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OnLine Routing of Virtual Circuits with Applications to Load Balancing and Machine Scheduling
, 1993
"... In this paper we study the problem of online allocation of routes to virtual circuits (both pointtopoint and multicast) where the goal is to minimize the required bandwidth. We concentrate on the case of permanent virtual circuits (i.e., once a circuit is established, it exists forever), and descr ..."
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Cited by 72 (7 self)
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In this paper we study the problem of online allocation of routes to virtual circuits (both pointtopoint and multicast) where the goal is to minimize the required bandwidth. We concentrate on the case of permanent virtual circuits (i.e., once a circuit is established, it exists forever), and describe an algorithm that achieves an O(log n) competitive ratio with respect to maximum congestion, where n is the number of nodes in the network. Informally, our results show that instead of knowing all of the future requests, it is sufficient to increase the bandwidth of the communication links by an O(log n) factor. We also show that this result is tight, i.e. for any online algorithm there exists a scenario in which O(log n) increase in bandwidth is necessary. We view virtual circuit routing as a generalization of an online load balancing problem, defined as follows: jobs arrive on line and each job must be assigned to one of the machines immediately upon arrival. Assigning a job to a machine increases this machine’s load by an amount that depends both on the job and on the machine. The goal is to minimize the maximum load. For the related machines case, we describe the first algorithm that achieves constant competitive ratio. For the unrelated case (with n machines), we describe a new method that yields O(log n)competitive
Optimal Hierarchical Decompositions for Congestion Minimization in Networks
, 2008
"... Hierarchical graph decompositions play an important role in the design of approximation and online algorithms for graph problems. This is mainly due to the fact that the results concerning the approximation of metric spaces by tree metrics (e.g. [10, 11, 14, 16]) depend on hierarchical graph decompo ..."
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Cited by 40 (1 self)
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Hierarchical graph decompositions play an important role in the design of approximation and online algorithms for graph problems. This is mainly due to the fact that the results concerning the approximation of metric spaces by tree metrics (e.g. [10, 11, 14, 16]) depend on hierarchical graph decompositions. In this line of work a probability distribution over tree graphs is constructed from a given input graph, in such a way that the tree distances closely resemble the distances in the original graph. This allows it, to solve many problems with a distancebased cost function on trees, and then transfer the tree solution to general undirected graphs with only a logarithmic loss in the performance guarantee. The results about oblivious routing [30, 22] in general undirected graphs are based on hierarchical decompositions of a different type in the sense that they are aiming to approximate the bottlenecks in the network (instead of the pointtopoint distances). We call such decompositions cutbased decompositions. It has been shown that they also can be used to design approximation and online algorithms for a wide variety of different problems, but at the current state of the art the performance guarantee goes down by an O(log 2 n log log n)factor when making the transition from tree networks to general graphs. In this paper we show how to construct cutbased decompositions that only result in a logarithmic loss in performance, which is asymptotically optimal. Remarkably, one major ingredient of our proof is a distancebased decomposition scheme due to Fakcharoenphol, Rao and Talwar [16]. This shows an interesting relationship between these seemingly different decomposition techniques. The main applications of the new decomposition are an optimal O(log n)competitive algorithm for oblivious routing in general undirected graphs, and an O(log n)approximation for Minimum Bisection, which improves the O(log 1.5 n) approximation
Competitive and Deterministic Embeddings of Virtual Networks
, 2012
"... Network virtualization is an important concept to overcome the ossification of today’s Internet as it facilitates innovation also in the network core and as it promises a more efficient use of the given resources and infrastructure. Virtual networks (VNets) provide an abstraction of the physical net ..."
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Cited by 13 (10 self)
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Network virtualization is an important concept to overcome the ossification of today’s Internet as it facilitates innovation also in the network core and as it promises a more efficient use of the given resources and infrastructure. Virtual networks (VNets) provide an abstraction of the physical network: multiple VNets may cohabit the same physical network, but can be based on completely different protocol stacks (also beyond IP). One of the main challenges in network virtualization is the efficient admission control and embedding of VNets. The demand for virtual networks (e.g., for a video conference) can be hard to predict, and once the request is accepted, the specification / QoS guarantees must be ensured throughout the VNet’s lifetime. This requires an admission control algorithm which only selects highbenefit VNets in times of scarce resources, and an embedding algorithm which realizes the VNet in such a way that the likelihood that future requests can be embedded as well is maximized. This paper describes a generic algorithm for the online VNet embedding problem which does not rely on any knowledge of the future VNet requests but whose performance is competitive to an optimal offline algorithm that has complete knowledge of the request sequence in advance: the socalled competitive ratio is, loosely speaking, logarithmic in the sum of the resources. Our algorithm is generic in the sense that it supports multiple traffic models, multiple routing models, and even allows for nonuniform benefits and durations of VNet requests.
