5,808 research outputs found
Fast network configuration in Software Defined Networking
Software Defined Networking (SDN) provides a framework to dynamically adjust and re-program the data plane with the use of flow rules. The realization of highly adaptive SDNs with the ability to respond to changing demands or recover after a network failure in a short period of time, hinges on efficient updates of flow rules. We model the time to deploy a set of flow rules by the update time at the bottleneck switch, and formulate the problem of selecting paths to minimize the deployment time under feasibility constraints as a mixed integer linear program (MILP). To reduce the computation time of determining flow rules, we propose efficient heuristics designed to approximate the minimum-deployment-time solution by relaxing the MILP or selecting the paths sequentially. Through extensive simulations we show that our algorithms outperform current, shortest path based solutions by reducing the total network configuration time up to 55% while having similar packet loss, in the considered scenarios. We also demonstrate that in a networked environment with a certain fraction of failed links, our algorithms are able to reduce the average time to reestablish disrupted flows by 40%
Efficient Construction of Probabilistic Tree Embeddings
In this paper we describe an algorithm that embeds a graph metric
on an undirected weighted graph into a distribution of tree metrics
such that for every pair , and
. Such embeddings have
proved highly useful in designing fast approximation algorithms, as many hard
problems on graphs are easy to solve on tree instances. For a graph with
vertices and edges, our algorithm runs in time with high
probability, which improves the previous upper bound of shown by
Mendel et al.\,in 2009.
The key component of our algorithm is a new approximate single-source
shortest-path algorithm, which implements the priority queue with a new data
structure, the "bucket-tree structure". The algorithm has three properties: it
only requires linear time in the number of edges in the input graph; the
computed distances have a distance preserving property; and when computing the
shortest-paths to the -nearest vertices from the source, it only requires to
visit these vertices and their edge lists. These properties are essential to
guarantee the correctness and the stated time bound.
Using this shortest-path algorithm, we show how to generate an intermediate
structure, the approximate dominance sequences of the input graph, in time, and further propose a simple yet efficient algorithm to converted
this sequence to a tree embedding in time, both with high
probability. Combining the three subroutines gives the stated time bound of the
algorithm.
Then we show that this efficient construction can facilitate some
applications. We proved that FRT trees (the generated tree embedding) are
Ramsey partitions with asymptotically tight bound, so the construction of a
series of distance oracles can be accelerated
Inner and Outer Rounding of Boolean Operations on Lattice Polygonal Regions
Robustness problems due to the substitution of the exact computation on real
numbers by the rounded floating point arithmetic are often an obstacle to
obtain practical implementation of geometric algorithms. If the adoption of the
--exact computation paradigm--[Yap et Dube] gives a satisfactory solution to
this kind of problems for purely combinatorial algorithms, this solution does
not allow to solve in practice the case of algorithms that cascade the
construction of new geometric objects. In this report, we consider the problem
of rounding the intersection of two polygonal regions onto the integer lattice
with inclusion properties. Namely, given two polygonal regions A and B having
their vertices on the integer lattice, the inner and outer rounding modes
construct two polygonal regions with integer vertices which respectively is
included and contains the true intersection. We also prove interesting results
on the Hausdorff distance, the size and the convexity of these polygonal
regions
Pseudo-Separation for Assessment of Structural Vulnerability of a Network
Based upon the idea that network functionality is impaired if two nodes in a
network are sufficiently separated in terms of a given metric, we introduce two
combinatorial \emph{pseudocut} problems generalizing the classical min-cut and
multi-cut problems. We expect the pseudocut problems will find broad relevance
to the study of network reliability. We comprehensively analyze the
computational complexity of the pseudocut problems and provide three
approximation algorithms for these problems.
Motivated by applications in communication networks with strict
Quality-of-Service (QoS) requirements, we demonstrate the utility of the
pseudocut problems by proposing a targeted vulnerability assessment for the
structure of communication networks using QoS metrics; we perform experimental
evaluations of our proposed approximation algorithms in this context
Hardness of Graph Pricing through Generalized Max-Dicut
The Graph Pricing problem is among the fundamental problems whose
approximability is not well-understood. While there is a simple combinatorial
1/4-approximation algorithm, the best hardness result remains at 1/2 assuming
the Unique Games Conjecture (UGC). We show that it is NP-hard to approximate
within a factor better than 1/4 under the UGC, so that the simple combinatorial
algorithm might be the best possible. We also prove that for any , there exists such that the integrality gap of
-rounds of the Sherali-Adams hierarchy of linear programming for
Graph Pricing is at most 1/2 + .
This work is based on the effort to view the Graph Pricing problem as a
Constraint Satisfaction Problem (CSP) simpler than the standard and complicated
formulation. We propose the problem called Generalized Max-Dicut(), which
has a domain size for every . Generalized Max-Dicut(1) is
well-known Max-Dicut. There is an approximation-preserving reduction from
Generalized Max-Dicut on directed acyclic graphs (DAGs) to Graph Pricing, and
both our results are achieved through this reduction. Besides its connection to
Graph Pricing, the hardness of Generalized Max-Dicut is interesting in its own
right since in most arity two CSPs studied in the literature, SDP-based
algorithms perform better than LP-based or combinatorial algorithms --- for
this arity two CSP, a simple combinatorial algorithm does the best.Comment: 28 page
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