B. Awerbuch and Y. Shavitt. Topology aggregation for directed graphs. Technical Report 98-14, DIMACS, Feb. 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....approaches have been already used in ATM networks with the PNNI routing protocol [9] In hierarchical QoS routing, network topology and resource information about a specific domain are summarized before being exchanged with other domains. This process is called topology aggregation [10] [11], 12] 13] 14] With the summarized (i.e. aggregated) network information, traffic sources run QoS routing algorithms to compute a source route. The computed path is then explored with proper signaling to reserve network resources, possibly in combination with a crankback feature [15] 16] ....

Y. Shavitt B. Awerbuch. Topology Aggregation for Directed Graphs. IEEE/ACM Transactions on Networking, 9(1), February 2001.

....Each node can collect information about its neighboring nodes by eavesdropping. The responding node can choose a fractionf of these neighbors and apply the filter specified by the query type parameter. Even, in case of topology discovery a more sophisticated aggregation scheme as proposed in [16] could be used. A different type of aggregation could be used for energy information as proposed in [4] Finally use of schemes like smart messages as proposed in [24] which would carry specific code along with the query to support infrequent queries could save valuable memory resources in ....

Baruch Awerbuch and Yuval Shavitt, "Topology Aggregation for Directed Graphs. ", IEEE/ACM Transactions on Networking, Vol.9, N0.1, Feb 2001.

....nodes formed in simulations compared to the number of black nodes from the analytical expectation of the number and shows that the analytical model is reasonably accurate. Figures 6 and 7 show comparison of STREAM against centralized log(n) approximate solution provided by the greedy algorithm [15] for set cover to find the black nodes. Figure 6 shows the impact of increasing the number of nodes in the field. Figure 7 shows the effect of communication range for 1000 nodes in the field. In both cases, STREAM performs almost as well as the centralized solution which has global knowledge. ....

....execute before sending the data in order to support the query. The type of information retrieved determines the semantics used to filter information of neighborhood when a node responds to a query. For example, in case of topology discovery a more sophisticated aggregation scheme as proposed in [15] could be used. Schemes like smart messages [23] may also be used which would carry specific code along with the query to support infrequent queries could save valuable memory resources in sensor nodes. In future, we plan to explore the parameter space of STREAM qualitatively and quantitatively. ....

Bamch Awerbuch and Yuval Shavitt, "Topology Aggregation for Directed Graphs. ' IEEE/ACM Transactions on Networking, Vol.9, N0.1, Feb 2001.

....peer groups. Although PNNI defines how the aggregated peer group looks like, it does not specify how to do the aggregation. Some aggregation schemes have been proposed. All aggregation algorithms suffer from distortion which means the resulted aggregation topology deviates from the original one. [1] describes how to aggregate a peer group of one metric with bounded distortion. However, the theoretical bound of distortion of networks having two or more parameters is still unknown. There are not many studies addressing topology aggregation of multiple parameters. Some studies can 1 This work ....

B. Awerbuch and Y. Shavitt. Topology aggregation for directed graphs. Technical Report 98-14, DIMACS, Feb. 1998. Also, in IEEE Proceedings of ISCC' 98, p. 47-52, 1998.

....always have a negative impact on routing performance. Some aggregation schemes have been proposed. Since the network is represented by a simple topology, all aggregation algorithms suffer from distortion, that is, the cost of routing through the aggregated network deviates from the original one. [3] proposes an algorithm that aggregates networks with one additive parameter with bounded distortion. However, the theoretical bound of distortion for networks with two or more quality of service (QoS) parameters is still unknown. There are only few studies addressing topology aggregation with ....

B. Awerbuch and Y. Shavitt. Topology aggregation for directed graphs. Technical Report 98-14, DIMACS, Feb. 1998. Also, in IEEE Proceedings of ISCC' 98, p. 47-52, 1998.