Bounds for the Online Multicast Problem in Directed Graphs
 Proceedings of 4th International Colloquium on Structural Information and Communication Complexity (SIROCCO '97), Monte Verita
, 1997
"... Online multicasting has received a lot of attention lately, because of its great practical importance. However, most research assumes undirected graphs, which fail to model the directivity of real networks. In this paper, we fill this gap by offering upper and lower bounds for the online direct ..."
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Cited by 6 (5 self)
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Online multicasting has received a lot of attention lately, because of its great practical importance. However, most research assumes undirected graphs, which fail to model the directivity of real networks. In this paper, we fill this gap by offering upper and lower bounds for the online directed multicast problem in a worst case analysis. We examine two types of online problems: the joinonly problem where destinations join arbitrarily but stay till the end of the session, and the joinleave problem, where destinations can join and leave arbitrarily. We define the asymmetry of a graph to be the maximum ratio of opposite directed edges between a pair of nodes for all nodepairs. For the joinonly online problem, we prove that a greedy online algorithm is log(A + 1)competitive compared to any online algorithm. For the joinleave problem on both undirected and directed graphs, we prove a new lower bound, which is exponential in the previous undirected bound (the number o...
The Greedy, the Naive, and the Optimal Multicast Routing: from Theory to Internet Protocols
, 1999
"... This work studies the problem of multicast routing both at a theoretical and a practical level. Multicasting involves the distribution of the same data to several receivers at the same time. Ecient multicast routing can reduce the communications cost of the distribution tree. In this document, we ex ..."
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Cited by 2 (1 self)
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This work studies the problem of multicast routing both at a theoretical and a practical level. Multicasting involves the distribution of the same data to several receivers at the same time. Ecient multicast routing can reduce the communications cost of the distribution tree. In this document, we extend and study the most widely used routing algorithms in a variety of problems, and we compare their performance theoretically and through simulations. First, we study how the asymmetry of directed networks and the membership behavior aect the performance of these algorithms. We prove bounds for the various cases of these problems in a worst case analysis. Second, we propose algorithms for multicast connections where the users have dierent quality expectations from the multicast connection. We prove bounds for the performance of our algorithms, and examine their performance in a variety of scenarios through simulations. Third, we propose, QoSMIC, a multicast protocol for the Internet. A major advantage of QoSMIC is that the routing decisions consider the quality requirements of the users. In addition, the protocol limits the role of precon guration decisions, which cause problems in the employment of some previous protocols. Another important feature of the protocol is its exibility; it can scale to large networks, and it can adapt and evolve with the needs of the applications and the requirements of the users.
Distributed Admission Control, Scheduling, and Routing with Stale Information
, 2000
"... We study the problem of distributed online admission control and routing of permanent virtual circuits in a capacitated network. We assume that we have k distinct decision makers, each of which is responsible for gathering its own information about the state of the network. Through simulation, we de ..."
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Cited by 1 (0 self)
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We study the problem of distributed online admission control and routing of permanent virtual circuits in a capacitated network. We assume that we have k distinct decision makers, each of which is responsible for gathering its own information about the state of the network. Through simulation, we demonstrate that an exponential based routing scheme will perform well in a distributed model provided granularity is sufficiently high. In order to ground these results theoretically, we prove that exponentialbased schemes attain bestpossible competitive ratios (same as for the centralized case) provided each edge can accommodate at least\Omega\Gamma k log n) requests. A matching lowerbound shows that no deterministic algorithm can attain bestpossible competitive ratios without requiring the same level of granularity. In the randomized case, we present a modified exponentialbased approach which obtains bestpossible competitive ratios provided the granularity is at least\Ome...
Online Multicasting in Directed Graphs
, 1998
"... In this paper we study the problem of online multicasting on directed graphs, and we demonstrate the competitiveness of a greedy algorithm in a worst case analysis. We prove that the greedy algorithm performs almost as well as any online algorithm: the greedy upper bound is very close to the lo ..."
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In this paper we study the problem of online multicasting on directed graphs, and we demonstrate the competitiveness of a greedy algorithm in a worst case analysis. We prove that the greedy algorithm performs almost as well as any online algorithm: the greedy upper bound is very close to the lower bound of any online algorithm. First, we improve on the upper bound of the offline greedy algorithm on undirected graphs with a simpler than the previous proof. Assume that A is the measure of asymmetry in a graph and M the size of the multicast group. For highly asymmetric graphs, we prove that the performance of the greedy algorithm is tightly bounded by \Theta(M ), and prove that this is also the lower bound for any algorithm. For less asymmetric graphs, the greedy algorithm is bounded above by O(A log(M )). For these graphs, we prove that any algorithm performs at least as bad as O(A log(M )= log(A)). Draft Version 1.0 1 Introduction In this paper we examine the bounds fo...