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MultiConstrained Optimal Path Selection
, 2001
"... Providing qualityofservice (QoS) guarantees in packet networks gives rise to several challenging issues. One of them is how to determine a feasible path that satisfies a set of constraints while maintaining high utilization of network resources. The latter objective implies the need to impose an a ..."
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Cited by 55 (1 self)
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Providing qualityofservice (QoS) guarantees in packet networks gives rise to several challenging issues. One of them is how to determine a feasible path that satisfies a set of constraints while maintaining high utilization of network resources. The latter objective implies the need to impose an additional optimality requirement on the feasibility problem. This can be done through a primary cost function (e.g., administrative weight, hopcount) according to which the selected feasible path is optimal. In general, multiconstrained path selection, with or without optimization, is an NPcomplete problem that cannot be exactly solved in polynomial time. Heuristics and approximation algorithms with polynomialand pseudopolynomialtime complexities are often used to deal with this problem. However, existing solutions suffer either from excessive computational complexities that cannot be used for online network operation or from low performance. Moreover, they only deal with special cases of the problem (e.g., two constraints without optimization, one constraint with optimization, etc.). For the feasibility problem under multiple constraints, some researchers have recently proposed a nonlinear cost function whose minimization provides a continuous spectrum of solutions ranging from a generalized linear approximation (GLA) to an asymptotically exact solution. In this paper, we propose an efficient heuristic algorithm for the most general form of the problem. We first formalize the theoretical properties of the above nonlinear cost function. We then introduce our heuristic algorithm (H MCOP), which attempts to minimize both the nonlinear cost function (for the feasibility part) and the primary cost function (for the optimality part). We prove that H MCOP guarantees at least t...
Lagrange Relaxation Based Method for the QoS Routing Problem
, 2001
"... In this paper a practically efficient QoS routing method is presented, which provides a solution to the delay constrained least cost routing problem. The algorithm uses the concept of aggregated costs and provides an efficient method to find the optimal multiplier based on Lagrange relaxation. This ..."
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Cited by 35 (0 self)
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In this paper a practically efficient QoS routing method is presented, which provides a solution to the delay constrained least cost routing problem. The algorithm uses the concept of aggregated costs and provides an efficient method to find the optimal multiplier based on Lagrange relaxation. This method is proven to be polynomial and it is also efficient in practice. The benefit of this method is that it also gives a lower bound on the theoretical optimal solution along with the result. The difference between the lower bound and the cost of the found path is very small proving the good quality of the result. Moreover, by further relaxing the optimality of paths, an easy way is provided to control the tradeoff between the running time of the algorithm and the quality of the found paths. We present a comprehensive numerical evaluation of the algorithm, by comparing it to a wide range of QoS routing algorithms proposed in the literature. It is shown that the performance of the proposed polynomial time algorithm is close to the optimal solution computed by an exponential algorithm. KeywordsQoS routing, delay, optimization, Lagrange relaxation I.
Efficient QoS partition and routing of unicast and multicast
 in Proc. of IWQoS 2000
, 2000
"... Abstract—In this paper, we study problems related to supporting unicast and multicast connections with quality of service (QoS) requirements. We investigate the problem of optimal routing and resource allocation in the context of performance dependent costs. In this context, each network element can ..."
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Cited by 16 (3 self)
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Abstract—In this paper, we study problems related to supporting unicast and multicast connections with quality of service (QoS) requirements. We investigate the problem of optimal routing and resource allocation in the context of performance dependent costs. In this context, each network element can offer several QoS guarantees, each associated with a different cost. This is a natural extension to the commonly used bicriteria model, where each link is associated with a single delay and a single cost. This framework is simple yet strong enough to model many practical interesting networking problems. An important problems in this framework is finding a good path for a connection that minimizes the cost while retaining the endtoend delay requirement. Once such a path (or a tree, in the multicast case) is found, one needs to partition the endtoend QoS requirements among the links of the path (tree). We consider the case of general integer cost functions (where delays and cost are integers). As the related problem is NP complete, we concentrate on finding efficientapproximation solutions. We improve on recent previous results by Ergün et al. Lorenz and Orda, and Raz and Shavitt, both in terms of generality as well as in terms of complexity of the solution. In particular, we present novel approximation techniques that yield the best known complexity for the unicast QoS routing problem, and the first approximation algorithm for the QoS partition problem on trees, both for the centralized and distributed cases. Index Terms—Approximation, multicast, QoSdependent costs, QoS, resource allocation, routing.