....examined compact graph representations [7, 2] with emphasis on the maximum cost distortion between any pair of nodes in the aggregated graph. Lee presents a spanning tree method for link state aggregation in [14] and shows the effect of state aggregation theoretically. Awerbuch and Shavitt [4] present a distortion bounded solution for aggregating the state of a subnetwork, and show how to apply it to PNNI. The effect of different aggregation schemes on network performance is compared by simulation in [3] However, they do not investigate the effect of workload distribution. Our ....

B. Awerbuch, Y. Shavitt. Topology Aggregation for Directed Graph. http://www.cnds.jhu.edu/publications/.

....amount of lossyness that results from graph reduction is not known in advance, and can vary depending on the actual values of the QoS parameters. To remedy this issue, some researchers proposed new TA approaches that minimize the average distortion (i.e. lossyness) in a least square sense [7] [5]. In [12] 16] the authors present several heuristic algorithms for route selection in the presence of inaccurate topological information, including inaccuracies that are caused by TA. The effects of several TA schemes on routing performance have been studied by simulation [4] 13] There have ....

B. Awerbuch and Y. Shavitt. Topology aggregation for directed graph. In Proceedings of ISCC'98, pages 47 --52. IEEE, 1998.

....the amount of lossyness that results from graph reduction is not known in advance, and can vary depending on the actual values of the QoS parameters. To remedy this issue, some researchers proposed new TA approaches that minimize the average distortion (i.e. lossyness) in a least square sense [7, 5]. In [11, 13] the authors present several heuristic algorithms for route selection in the presence of inaccurate topological information, including inaccuracies that are caused by TA. No particular TA schemes were discussed. The effects of several TA schemes on routing performance have been ....

B. Awerbuch and Y. Shavitt. Topology aggregation for directed graph. In Proceedings of ISCC'98, pages 47 --52. IEEE, 1998.

....analysis, and finally, we draw conclusions in Section 7. 2. Related Work Topology aggregation and QoS routing, have been discussed, mostly independently, by various studies. A topology aggregation algorithm, that achieves bounded distortion in domains with only one parameter, is studied in [1]. However, the theoretical bound of distortion of networks having two or more parameters is still unknown. There are not many studies addressing topology aggregation of multiple parameters. Some studies can be found in [9] 10] and [11] Traditional approaches usually represent each logical link ....

....Figure 1 presents an example of aggregation. Ideally, given a pair of border nodes b 1 and b 2 , the QoS parameter of going from b 1 to b 2 in the aggregation should be the same as the QoS parameter of the best path in the original domain. Even for a single metric, it is difficult to achieve [1]. There is another issue for networks with multiple metrics: how to pick the best parameter. One path may be the best in terms of delay but the other may be the best if bandwidth is considered. For example, a delay bandwidth QoS pair (5; 8) is better than another pair (10; 10) in terms of delay ....

B. Awerbuch and Y. Shavitt. Topology aggregation for directed graphs. Technical Report 98-14, DIMACS, Feb. 1998. Also, in In IEEE Proceedings of the ISCC' 98, p. 47-52, 1998.

.... in the context of mobile packet radio networks where the primary objective has been to produce connected clusters of bounded size [23] 30] 25] 31] and in the context of ATM PNNI where the objective has been to produce a reduced representation of the topology of a cluster [24] [3]. In this paper, we focus on the computationally complex problem of clustering elements of a large stationary internetwork to form a hierarchical routing structure. The clustering algorithm is a computationally intensive centralized procedure that executes in selected elements using global ....

B. Awerbuch and Y. Shavitt, "Topology Aggregation for Directed Graph," Third IEEE Symposium on Computers and Communication, Jun 1998.

....Although PNNI de nes how the aggregated peer group looks like, it does not specify how to do the aggregation. A number of aggregation schemes have been proposed. All aggregation algorithms su er from distortion which means the resulted aggregation topology deviates from the original one. In [1], an algorithm that minimizes distortion in peer groups with only one parameter is proposed. However, the theoretical bound of distortion of networks having two or more parameters is still unknown. There are not many studies addressing topology aggregation of multiple parameters. Some studies can ....

