2,576 research outputs found
Dynamic vs Oblivious Routing in Network Design
Consider the robust network design problem of finding a minimum cost network
with enough capacity to route all traffic demand matrices in a given polytope.
We investigate the impact of different routing models in this robust setting:
in particular, we compare \emph{oblivious} routing, where the routing between
each terminal pair must be fixed in advance, to \emph{dynamic} routing, where
routings may depend arbitrarily on the current demand. Our main result is a
construction that shows that the optimal cost of such a network based on
oblivious routing (fractional or integral) may be a factor of
\BigOmega(\log{n}) more than the cost required when using dynamic routing.
This is true even in the important special case of the asymmetric hose model.
This answers a question in \cite{chekurisurvey07}, and is tight up to constant
factors. Our proof technique builds on a connection between expander graphs and
robust design for single-sink traffic patterns \cite{ChekuriHardness07}
A Constant Factor Approximation for the Single Sink Edge Installation Problem
We present the first constant approximation to the single sink buy-at-bulk network design problem, where we have to design a network by buying pipes of different costs and capacities per unit length to route demands at a set of sources to a single sink. The distances in the underlying network form a metric. This result improves the previous bound of O(log |R|), where R is the set of sources. We also present a better constant approximation to the related Access Network Design problem. Our algorithms are randomized and combinatorial. As a subroutine in our algorithm, we use an interesting variant of facility location with lower bounds on the amount of demand an open facility needs to serve. We call this variant load balanced facility location and present a constant factor approximation for it, while relaxing the lower bounds by a constant factor
Network Design with Coverage Costs
We study network design with a cost structure motivated by redundancy in data
traffic. We are given a graph, g groups of terminals, and a universe of data
packets. Each group of terminals desires a subset of the packets from its
respective source. The cost of routing traffic on any edge in the network is
proportional to the total size of the distinct packets that the edge carries.
Our goal is to find a minimum cost routing. We focus on two settings. In the
first, the collection of packet sets desired by source-sink pairs is laminar.
For this setting, we present a primal-dual based 2-approximation, improving
upon a logarithmic approximation due to Barman and Chawla (2012). In the second
setting, packet sets can have non-trivial intersection. We focus on the case
where each packet is desired by either a single terminal group or by all of the
groups, and the graph is unweighted. For this setting we present an O(log
g)-approximation.
Our approximation for the second setting is based on a novel spanner-type
construction in unweighted graphs that, given a collection of g vertex subsets,
finds a subgraph of cost only a constant factor more than the minimum spanning
tree of the graph, such that every subset in the collection has a Steiner tree
in the subgraph of cost at most O(log g) that of its minimum Steiner tree in
the original graph. We call such a subgraph a group spanner.Comment: Updated version with additional result
Optimization in Telecommunication Networks
Network design and network synthesis have been the classical optimization problems intelecommunication for a long time. In the recent past, there have been many technologicaldevelopments such as digitization of information, optical networks, internet, and wirelessnetworks. These developments have led to a series of new optimization problems. Thismanuscript gives an overview of the developments in solving both classical and moderntelecom optimization problems.We start with a short historical overview of the technological developments. Then,the classical (still actual) network design and synthesis problems are described with anemphasis on the latest developments on modelling and solving them. Classical results suchas Mengerās disjoint paths theorem, and Ford-Fulkersonās max-flow-min-cut theorem, butalso Gomory-Hu trees and the Okamura-Seymour cut-condition, will be related to themodels described. Finally, we describe recent optimization problems such as routing andwavelength assignment, and grooming in optical networks.operations research and management science;
Fault tolerant network design inspired by Physarum polycephalum
Physarum polycephalum, a true slime mould, is a primitive, unicellular organism that creates networks to transport nutrients while foraging. The design of these natural networks proved to be advanced, e.g. the slime mould was able to find the shortest path through a maze. The underlying principles of this design have been mathematically modelled in literature. As in real life the slime mould can design fault tolerant networks, its principles can be applied to the design of man-made networks. In this paper, an existing model and algorithm are adapted and extended with stimulation and migration mechanisms which encourage formation of alternative paths, optimize edge positioning and allow for automated design. The extended model can then be used to better design fault tolerant networks. The extended algorithm is applied to several national and international network configurations. Results show that the extensions allow the model to capture the fault tolerance requirements more accurately. The resulting extended algorithm overcomes weaknesses in geometric graph design and can be used to design fault tolerant networks such as telecommunication networks with varying fault tolerance requirements
Single-Sink Network Design with Vertex Connectivity Requirements
We study single-sink network design problems in undirected graphs
with vertex connectivity requirements. The input to these problems
is an edge-weighted undirected graph , a sink/root vertex
, a set of terminals , and integer . The goal is
to connect each terminal to via emph{vertex-disjoint}
paths. In the {em connectivity} problem, the objective is to find a
min-cost subgraph of that contains the desired paths. There is a
-approximation for this problem when cite{FleischerJW}
but for , the first non-trivial approximation was obtained
in the recent work of Chakraborty, Chuzhoy and Khanna
cite{ChakCK08}; they describe and analyze an algorithm with an
approximation ratio of where .
In this paper, inspired by the results and ideas in cite{ChakCK08},
we show an -approximation bound for a simple
greedy algorithm. Our analysis is based on the dual of a natural
linear program and is of independent technical interest. We use the
insights from this analysis to obtain an -approximation for the more general single-sink {em
rent-or-buy} network design problem with vertex connectivity
requirements. We further extend the ideas to obtain a
poly-logarithmic approximation for the single-sink {em buy-at-bulk}
problem when and the number of cable-types is a fixed
constant; we believe that this should extend to any fixed . We
also show that for the non-uniform buy-at-bulk problem, for each
fixed , a small variant of a simple algorithm suggested by
Charikar and Kargiazova cite{CharikarK05} for the case of
gives an approximation for larger .
These results show that for each of these problems, simple and
natural algorithms that have been developed for have good
performance for small
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