133 research outputs found
The splittable flow arc set with capacity and minimum load constraints
Cataloged from PDF version of article.We study the convex hull of the splittable flow arc set with capacity and minimum load constraints. This set arises as a relaxation of problems where clients have demand for a resource that can be installed in integer amounts and that has capacity limitations and lower bounds on utilization. We prove that the convex hull of this set is the intersection of the convex hull of the set with a capacity constraint and the convex hull of the set with a minimum load constraint
Energy management in communication networks: a journey through modelling and optimization glasses
The widespread proliferation of Internet and wireless applications has
produced a significant increase of ICT energy footprint. As a response, in the
last five years, significant efforts have been undertaken to include
energy-awareness into network management. Several green networking frameworks
have been proposed by carefully managing the network routing and the power
state of network devices.
Even though approaches proposed differ based on network technologies and
sleep modes of nodes and interfaces, they all aim at tailoring the active
network resources to the varying traffic needs in order to minimize energy
consumption. From a modeling point of view, this has several commonalities with
classical network design and routing problems, even if with different
objectives and in a dynamic context.
With most researchers focused on addressing the complex and crucial
technological aspects of green networking schemes, there has been so far little
attention on understanding the modeling similarities and differences of
proposed solutions. This paper fills the gap surveying the literature with
optimization modeling glasses, following a tutorial approach that guides
through the different components of the models with a unified symbolism. A
detailed classification of the previous work based on the modeling issues
included is also proposed
Routing Games with Progressive Filling
Max-min fairness (MMF) is a widely known approach to a fair allocation of
bandwidth to each of the users in a network. This allocation can be computed by
uniformly raising the bandwidths of all users without violating capacity
constraints. We consider an extension of these allocations by raising the
bandwidth with arbitrary and not necessarily uniform time-depending velocities
(allocation rates). These allocations are used in a game-theoretic context for
routing choices, which we formalize in progressive filling games (PFGs).
We present a variety of results for equilibria in PFGs. We show that these
games possess pure Nash and strong equilibria. While computation in general is
NP-hard, there are polynomial-time algorithms for prominent classes of
Max-Min-Fair Games (MMFG), including the case when all users have the same
source-destination pair. We characterize prices of anarchy and stability for
pure Nash and strong equilibria in PFGs and MMFGs when players have different
or the same source-destination pairs. In addition, we show that when a designer
can adjust allocation rates, it is possible to design games with optimal strong
equilibria. Some initial results on polynomial-time algorithms in this
direction are also derived
path-constrained network flows
This thesis focuses on approximation algorithms and complexity assessments concerning network flows. It deals with various network flow problems with path restrictions. These restrictions cover the number of paths that are used to route commodities as well as the amount of flow that is routed along a single path or the path's length.
Concerning the first restriction we study the unsplittable flow problem-a generalization of the NP-hard edge-disjoint paths problem. Given a network with commodities that must be routed from their sources to their sinks, the unsplittable flow problem forbids each commodity to use more than one path. For this problem we prove a new lower bound on the performance guarantee of randomized rounding which so far belongs to the best approximation algorithms known for this problem. Further, we present an interesting relation between unsplittable flows and classical (splittable) multicommodity flows in the case that all commodities share a common source: Each single source multicommodity flow can be represented as a convex combination of unsplittable flows of congestion at most 2.
Further, we combine different path restrictions from the ones mentioned above. In the k-splittable flow problem with path capacities, we study the NP-hard problem that each commodity may be sent along a limited number of paths while the flow value of each path is bounded. This yields a generalization of the unsplittable flow problem, but we show how one can obtain the same asymptotic approximation ratios. For the length-bounded k-splittable flow problem, we consider the single commodity case and develop a constant factor approximation algorithm.
A crucial characteristic of network flows occurring in real-world applications is flow variation over time and the fact that flow does not travel instantaneously through a network but requires a certain amount of time to travel through each arc. Both characteristics are captured by "flows over time" which specify a flow rate for each arc and each point in time. We consider the quickest single commodity k-splittable flow problem and give a constant factor approximation algorithm for it. So far only results for k-splittable flows as well as for length-bounded flows and flows over time have been known, but nothing was known for combinations of them.