B. Awerbuch and Y. Shavitt. Topology aggregation for directed graphs. Technical Report 98-14, DIMACS, Feb. 1998. Also, in IEEE Proceedings of ISCC' 98, p. 47-52, 1998.

....examined compact graph representations [7, 2] with emphasis on the maximum cost distortion between any pair of nodes in the aggregated graph. Lee presents a spanning tree method for link state aggregation in [14] and shows the effect of state aggregation theoretically. Awerbuch and Shavitt [4] present a distortion bounded solution for aggregating the state of a subnetwork, and show how to apply it to PNNI. The effect of different aggregation schemes on network performance is compared by simulation in [3] However, the model only considers a single source destination pair. Our results: ....

B. Awerbuch, Y. Shavitt. Topology Aggregation for Directed Graph. http://www.cnds.jhu.edu/publications/.

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B. Awerbuch and Y. Shavitt, \Topology aggregation for directed graphs," IEEE/ACM Trans. on Net., Feb 2001.

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B. Awerbuch and Y. Shavitt, "Topology aggregation for directed graphs," IEEE/ACM Trans. Networking, vol. 9, pp. 82--90, Feb. 2001.

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B. Awerbuch and Y. Shavitt, "Topology aggregation for directed graphs," IEEE/ACM Trans. Networking, Feb. 2001.

.... cheapest) path through the cloud [1] For this end, each network advertises its distance matrix in a compressed manner, and it is recommended that the matrix representation is smaller than 3b, where b is the number of border nodes [1] The best compression technique that was suggested in the past [2] will be presented later. This research was supported by a grant from the United States Israel Binational Science Foundation (BSF) Jerusalem, Israel. Selecting the closest mirror. Recently, there was a large interest in using distance maps of the Internet to aid in tasks such as closest ....

....In Sec. III, BBS is compared to four other methods, using simulated graphs created according to both Waxman [12] and Barab asi Albert (BA) 13] methods. In Sec. IV we apply BBS in two practical applications, topology aggregation and Internet distance maps, comparing it with previous results from [2] and [4] 5] respectively. II. BIG BANG SIMULATION A. The Model The vertices of the graph, the network nodes, are modeled as a set of particles, traveling in the Euclidean space under the affect of potential force field. Each particle is the geometric image of a vertex. The field force is ....

[Article contains additional citation context not shown here]

B. Awerbuch and Y. Shavitt, "Topology aggregation for directed graphs," IEEE/ACM Trans. Networking, Feb 2001.

....virtual node in a parent partition becomes the parent of the virtual nodes of the child partitions. The length of the links from a virtual node to its children is half the partition diameter. We embed the virtual nodes in the original graph based on a technique developed by Awerbuch and Shavitt [42]. Together, the virtual nodes also form a tree. The randomization of a partition radius is done so that the probability of a short link being cut by partitioning decreases exponentially as one climbs up the tree. Hence nodes close together are more likely to be partitioned lower down the tree. We ....

Baruch Awerbuch and Yuval Shavitt, "Topology aggregation for directed graphs," in Third IEEE Symposium on Computers and Communications, June 1998, pp. 47 -- 52.

....virtual node in a parent partition becomes the parent of the virtual nodes of the child partitions. The length of the links from a virtual node to its children is half the partition diameter. We embed the virtual nodes in the original graph based on a technique developed by Awerbuch and Shavitt [19]. Together, the virtual nodes also form a tree. The randomization of a partition radius is done so that the probability of a short link being cut by partitioning decreases exponentially as one climbs up the tree. Hence nodes close together are more likely to be partitioned lower down the tree. We ....

