447 research outputs found
Cluster Before You Hallucinate: Approximating Node-Capacitated Network Design and Energy Efficient Routing
We consider circuit routing with an objective of minimizing energy, in a
network of routers that are speed scalable and that may be shutdown when idle.
We consider both multicast routing and unicast routing. It is known that this
energy minimization problem can be reduced to a capacitated flow network design
problem, where vertices have a common capacity but arbitrary costs, and the
goal is to choose a minimum cost collection of vertices whose induced subgraph
will support the specified flow requirements. For the multicast (single-sink)
capacitated design problem we give a polynomial-time algorithm that is
O(log^3n)-approximate with O(log^4 n) congestion. This translates back to a
O(log ^(4{\alpha}+3) n)-approximation for the multicast energy-minimization
routing problem, where {\alpha} is the polynomial exponent in the dynamic power
used by a router. For the unicast (multicommodity) capacitated design problem
we give a polynomial-time algorithm that is O(log^5 n)-approximate with
O(log^12 n) congestion, which translates back to a O(log^(12{\alpha}+5)
n)-approximation for the unicast energy-minimization routing problem.Comment: 22 pages (full version of STOC 2014 paper
Optimizing Emergency Transportation through Multicommodity Quickest Paths
In transportation networks with limited capacities and travel times on the arcs, a class of problems attracting a growing scientific interest is represented by the optimal routing and scheduling of given amounts of flow to be transshipped from the origin points to the specific destinations in minimum time. Such problems are of particular concern to emergency transportation where evacuation plans seek to minimize the time evacuees need to clear the affected area and reach the safe zones. Flows over time approaches are among the most suitable mathematical tools to provide a modelling representation of these problems from a macroscopic point of view. Among them, the Quickest Path Problem (QPP), requires an origin-destination flow to be routed on a single path while taking into account inflow limits on the arcs and minimizing the makespan, namely, the time instant when the last unit of flow reaches its destination. In the context of emergency transport, the QPP represents a relevant modelling tool, since its solutions are based on unsplittable dynamic flows that can support the development of evacuation plans which are very easy to be correctly implemented, assigning one single evacuation path to a whole population. This way it is possible to prevent interferences, turbulence, and congestions that may affect the transportation process, worsening the overall clearing time. Nevertheless, the current state-of-the-art presents a lack of studies on multicommodity generalizations of the QPP, where network flows refer to various populations, possibly with different origins and destinations. In this paper we provide a contribution to fill this gap, by considering the Multicommodity Quickest Path Problem (MCQPP), where multiple commodities, each with its own origin, destination and demand, must be routed on a capacitated network with travel times on the arcs, while minimizing the overall makespan and allowing the flow associated to each commodity to be routed on a single path. For this optimization problem, we provide the first mathematical formulation in the scientific literature, based on mixed integer programming and encompassing specific features aimed at empowering the suitability of the arising solutions in real emergency transportation plans. A computational experience performed on a set of benchmark instances is then presented to provide a proof-of-concept for our original model and to evaluate the quality and suitability of the provided solutions together with the required computational effort. Most of the instances are solved at the optimum by a commercial MIP solver, fed with a lower bound deriving from the optimal makespan of a splittable-flow relaxation of the MCQPP
An Improved Upper Bound for the Ring Loading Problem
The Ring Loading Problem emerged in the 1990s to model an important special
case of telecommunication networks (SONET rings) which gained attention from
practitioners and theorists alike. Given an undirected cycle on nodes
together with non-negative demands between any pair of nodes, the Ring Loading
Problem asks for an unsplittable routing of the demands such that the maximum
cumulated demand on any edge is minimized. Let be the value of such a
solution. In the relaxed version of the problem, each demand can be split into
two parts where the first part is routed clockwise while the second part is
routed counter-clockwise. Denote with the maximum load of a minimum split
routing solution. In a landmark paper, Schrijver, Seymour and Winkler [SSW98]
showed that , where is the maximum demand value. They
also found (implicitly) an instance of the Ring Loading Problem with . Recently, Skutella [Sku16] improved these bounds by showing that , and there exists an instance with .
We contribute to this line of research by showing that . We
also take a first step towards lower and upper bounds for small instances
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%
Virtual topology design and flow routing in optical networks under multi-hour traffic demand
This paper addresses the problem of finding a static
virtual topology design and flow routing in transparent optical
WDM networks under a time-varying (multi-hour) traffic
demand. Four variants of the problem are considered, using
fixed or dynamically adaptable (i.e., variable) flow routing,
which can be splittable or unsplittable. Our main objective is
to minimize the number of transceivers needed which make up
for the main network cost. We formulate the problem variants
as exact ILPs (Integer Linear Programs) and MILPs (Mixed
ILPs). For larger problem instances, we also propose a family
of heuristics based on the concept of domination between
traffic matrices. This concept provides the theoretical
foundations for a set of techniques proposed to reduce the
problem complexity. We present a lower bound to the network
cost for the case in which the virtual topology could be
dynamically reconfigured along time. This allows us to assess
the limit on the maximum possible benefit that could be
achieved by using optical reconfigurable equipment.
Extensive tests have been conducted, using both synthetically
generated and real-traced traffic demands. In the cases
studied, results show that combining variable routing with splittable flows obtains a significant, although moderate, cost
reduction. The maximum cost reduction achievable with
reconfigurable virtual topologies was shown to be negligible
compared to the static case in medium and high loads.The work described in this paper was
carried out with the support of the BONE project (“Building the Future Optical Network in Europe”); a Network of Excellence funded by the European Commission through the
7th ICT-Framework Program. This research has been partially supported by the projects from the Spanish Ministry Of Education TEC2007-67966-01/TCM CON-PARTE-1, and
TEC2008-02552-E, and it is also developed in the framework of the projects from Fundación Seneca (Regional Agency of Science and Technology of Region of Murcia ) 00002/CS/08
(FORMA) and "Programa de Ayudas a Grupos de Excelencia de la Región. de Murcia”, F. Séneca (Plan Regional de Ciencia y Tecnología 2007/2010)."
A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths
In the unsplittable flow problem on a path, we are given a capacitated path
and tasks, each task having a demand, a profit, and start and end
vertices. The goal is to compute a maximum profit set of tasks, such that for
each edge of , the total demand of selected tasks that use does not
exceed the capacity of . This is a well-studied problem that has been
studied under alternative names, such as resource allocation, bandwidth
allocation, resource constrained scheduling, temporal knapsack and interval
packing.
We present a polynomial time constant-factor approximation algorithm for this
problem. This improves on the previous best known approximation ratio of
. The approximation ratio of our algorithm is for any
.
We introduce several novel algorithmic techniques, which might be of
independent interest: a framework which reduces the problem to instances with a
bounded range of capacities, and a new geometrically inspired dynamic program
which solves a special case of the maximum weight independent set of rectangles
problem to optimality. In the setting of resource augmentation, wherein the
capacities can be slightly violated, we give a -approximation
algorithm. In addition, we show that the problem is strongly NP-hard even if
all edge capacities are equal and all demands are either~1,~2, or~3.Comment: 37 pages, 5 figures Version 2 contains the same results as version 1,
but the presentation has been greatly revised and improved. References have
been adde
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
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