5,851 research outputs found
Cut-Matching Games on Directed Graphs
We give O(log^2 n)-approximation algorithm based on the cut-matching
framework of [10, 13, 14] for computing the sparsest cut on directed graphs.
Our algorithm uses only O(log^2 n) single commodity max-flow computations and
thus breaks the multicommodity-flow barrier for computing the sparsest cut on
directed graph
Distributed Broadcasting and Mapping Protocols in Directed Anonymous Networks
We initiate the study of distributed protocols over directed anonymous networks that are not necessarily strongly connected. In such networks, nodes are aware only of their incoming and outgoing edges, have no unique identity, and have no knowledge of the network topology or even bounds on its parameters, like the number of nodes or the network diameter. Anonymous networks are of interest in various settings such as wireless ad-hoc networks and peer to peer networks. Our goal is to create distributed protocols that reduce the uncertainty by distributing the knowledge of the network topology to all the nodes.
We consider two basic protocols: broadcasting and unique label assignment. These two protocols enable a complete mapping of the network and can serve as key building blocks in more advanced protocols. We develop distributed asynchronous protocols as well as derive lower bounds on their communication complexity, total bandwidth complexity, and node label complexity. The resulting lower bounds are sometimes surprisingly high, exhibiting the complexity of topology extraction in directed anonymous networks
Compact Oblivious Routing
Oblivious routing is an attractive paradigm for large distributed systems in which centralized control and frequent reconfigurations are infeasible or undesired (e.g., costly). Over the last almost 20 years, much progress has been made in devising oblivious routing schemes that guarantee close to optimal load and also algorithms for constructing such schemes efficiently have been designed. However, a common drawback of existing oblivious routing schemes is that they are not compact: they require large routing tables (of polynomial size), which does not scale.
This paper presents the first oblivious routing scheme which guarantees close to optimal load and is compact at the same time - requiring routing tables of polylogarithmic size. Our algorithm maintains the polylogarithmic competitive ratio of existing algorithms, and is hence particularly well-suited for emerging large-scale networks
Graph Orientation and Flows Over Time
Flows over time are used to model many real-world logistic and routing
problems. The networks underlying such problems -- streets, tracks, etc. -- are
inherently undirected and directions are only imposed on them to reduce the
danger of colliding vehicles and similar problems. Thus the question arises,
what influence the orientation of the network has on the network flow over time
problem that is being solved on the oriented network. In the literature, this
is also referred to as the contraflow or lane reversal problem.
We introduce and analyze the price of orientation: How much flow is lost in
any orientation of the network if the time horizon remains fixed? We prove that
there is always an orientation where we can still send of the
flow and this bound is tight. For the special case of networks with a single
source or sink, this fraction is which is again tight. We present
more results of similar flavor and also show non-approximability results for
finding the best orientation for single and multicommodity maximum flows over
time
Markov Chain Methods For Analyzing Complex Transport Networks
We have developed a steady state theory of complex transport networks used to
model the flow of commodity, information, viruses, opinions, or traffic. Our
approach is based on the use of the Markov chains defined on the graph
representations of transport networks allowing for the effective network
design, network performance evaluation, embedding, partitioning, and network
fault tolerance analysis. Random walks embed graphs into Euclidean space in
which distances and angles acquire a clear statistical interpretation. Being
defined on the dual graph representations of transport networks random walks
describe the equilibrium configurations of not random commodity flows on
primary graphs. This theory unifies many network concepts into one framework
and can also be elegantly extended to describe networks represented by directed
graphs and multiple interacting networks.Comment: 26 pages, 4 figure
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