.... center [18] 1. Construct 2 43 2 53 3 6 2. Compute 7 8 for each 2 8 3. Find smallest such that 9 7 9; 1 , say = 4. 7 is the set of 1 centers Fig. 5. Two approximate algorithm for the minimum center problem. greedy algorithm on the HST tree (see [19] for a more formal presentation of the algorithm) The algorithm pushes the centers down the tree until it discovers a partition with diameter . The number of partitions, is the minimum number of centers required to satisfy the performance metric . To select the actual ....

Baruch Awerbuch and Yuval Shavitt, "Topology aggregation for directed graphs," IEEE/ACM Transactions on Networking, vol. 9, no. 1, pp. 82--90, February 2001.

....virtual node in a parent partition becomes the parent of the virtual nodes of the child partitions. The length of the links from a virtual node to its children is half the partition diameter. We embed the virtual nodes in the original graph based on a technique developed by Awerbuch and Shavitt [43]. Together, the virtual nodes also form a tree. The randomization of a partition radius is done so that the probability of a short link being cut by partitioning decreases exponentially as one climbs up the tree. Hence nodes close together are more likely to be partitioned lower down the tree. We ....

....N i be the children of node i on the partition tree, and L be a list of partitions sorted in the decreasing order of the partition diameter at all times. max(L) denotes the partition at the head of the list, and diam(max(L) its diameter. Fig. 4 presents our greedy algorithm on the k HST tree (see [43] for a more formal presentation of the algorithm) The algorithm pushes the centers down the tree until it discovers a partition with diameter D. The number of partitions, jLj, is the minimum number of centers required to satisfy the performance metric P diam . To select the actual centers, we ....

Baruch Awerbuch and Yuval Shavitt, "Topology aggregation for directed graphs," IEEE/ACM Transactions on Networking, vol. 9, no. 1, pp. 82--90, February 2001.

....virtual node in a parent partition becomes the parent of the virtual nodes of the child partitions. The length of the links from a virtual node to its children is half the partition diameter. We embed the virtual nodes in the original graph based on a technique developed by Awerbuch and Shavitt [6]. Together, the virtual nodes also form a tree. The randomization of a partition radius is done so that the probability of a short link being cut by partitioning decreases exponentially as one climbs the tree. Hence nodes close together are more likely to be partitioned lower down the tree. We ....

Baruch Awerbuch and Yuval Shavitt, "Topology aggregation for directed graphs," in Third IEEE Symposium on Computers and Communications, June 1998, pp. 47 -- 52.

....virtual node in a parent partition becomes the parent of the virtual nodes of the child partitions. The length of the links from a virtual node to its children is half the partition diameter. We embed the virtual nodes in the original graph based on a technique developed by Awerbuch and Shavitt [6]. Together, the virtual nodes also form a tree. The randomization of a partition radius is done so that the probability of a short link being cut by partitioning decreases exponentially as one climbs the tree. Hence nodes close together are more likely to be partitioned lower down the tree. We ....

Baruch Awerbuch and Yuval Shavitt, "Topology aggregation for directed graphs," in Third IEEE Symposium on Computers and Communications, June 1998, pp. 47 -- 52.

....with equal capacities in both directions of each link, the dummy trac required is no greater than the real trac itself, resulting in a modest factor of two loss. Once the directed graph is reduced to an undirected graph, any of the undirected compact representations can be used to compress it. AS98] considers an alternate model in which dummy trac is not sent. Instead, the directed graph is characterized in terms of the maximum asymmetry, of its edge weights. AS98] present a scheme to represent a directed graph with asymmetry and b border nodes in O(b) space with O( p log b) ....

....directed graph is reduced to an undirected graph, any of the undirected compact representations can be used to compress it. AS98] considers an alternate model in which dummy trac is not sent. Instead, the directed graph is characterized in terms of the maximum asymmetry, of its edge weights. AS98] present a scheme to represent a directed graph with asymmetry and b border nodes in O(b) space with O( p log b) distortion. In a recent experimental work [ADKS98] Awerbuch, Du, Khan and Shavitt study simple and practical techniques for directed graph compression. Their work is based on ....

