgoing streams, which are then sent on to
nodes in the third and final stage that act as sinks and are located in edge
networks near end-users. As the packets in a stream travel from one stage to
the next, some of them may be lost. A sink combines the packets from multiple
instances of the same stream (by reordering packets and discarding duplicates)
to form a single instance of the stream with minimal loss. Our primary
contribution is an algorithm that constructs an overlay network that provably
satisfies capacity and reliability constraints to within a constant factor of
optimal, and minimizes cost to within a logarithmic factor of optimal. Further
in the common case where only the transmission costs are minimized, we show
that our algorithm produces a solution that has cost within a factor of 2 of
optimal. We also implement our algorithm and evaluate it on realistic traces
derived from Akamai's live streaming network. Our empirical results show that
our algorithm can be used to efficiently construct large-scale overlay networks
in practice with near-optimal cost
An approximation algorithm for a facility location problem with stochastic demands
In this article we propose, for any , a -approximation algorithm for a facility location problem with stochastic demands. This problem can be described as follows. There are a number of locations, where facilities may be opened and a number of demand points, where requests for items arise at random. The requests are sent to open facilities. At the open facilities, inventory is kept such that arriving requests find a zero inventory with (at most) some pre-specified probability. After constant times, the inventory is replenished to a fixed order up to level. The time interval between consecutive replenishments is called a reorder period. The problem is where to locate the facilities and how to assign the demand points to facilities at minimal cost per reorder period such that the above mentioned quality of service is insured. The incurred costs are the expected transportation costs from the demand points to the facilities, the operating costs (opening costs) of the facilities and the investment in inventory (inventory costs). \u
Centrality of Trees for Capacitated k-Center
There is a large discrepancy in our understanding of uncapacitated and
capacitated versions of network location problems. This is perhaps best
illustrated by the classical k-center problem: there is a simple tight
2-approximation algorithm for the uncapacitated version whereas the first
constant factor approximation algorithm for the general version with capacities
was only recently obtained by using an intricate rounding algorithm that
achieves an approximation guarantee in the hundreds.
Our paper aims to bridge this discrepancy. For the capacitated k-center
problem, we give a simple algorithm with a clean analysis that allows us to
prove an approximation guarantee of 9. It uses the standard LP relaxation and
comes close to settling the integrality gap (after necessary preprocessing),
which is narrowed down to either 7, 8 or 9. The algorithm proceeds by first
reducing to special tree instances, and then solves such instances optimally.
Our concept of tree instances is quite versatile, and applies to natural
variants of the capacitated k-center problem for which we also obtain improved
algorithms. Finally, we give evidence to show that more powerful preprocessing
could lead to better algorithms, by giving an approximation algorithm that
beats the integrality gap for instances where all non-zero capacities are
uniform.Comment: 21 pages, 2 figure
Design of Closed Loop Supply Chains
Increased concern for the environment has lead to new techniques to design products and supply chains that are both economically and ecologically feasible. This paper deals with the product - and corresponding supply chain design for a refrigerator. Literature study shows that there are many models to support product design and logistics separately, but not in an integrated way. In our research we develop quantitative modelling to support an optimal design structure of a product, i.e. modularity, repairability, recyclability, as well as the optimal locations and goods flows allocation in the logistics system. Environmental impacts are measured by energy and waste. Economic costs are modelled as linear functions of volumes with a fixed set-up component for facilities. We apply this model using real life R&D data of a Japanese consumer electronics company. The model is run for different scenarios using different parameter settings such as centralised versus decentralised logistics, alternative product designs, varying return quality and quantity, and potential environmental legislation based on producer responsibility.supply chain management;reverse logistics;facility location;network design;product design
Sherali-Adams gaps, flow-cover inequalities and generalized configurations for capacity-constrained Facility Location
Metric facility location is a well-studied problem for which linear
programming methods have been used with great success in deriving approximation
algorithms. The capacity-constrained generalizations, such as capacitated
facility location (CFL) and lower-bounded facility location (LBFL), have proved
notorious as far as LP-based approximation is concerned: while there are
local-search-based constant-factor approximations, there is no known linear
relaxation with constant integrality gap. According to Williamson and Shmoys
devising a relaxation-based approximation for \cfl\ is among the top 10 open
problems in approximation algorithms.
This paper advances significantly the state-of-the-art on the effectiveness
of linear programming for capacity-constrained facility location through a host
of impossibility results for both CFL and LBFL. We show that the relaxations
obtained from the natural LP at levels of the Sherali-Adams
hierarchy have an unbounded gap, partially answering an open question of
\cite{LiS13, AnBS13}. Here, denotes the number of facilities in the
instance. Building on the ideas for this result, we prove that the standard CFL
relaxation enriched with the generalized flow-cover valid inequalities
\cite{AardalPW95} has also an unbounded gap. This disproves a long-standing
conjecture of \cite{LeviSS12}. We finally introduce the family of proper
relaxations which generalizes to its logical extreme the classic star
relaxation and captures general configuration-style LPs. We characterize the
behavior of proper relaxations for CFL and LBFL through a sharp threshold
phenomenon.Comment: arXiv admin note: substantial text overlap with arXiv:1305.599
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