99,664 research outputs found
Faster Approximate Multicommodity Flow Using Quadratically Coupled Flows
The maximum multicommodity flow problem is a natural generalization of the
maximum flow problem to route multiple distinct flows. Obtaining a
approximation to the multicommodity flow problem on graphs is a well-studied
problem. In this paper we present an adaptation of recent advances in
single-commodity flow algorithms to this problem. As the underlying linear
systems in the electrical problems of multicommodity flow problems are no
longer Laplacians, our approach is tailored to generate specialized systems
which can be preconditioned and solved efficiently using Laplacians. Given an
undirected graph with m edges and k commodities, we give algorithms that find
approximate solutions to the maximum concurrent flow problem and
the maximum weighted multicommodity flow problem in time
\tilde{O}(m^{4/3}\poly(k,\epsilon^{-1}))
Network Flow Optimization for Restoration of Images
The network flow optimization approach is offered for restoration of
grayscale and color images corrupted by noise. The Ising models are used as a
statistical background of the proposed method. The new multiresolution network
flow minimum cut algorithm, which is especially efficient in identification of
the maximum a posteriori estimates of corrupted images, is presented. The
algorithm is able to compute the MAP estimates of large size images and can be
used in a concurrent mode. We also describe the efficient solutions of the
problem of integer minimization of two energy functions for the Ising models of
gray-scale and color images
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
Performance analysis of wireless LANs: an integrated packet/flow level approach
In this paper we present an integrated packet/flow level modelling approach for analysing flow throughputs and transfer times in IEEE 802.11 WLANs. The packet level model captures the statistical characteristics of the transmission of individual packets at the MAC layer, while the flow level model takes into account the system dynamics due to the initiation and completion of data flow transfers. The latter model is a processor sharing type of queueing model reflecting the IEEE 802.11 MAC design principle of distributing the transmission capacity fairly among the active flows. The resulting integrated packet/flow level model is analytically tractable and yields a simple approximation for the throughput and flow transfer time. Extensive simulations show that the approximation is very accurate for a wide range of parameter settings. In addition, the simulation study confirms the attractive property following from our approximation that the expected flow transfer delay is insensitive to the flow size distribution (apart from its mean)
On the Effect of Quantum Interaction Distance on Quantum Addition Circuits
We investigate the theoretical limits of the effect of the quantum
interaction distance on the speed of exact quantum addition circuits. For this
study, we exploit graph embedding for quantum circuit analysis. We study a
logical mapping of qubits and gates of any -depth quantum adder
circuit for two -qubit registers onto a practical architecture, which limits
interaction distance to the nearest neighbors only and supports only one- and
two-qubit logical gates. Unfortunately, on the chosen -dimensional practical
architecture, we prove that the depth lower bound of any exact quantum addition
circuits is no longer , but . This
result, the first application of graph embedding to quantum circuits and
devices, provides a new tool for compiler development, emphasizes the impact of
quantum computer architecture on performance, and acts as a cautionary note
when evaluating the time performance of quantum algorithms.Comment: accepted for ACM Journal on Emerging Technologies in Computing
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