26,185 research outputs found
Designing Multi-Commodity Flow Trees
The traditional multi-commodity flow problem assumes a given flow network in
which multiple commodities are to be maximally routed in response to given
demands. This paper considers the multi-commodity flow network-design problem:
given a set of multi-commodity flow demands, find a network subject to certain
constraints such that the commodities can be maximally routed.
This paper focuses on the case when the network is required to be a tree. The
main result is an approximation algorithm for the case when the tree is
required to be of constant degree. The algorithm reduces the problem to the
minimum-weight balanced-separator problem; the performance guarantee of the
algorithm is within a factor of 4 of the performance guarantee of the
balanced-separator procedure. If Leighton and Rao's balanced-separator
procedure is used, the performance guarantee is O(log n). This improves the
O(log^2 n) approximation factor that is trivial to obtain by a direct
application of the balanced-separator method.Comment: Conference version in WADS'9
Distributed Averaging via Lifted Markov Chains
Motivated by applications of distributed linear estimation, distributed
control and distributed optimization, we consider the question of designing
linear iterative algorithms for computing the average of numbers in a network.
Specifically, our interest is in designing such an algorithm with the fastest
rate of convergence given the topological constraints of the network. As the
main result of this paper, we design an algorithm with the fastest possible
rate of convergence using a non-reversible Markov chain on the given network
graph. We construct such a Markov chain by transforming the standard Markov
chain, which is obtained using the Metropolis-Hastings method. We call this
novel transformation pseudo-lifting. We apply our method to graphs with
geometry, or graphs with doubling dimension. Specifically, the convergence time
of our algorithm (equivalently, the mixing time of our Markov chain) is
proportional to the diameter of the network graph and hence optimal. As a
byproduct, our result provides the fastest mixing Markov chain given the
network topological constraints, and should naturally find their applications
in the context of distributed optimization, estimation and control
On Routing Disjoint Paths in Bounded Treewidth Graphs
We study the problem of routing on disjoint paths in bounded treewidth graphs
with both edge and node capacities. The input consists of a capacitated graph
and a collection of source-destination pairs . The goal is to maximize the number of pairs that
can be routed subject to the capacities in the graph. A routing of a subset
of the pairs is a collection of paths such that,
for each pair , there is a path in
connecting to . In the Maximum Edge Disjoint Paths (MaxEDP) problem,
the graph has capacities on the edges and a routing
is feasible if each edge is in at most of
the paths of . The Maximum Node Disjoint Paths (MaxNDP) problem is
the node-capacitated counterpart of MaxEDP.
In this paper we obtain an approximation for MaxEDP on graphs of
treewidth at most and a matching approximation for MaxNDP on graphs of
pathwidth at most . Our results build on and significantly improve the work
by Chekuri et al. [ICALP 2013] who obtained an approximation
for MaxEDP
Optimization of Free Space Optical Wireless Network for Cellular Backhauling
With densification of nodes in cellular networks, free space optic (FSO)
connections are becoming an appealing low cost and high rate alternative to
copper and fiber as the backhaul solution for wireless communication systems.
To ensure a reliable cellular backhaul, provisions for redundant, disjoint
paths between the nodes must be made in the design phase. This paper aims at
finding a cost-effective solution to upgrade the cellular backhaul with
pre-deployed optical fibers using FSO links and mirror components. Since the
quality of the FSO links depends on several factors, such as transmission
distance, power, and weather conditions, we adopt an elaborate formulation to
calculate link reliability. We present a novel integer linear programming model
to approach optimal FSO backhaul design, guaranteeing -disjoint paths
connecting each node pair. Next, we derive a column generation method to a
path-oriented mathematical formulation. Applying the method in a sequential
manner enables high computational scalability. We use realistic scenarios to
demonstrate our approaches efficiently provide optimal or near-optimal
solutions, and thereby allow for accurately dealing with the trade-off between
cost and reliability
The Capacity of Smartphone Peer-To-Peer Networks
We study three capacity problems in the mobile telephone model, a network abstraction that models the peer-to-peer communication capabilities implemented in most commodity smartphone operating systems. The capacity of a network expresses how much sustained throughput can be maintained for a set of communication demands, and is therefore a fundamental bound on the usefulness of a network. Because of this importance, wireless network capacity has been active area of research for the last two decades.
The three capacity problems that we study differ in the structure of the communication demands. The first problem is pairwise capacity, where the demands are (source, destination) pairs. Pairwise capacity is one of the most classical definitions, as it was analyzed in the seminal paper of Gupta and Kumar on wireless network capacity. The second problem we study is broadcast capacity, in which a single source must deliver packets to all other nodes in the network. Finally, we turn our attention to all-to-all capacity, in which all nodes must deliver packets to all other nodes. In all three of these problems we characterize the optimal achievable throughput for any given network, and design algorithms which asymptotically match this performance. We also study these problems in networks generated randomly by a process introduced by Gupta and Kumar, and fully characterize their achievable throughput.
Interestingly, the techniques that we develop for all-to-all capacity also allow us to design a one-shot gossip algorithm that runs within a polylogarithmic factor of optimal in every graph. This largely resolves an open question from previous work on the one-shot gossip problem in this model
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