ConstraintBased Routing in the Internet: Basic Principles and Recent Research
, 2003
"... Novel routing paradigms based on policies, quality of service (QoS) requirements, and packet content have been proposed for the Internet over the last decade. Constraintbased routing algorithms select a routing path satisfying constraints which are either administrativeoriented (policy routing), or ..."
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Cited by 13 (0 self)
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Novel routing paradigms based on policies, quality of service (QoS) requirements, and packet content have been proposed for the Internet over the last decade. Constraintbased routing algorithms select a routing path satisfying constraints which are either administrativeoriented (policy routing), or serviceoriented (QoS routing). The routes, in addition to satisfying constraints, are selected to reduce costs, balance network load, or increase security. In this paper, we discuss several constraintbased routing approaches and explain their requirements, complexity, and recent research proposals. In addition, we illustrate how these approaches can be integrated with Internet label switching and QoS architectures. We also discuss examples of applicationlevel routing techniques used in today's Internet.
Mieghem, “A Review of ConstraintBased Routing Algorithms
 in Technical Report
, 2002
"... Constraintbased routing is an invaluable part of a fullßedged Quality of Service (QoS) architecture. Unfortunately, routing with multiple additive constraints is known to be a NPcomplete problem. Hence, accurate constraintbased routing algorithms with a fast running time are scarce, perhaps even ..."
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Cited by 7 (0 self)
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Constraintbased routing is an invaluable part of a fullßedged Quality of Service (QoS) architecture. Unfortunately, routing with multiple additive constraints is known to be a NPcomplete problem. Hence, accurate constraintbased routing algorithms with a fast running time are scarce, perhaps even nonexistent. The expected impact of such a constrainedbased routing algorithm has resulted in the proposal of numerous heuristics and a few exact QoS algorithms. Although at times an overview of QoS algorithms has been published, a comparative study to the performance of QoS algorithms is still missing. With this paper we attempt to Þll this gap. This paper aims to give a thorough, concise and fair evaluation of the most important constraintbased routing algorithms known today. We will provide a descriptive overview of restricted shortest path algorithms and multiconstrained path algorithms. A performance evaluation of these two classes of algorithms is presented based on complexity analysis and simulation results. 1
A Scalable Approach to the Partition of QoS Requirements in Unicast and Multicast
 in Proceedings of the IEEE INFOCOM’02
, 2002
"... Supporting Quality of Service (QoS) in largescale broadband networks poses major challenges, due to the intrinsic complexity of the corresponding resource allocation problems. An important problem in this context is how to partition QoS requirements along a selected topology (path for unicast, tree ..."
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Cited by 6 (1 self)
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Supporting Quality of Service (QoS) in largescale broadband networks poses major challenges, due to the intrinsic complexity of the corresponding resource allocation problems. An important problem in this context is how to partition QoS requirements along a selected topology (path for unicast, tree for multicast) . As networks grow in size, the scalability of the solution becomes increasingly important. This requires to devise efficient algorithms, whose computational complexity is less dependent on the network size. In addition, recently proposed precomputation based methods can be employed to facilitate scalability by significantly reducing the time needed for handling incoming requests.
Optimal Partition of QoS Requirements for ManytoMany Connections
 In Proc. of INFOCOM’2003
, 2003
"... We studypr oblemsr elated tosupporIA4 multicast connections with Quality ofSer vice (QoS)r equir ements. We investigate thepr oblem of optimalr esour ce allocation in the context ofper or643 dependent costs. In this context each networ element canoffer sever3 QoSguar468IA4 each associated with a di ..."
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Cited by 4 (0 self)
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We studypr oblemsr elated tosupporIA4 multicast connections with Quality ofSer vice (QoS)r equir ements. We investigate thepr oblem of optimalr esour ce allocation in the context ofper or643 dependent costs. In this context each networ element canoffer sever3 QoSguar468IA4 each associated with a differ ent cost. This is anatur7 extension to the commonly used bicrMMM2I model,wher e each link is associated with a single delay and a single cost. ThisfrsIU or is simple yetstr ong enough to model manyprIUM798 inter esting networwI2 pr oblems. The fundamental multicastr esour ce allocationpr oblemunder thisfrsI6 or is how to optimally allocate QoSr equir ements on the links of the multicasttr ee. One needs toparU839I the endtoend QoSr equir ement along the var784 paths in a tr ee. The goal is to satisfy the endtoend QoSr equir ement with minimum cost. Pr evious studiesunder thisfrsIU or consider edsing713y347 multicast connections,wher e the Endtoend QoSr equir ement is specifiedfr om thesour ce to allother multicastgr oupmemberU In thispaper we extend theser esults to themor egener9I and considerIA3 harid case of multicast sessions,wher e the endtoendr equir ement hold for ever path between any two multicast gr oupmember2 Our aim is topr ovide rdeI ous solutions, with pr ovenper or52I guarA27737 by way ofalgor5IA27 analysis. Thepr oblemunder investigation is NPhar for gener2 cost functions, thus wefirU pr esent a pseudopolynomial exact solution.Fr om this solution weder ve two efficient #appr oximate solutions. One achieves optimal cost, but may violate the endto end delayr equir ement by afactor of (1 + #), and theother strer5 obeys the bounds and achieves a cost within afactor of (1+#) of the optimum.Furm.IU35 e, wepr esentimpr ovedr esults for discr ete c...