Bounding the flow value of each path is also interesting in the classical maximum s-t-flow problem. We study the case that each path may carry at most one unit of flow and prove that this restriction makes the maximum s-t-flow problem strongly NP-hard. In contrast to the classical maximum s-t-flow problem, the fractional and the integral problem diverge strongly with the new restriction. For the integral problem, we even prove APX-hardness. We develop an FPTAS for the fractional problem and an O(log m)-approximation algorithm for the integral one. (Here, m is the number of arcs in the network under consideration.) Similar results emerge for the multicommodity case. For the objective to find a maximum integral multicommodity flow our asymptotic approximation ratio of O(m^{0.5}) is proven to be best possible, unless P = NP
Survey of Consistent Network Updates
Computer networks have become a critical infrastructure. Designing dependable computer networks however is challenging, as such networks should not only meet strict requirements in terms of correctness, availability, and performance, but they should also be flexible enough to support fast updates, e.g., due to a change in the security policy, an increasing traffic demand, or a failure. The advent of Software-Defined Networks (SDNs) promises to provide such flexiblities, allowing to update networks in a fine-grained manner, also enabling a more online traffic engineering. In this paper, we present a structured survey of mechanisms and protocols to update computer networks in a fast and consistent manner. In particular, we identify and discuss the different desirable update consistency properties a network should provide, the algorithmic techniques which are needed to meet these consistency properties, their implications on the speed and costs at which updates can be performed. We also discuss the relationship of consistent network update problems to classic algorithmic optimization problems. While our survey is mainly motivated by the advent of Software-Defined Networks (SDNs), the fundamental underlying problems are not new, and we also provide a historical perspective of the subject
Robust network design under polyhedral traffic uncertainty
Ankara : The Department of Industrial Engineering and The Institute of Engineering and Science of Bilkent Univ., 2007.Thesis (Ph.D.) -- Bilkent University, 2007.Includes bibliographical references leaves 160-166.In this thesis, we study the design of networks robust to changes in demand
estimates. We consider the case where the set of feasible demands is defined by
an arbitrary polyhedron. Our motivation is to determine link capacity or routing
configurations, which remain feasible for any realization in the corresponding
demand polyhedron. We consider three well-known problems under polyhedral
demand uncertainty all of which are posed as semi-infinite mixed integer programming
problems. We develop explicit, compact formulations for all three problems
as well as alternative formulations and exact solution methods.
The first problem arises in the Virtual Private Network (VPN) design field.
We present compact linear mixed-integer programming formulations for the problem
with the classical hose traffic model and for a new, less conservative, robust
variant relying on accessible traffic statistics. Although we can solve these formulations
for medium-to-large instances in reasonable times using off-the-shelf MIP
solvers, we develop a combined branch-and-price and cutting plane algorithm to
handle larger instances. We also provide an extensive discussion of our numerical
results.
Next, we study the Open Shortest Path First (OSPF) routing enhanced with
traffic engineering tools under general demand uncertainty with the motivation to
discuss if OSPF could be made comparable to the general unconstrained routing
(MPLS) when it is provided with a less restrictive operating environment. To
the best of our knowledge, these two routing mechanisms are compared for the
first time under such a general setting. We provide compact formulations for
both routing types and show that MPLS routing for polyhedral demands can
be computed in polynomial time. Moreover, we present a specialized branchand-price
algorithm strengthened with the inclusion of cuts as an exact solution tool. Subsequently, we compare the new and more flexible OSPF routing with
MPLS as well as the traditional OSPF on several network instances. We observe
that the management tools we use in OSPF make it significantly better than the
generic OSPF. Moreover, we show that OSPF performance can get closer to that
of MPLS in some cases.
Finally, we consider the Network Loading Problem (NLP) under a polyhedral
uncertainty description of traffic demands. After giving a compact multicommodity
formulation of the problem, we prove an unexpected decomposition
property obtained from projecting out the flow variables, considerably simplifying
the resulting polyhedral analysis and computations by doing away with metric inequalities,
an attendant feature of most successful algorithms on NLP. Under the
hose model of feasible demands, we study the polyhedral aspects of NLP, used as
the basis of an efficient branch-and-cut algorithm supported by a simple heuristic
for generating upper bounds. We provide the results of extensive computational
experiments on well-known network design instances.Altın, AyşegülPh.D
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