Baruch Awerbuch and Yuval Shavitt. Topology aggregation for directed graphs. In Proceedings of IEEE ISCC, 1998.

....virtual node becomes the parent of the virtual nodes that are assigned to the subpartitions of its partition. The length of the links from a node to its children is half the partition diameter. We embed the virtual nodes in the original graph based on a technique developed by Awerbuch and Shavitt [6]. The randomization of a partition radius is done so that the probability for a short link to be cut by a partition border decreases exponentially as one goes up the tree. Hence nodes close together are more probably partitioned lower down the tree. We take advantage of this characteristics of ....

Baruch Awerbuch and Yuval Shavitt, "Topology aggregation for directed graphs," in Third IEEE Symposium on Computers and Communications, June 1998, pp. 47 -- 52.

....the network control load several fold. Aggregation using the minimum spanning tree (MST) is seen to yield very good overall network performance. This fact, together with the simplicity of calculating spanning trees makes them an attractive candidate for use in practice, e.g. Awerbuch and Shavitt [AS98] suggest a profitable enhancement to the current PNNI standard based on random trees. In addition, we also investigate the impact of link cost functions, and re aggregation policy. A link cost function is a mapping from the resources available on the link (e.g. bandwidth) to a real number. Link ....

....already be partially implemented by using the exception (borderto border) link mechanism in the complex node representation of PNNI [PNN96, section 3.3. 8] An algorithm for another tree based construction within the guidelines of the PNNI aggregation specification is described and analyzed in [AS98] We intend to simulate the performance of this construction as part of our future work. We demonstrate that using our proposed logarithmic update policy reduces the number of re aggregation computations drastically, while not compromising network performance in any significant way. Finally, we ....

Baruch Awerbuch and Yuval Shavitt. Topology aggregation for directed graphs. In Third IEEE Symposium on Computers and Communications, June 1998.

....a metric space. In the following, we investigate the influence the edge deletion has on the distortion. We show first that the graph remains connected, and then we give a bound on the additional distortion due to edge deletion. Due to space limitation we omit the proofs and refer the reader to [2]. Theorem 1 The link deletion from the undirected clique results in a connected graph. Lemma 1 For a link with asymmetry ratio ae e , the maximum distortion due to link deletion from the undirected clique is p ae=ae e . Theorem 2 The maximum distortion of applying the square root ....

....iteratively created until the cumulative number of links (exceptions) exceeded 2b. Table 3 summarizes the link distortions for the same random weight assignments that were used in table 1. The average distortion is shown to be about 1.5. When the number of border nodes is 33 the average is about 2 [2]. However, more to appear in IEEE ISCC 98, Athens, Greece. Histogram l. max ave var 1 2 3 4 5 6 u. 2.68 1.31 .10 31 192 8 0 0 0 54 2.90 1.32 .13 33 180 18 0 0 0 52 4.63 1.46 .47 45 150 22 11 3 0 45 6.00 1.64 .44 21 161 38 9 1 1 52 Table 3. Summary of the distortion for the graph with 22 border ....

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B. Awerbuch and Y. Shavitt. Topology aggregation for directed graphs. Technical Report 98-14, DIMACS, Feb. 1998.

....a a logarithmic bound on the worst case distortion of costs between any pair of nodes. In other words, for any pair of nodes the ratio between the advertised and the true cost of the shortest path that connect them is bounded by a log b, where b is the number of border nodes. Awerbuch and Shavitt [4] presented an aggregation scheme based on Bartal trees [5] and showed that it achieves the promised logarithmic bound. Awerbuch et al. 3] conducted a simulation study of PNNI routing where they found that using a Minimum Spanning Tree (MST) aggregation does not degrade performance. Lee [7] ....

....maximum and the minimum traversing delay is high, a situation occurring, e.g. when the original topology is sparse. In this work, we investigate the aggregation performance of some heuristics based on MST and Random Spanning Tree (RST) and compare them with the t tree aggregation suggested in [4], and with the maximum spanning tree suggested by Lee [7] We show that MST is a good aggregation scheme, which corresponds to the simulations conducted in [3] and show that it can be enhanced by combining the MST with RSTs. We also show that a combination of three RSTs is very bad, which again ....