On resource constrained optimization problems
 In: 4th JapaneseHungarian Symposium on Discrete Mathematics and Its Applications
, 2005
"... Abstract: This paper shows that a method that has long been used to solve Resource Constrained Optimization Problems and found extremely effective in practice, is effective in the theoretical sense as well, it is proved to be strongly polynomial. In the special case of Resource Constrained Shortest ..."
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Cited by 4 (0 self)
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Abstract: This paper shows that a method that has long been used to solve Resource Constrained Optimization Problems and found extremely effective in practice, is effective in the theoretical sense as well, it is proved to be strongly polynomial. In the special case of Resource Constrained Shortest Path Problem a better running time estimation is also presented.
Nearoptimal allocation of delay requirements on multicast trees
 in IFIP Interworking 2002  Converged Networking: Data and Realtime over IP
, 2002
"... Abstract Knowing the QoS requirement for each link involved in a multicast connection, such that overall QoS requirement is satisfied, would greatly assist both QoSbased multicast routing and resource reservation processes. In the case of delay, the question of what delay requirements should be imp ..."
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Cited by 1 (1 self)
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Abstract Knowing the QoS requirement for each link involved in a multicast connection, such that overall QoS requirement is satisfied, would greatly assist both QoSbased multicast routing and resource reservation processes. In the case of delay, the question of what delay requirements should be imposed on each link of a sourcebased multicast tree, such that the overall sourcetodestination delay and interdestination delay variation requirements are satisfied at minimum total tree cost, is the focal point of this paper. A major contribution of this paper is the development of a number of heuristic algorithms for (near)optimal allocation of delay requirements using Genetic Algorithms (GAs). Initial tests, with multicast trees of different sizes (10 and 30node trees), configurations (in terms of number of destinations and destination distribution), and overall delay requirements, show the ability of the algorithms in providing good solutions within a reasonable amount of time.
Hopbyhop Computing for Green Internet Routing (Technical report, under revision)
"... Abstract—Energy conservation is a global concern nowadays and it is widely expected that energy cost will continuously increase in the near future. The design of the Internet, unfortunately, has not taken energy issues into consideration at the very beginning. There are emerging studies on reducing ..."
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Abstract—Energy conservation is a global concern nowadays and it is widely expected that energy cost will continuously increase in the near future. The design of the Internet, unfortunately, has not taken energy issues into consideration at the very beginning. There are emerging studies on reducing Internet energy footprint. These studies aim at turning network components such as line cards or routers into sleeping modes. We make an observation that different traffic volumes on links result in different energy consumption, even without turningoff network devices. As such, we for the first time design a green Internet traffic routing scheme; and it is orthogonal to those turningoff network components schemes. There can be many design choices for our green routing schemes. As an example, an optimization problem can be formulated where we centralized compute routing paths to minimize the overall energy consumption. Such approach, however, requires to deploy additional protocols for the Internet. In this paper, we propose a hopbyhop routing scheme. Such scheme can be easily incorporated into current OSPF protocol. We solve many challenges. First, we present a power model to quantify link rate and power consumption. We validate our model using real world experiments. Second, unlike centralized computing, a key challenge for hopbyhop computing is to avoid routing loops. We thus design green routing algorithms that are isotonic and guarantee that no loop will be formulated. Third, hopbyhop routing without loops does not naturally lead to minimized energy consumption. Therefore, we develop a set of enhanced algorithms that substantially improve the performance. Fourth, a “green” path may degrade QoS performance such as endtoend delay. We study this problem and develop an algorithm that coconsiders energy conservation and path stretch. We comprehensively evaluate our algorithms through simulations on synthetic and real topologies and traffic traces. We show that with green routing, we can save the power that is consumed by line cards for as much as 50%. I.