1,322 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}))
NeuRoute: Predictive Dynamic Routing for Software-Defined Networks
This paper introduces NeuRoute, a dynamic routing framework for Software
Defined Networks (SDN) entirely based on machine learning, specifically, Neural
Networks. Current SDN/OpenFlow controllers use a default routing based on
Dijkstra algorithm for shortest paths, and provide APIs to develop custom
routing applications. NeuRoute is a controller-agnostic dynamic routing
framework that (i) predicts traffic matrix in real time, (ii) uses a neural
network to learn traffic characteristics and (iii) generates forwarding rules
accordingly to optimize the network throughput. NeuRoute achieves the same
results as the most efficient dynamic routing heuristic but in much less
execution time.Comment: Accepted for CNSM 201
Sequential and Parallel Algorithms for Mixed Packing and Covering
Mixed packing and covering problems are problems that can be formulated as
linear programs using only non-negative coefficients. Examples include
multicommodity network flow, the Held-Karp lower bound on TSP, fractional
relaxations of set cover, bin-packing, knapsack, scheduling problems,
minimum-weight triangulation, etc. This paper gives approximation algorithms
for the general class of problems. The sequential algorithm is a simple greedy
algorithm that can be implemented to find an epsilon-approximate solution in
O(epsilon^-2 log m) linear-time iterations. The parallel algorithm does
comparable work but finishes in polylogarithmic time.
The results generalize previous work on pure packing and covering (the
special case when the constraints are all "less-than" or all "greater-than") by
Michael Luby and Noam Nisan (1993) and Naveen Garg and Jochen Konemann (1998)
Throughput Optimal On-Line Algorithms for Advanced Resource Reservation in Ultra High-Speed Networks
Advanced channel reservation is emerging as an important feature of ultra
high-speed networks requiring the transfer of large files. Applications include
scientific data transfers and database backup. In this paper, we present two
new, on-line algorithms for advanced reservation, called BatchAll and BatchLim,
that are guaranteed to achieve optimal throughput performance, based on
multi-commodity flow arguments. Both algorithms are shown to have
polynomial-time complexity and provable bounds on the maximum delay for
1+epsilon bandwidth augmented networks. The BatchLim algorithm returns the
completion time of a connection immediately as a request is placed, but at the
expense of a slightly looser competitive ratio than that of BatchAll. We also
present a simple approach that limits the number of parallel paths used by the
algorithms while provably bounding the maximum reduction factor in the
transmission throughput. We show that, although the number of different paths
can be exponentially large, the actual number of paths needed to approximate
the flow is quite small and proportional to the number of edges in the network.
Simulations for a number of topologies show that, in practice, 3 to 5 parallel
paths are sufficient to achieve close to optimal performance. The performance
of the competitive algorithms are also compared to a greedy benchmark, both
through analysis and simulation.Comment: 9 pages, 8 figure
On the Number of Iterations for Dantzig-Wolfe Optimization and Packing-Covering Approximation Algorithms
We give a lower bound on the iteration complexity of a natural class of
Lagrangean-relaxation algorithms for approximately solving packing/covering
linear programs. We show that, given an input with random 0/1-constraints
on variables, with high probability, any such algorithm requires
iterations to compute a
-approximate solution, where is the width of the input.
The bound is tight for a range of the parameters .
The algorithms in the class include Dantzig-Wolfe decomposition, Benders'
decomposition, Lagrangean relaxation as developed by Held and Karp [1971] for
lower-bounding TSP, and many others (e.g. by Plotkin, Shmoys, and Tardos [1988]
and Grigoriadis and Khachiyan [1996]). To prove the bound, we use a discrepancy
argument to show an analogous lower bound on the support size of
-approximate mixed strategies for random two-player zero-sum
0/1-matrix games
Approximation Algorithms for Survivable Multicommodity Flow Problems with Applications to Network Design
Multicommodity flow (MF) problems have a wide variety of applications in areas such as VLSI circuit design, network design, etc., and are therefore very well studied. The fractional MF problems are polynomial time solvable while integer versions are NP-complete. However, exact algorithms to solve the fractional MF problems have high computational complexity. Therefore approximation algorithms to solve the fractional MF problems have been explored in the literature to reduce their computational complexity. Using these approximation algorithms and the randomized rounding technique, polynomial time approximation algorithms have been explored in the literature. In the design of high-speed networks, such as optical wavelength division multiplexing (WDM) networks, providing survivability carries great significance. Survivability is the ability of the network to recover from failures. It further increases the complexity of network design and presents network designers with more formidable challenges. In this work we formulate the survivable versions of the MF problems. We build approximation algorithms for the survivable multicommodity flow (SMF) problems based on the framework of the approximation algorithms for the MF problems presented in [1] and [2]. We discuss applications of the SMF problems to solve survivable routing in capacitated networks
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