[Article contains additional citation context not shown here]

Baruch Awerbuch and Yuval Shavitt. Topology aggregation for directed graphs. In Third IEEE Symposium on Computers and Communications, pages 47 -- 52, June 1998.

....the network control load several fold. Aggregation using the minimum spanning tree (MST) is seen to yield very good overall network performance. This fact, together with the simplicity of calculating spanning trees makes them an attractive candidate for use in practice, e.g. Awerbuch and Shavitt [AS98] suggest a profitable enhancement to the current PNNI standard based on random trees. In addition, we also investigate the impact of link cost functions, and re aggregation policy. A link cost function is a mapping from the resources available on the link (e.g. bandwidth) to a real number. Link ....

....on the latest reported topology induced by the border nodes, no averaging was used. The are several reasons not to use the full network topology in calculating the aggregation. The most obvious one is that this way it is easy to encode the aggregation in the PNNI standard using exceptions [AS98] When security is of concern, this way no details of the internal network structure are revealed. Finally, for aggregation schemes with high calculation complexity, the use of a smaller topology reduces the calculation overhead. It is important to note that aggregation calculation does not come ....

[Article contains additional citation context not shown here]

Baruch Awerbuch and Yuval Shavitt. Topology aggregation for directed graphs. In Third IEEE Symposium on Computers and Communications, June 1998.

....the network control load several fold. Aggregation using the minimum spanning tree (MST) is seen to yield very good overall network performance. This fact, together with the simplicity of calculating spanning trees makes them an attractive candidate for use in practice, e.g. Awerbuch and Shavitt [4] suggest a profitable enhancement to the current PNNI standard based on random trees. In addition, we also investigate the impact of link cost functions, and re aggregation policy. A link cost function is a mapping from the resources available on the link (e.g. bandwidth) to a real number. Link ....

....MST can already be partially implemented by using the exception (border to border) link mechanism in the complex node representation of PNNI [9, section 3.3. 8] An algorithm for another tree based construction within the guidelines of the PNNI aggregation specification is described and analyzed in [4]. We intend to simulate the performance of this construction as part of our future work. We demonstrate that using our proposed logarithmic update policy reduces the number of re aggregation computations drastically, while not compromising network performance in any significant way. Finally, we ....

B. Awerbuch and Y. Shavitt. Topology aggregation for directed graphs. In Third IEEE Symposium on Computers and Communications, June 1998.

....logarithmic updates are used and when full update is used for the topology of figure 16. exceptions allowed by PNNI [tc96, section 3.3. 8] An algorithm for a tree based construction within the PNNI aggregation framework (using bypass exception) is described and analyzed by Awerbuch and Shavitt [AS97] We intend to simulate it in our future work. This paper shows that performing re aggregation using our logarithmic update policy reduces the number of aggregations drastically, yet the performance is not compromised. We also show that exponential cost metric results in better performance than ....

Baruch Awerbuch and Yuval Shavitt. Topology aggregation for directed graphs. Submitted for publication, 1997.

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B. Awerbuch and Y. Shavitt. Topology aggregation for directed graphs. Technical Report 98-14, DIMACS, Feb. 1998.

No context found.

Baruch Awerbuch and Yuval Shavitt. Topology Aggregation for Directed Graphs. To appear in Proc. of the 3rd Ann. IEEE Symp. on Computers and Communications, June 1998.

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B. Awerbuch and Y. Shavitt. Topology aggregation for directed graphs. In Proceedings of IEEE ISCC (Athens, Greece),pp. 47--52, 1998.

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Bamch Awerbuch and Yuval Shavitt, "Topology Aggregation for Directed Graphs. '; IEEE/ACM Transactions on Networking, Vol.9, N0.1, Feb 2001.

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