Matthew Doar and Ian Leslie, "How Bad Is Naive Multicast Routing ?," in IEEE INFOCOM, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....local search heuristic within version 1 of the LBNL network simulator ns [31] Because its performance depends heavily on the topology, we used two different network models: a flat random network and a transit stub network. Flat networks are created using the Doar Leslie edge connection method [32] so that edges mostly connect nodes near each other. Transitstub networks model a two level hierarchy, with each stub network consisting of a flat network. It is important to note that the networks we chose represent extremes and are thus good test cases for examining the performance of local ....

Matthew Doar and Ian Leslie, "How Bad Is Naive Multicast Routing ?," in IEEE INFOCOM, 1993.

....allocation problem which is a generalization of the minimum Steiner tree problem. First we show a disjointness property of the minimum cost allocation problem. Then we show an approach to transform the problem into a Steiner tree problem. This allows us to use any of the Steiner tree algorithms [27 31]. 3.1 Property Lemma Given a graph G = V; E) with C(e) 0 for any e 2 E, if T i = V i ; E i ) 1 i n) is a minimum cost allocation, then we have V i V j = i 6= j) This is called the mutual disjointness property. Proof. For a minimum cost allocation, if V i V j 6= then there ....

M. Doar and I. Leslie, "How bad is naive multicast routing?," in Proceedings of INFOCOM '93, 1993.

....nodes. Likewise, the simulated networks have 10 or 30 of its nodes in the multicast group because multicast applications running on such a WAN are likely to involve only a minority of nodes in the network. The 2000 networks were generated to resemble networks in a manner similar to that of Doar [9]. Each of the n nodes is distributed across a Cartesian coordinate plane with minimum and maximum coordinates 18 0 2 4 6 8 10 12 14 16 18 20 460 480 500 520 540 560 580 600 Number of Edges Percentage of Cases Figure 15: The histogram of the number of edges in the test ....

....is accepted. Each edge s distance is its rectilinear distance plus a small constant. This distance is also the time it takes for a message to traverse this edge. We used the probability function P (x; y) fie Gammad x;y 2ffn ; where d x;y is the rectilinear distance between nodes x and y [9]. The parameters ff and fi govern the density of the graph. Increasing ff increases the number of connections to nodes far away and increasing fi increases the number of edges from each node. After some experimentation, we chose ff = 0:10 and fi = 0:20 for generating the graphs used in this ....

M. Doar and I. Leslie. "How bad is naive multicast routing?," in Proc. IEEE INFOCOM, San Francisco, CA, Apr. 1993, pp. 82--89.

....algorithms. The performance should be independent of the number of joining nodes. 4) Minimized worst case cost of the multicast tree. The worst case cost produced by the algorithm should be theoretically bounded as small as possible. Many dynamic multicast routing algorithms have been proposed [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. However, none of there algorithms can satisfy all of the above requirements. The greedy algorithm [8, 9] selects the shortest path to an existing multicast tree when a node is added. It can construct a near optimal multicast tree, but requires many query reply messages between nodes when ....

....tree when a node is added. It can construct a near optimal multicast tree, but requires many query reply messages between nodes when implemented in a distributed environment [13, 14] Thus, the algorithm is not scalable in a distributed environment. The pruned shortest path tree algorithm [4, 5, 6, 7] finds the shortest path from the source node (or the center node) to the nodes in the multicast group when a node is added to the multicast tree. This algorithm cannot construct an appropriate multicast tree, though, from the viewpoint of tree cost. The virtual trunk dynamic multicast (VTDM) ....

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M. Doar and I. Leslie, "How Bad is Naive Multicast Routing?" IEEE INFOCOM '93, pp. 82--89, March 1993.

....the appropriate value to delay the retransmission is a subject of on going research by the PGM designers. 5.5. Topology Generation Topology generation is an important aspect of our simulation experiments because the performance of multicast protocols is often sensitive to the underlying topology [52, 53, 54]. By topology we mean both link topology, i.e. the way links are connected together, as well as receiver topology, i.e. the way receivers are distributed over the multicast tree. Both link and receiver topology affect recovery in a similar manner. Consider, for example, the factors that ....

Doar, M., Leslie, I., "How bad is naive multicast routing?" Proc. IEEE INFOCOM `93, pp. 82-89, 1993.

....local search heuristic within version 1 of the LBNL network simulator ns [35] Because its performance depends heavily on the topology, we used two different network models: a flat random network and a transit stub network. Flat networks are created using the Doar Leslie edge connection method [36] so that edges mostly connect nodes near each other. Transit stub networks model a two level hierarchy, with each stub network consisting of a flat network. It is important to note that the networks we chose represent extremes and are thus good test cases for examining the performance of local ....

M. Doar and I. Leslie, "How Bad Is Naive Multicast Routing?," in IEEE INFOCOM, 1993.

....C(e) E R . 4. A set of destinations D and D V. 5. The node degree constraints k v 2, v V . Goals: Find a MST, T in G, such that d v k v v in T and is minimized. 2.4.2 Algorithms for the MST problem: A. Unconstrained Steiner Tree Heuristics: A. 1 Heuristic Naive: [13] It starts with an arbitrary multicast member as the multicast tree. It then repeatedly connects another random multicast member to the multicast tree by the shortest path between the new member and the multicast tree until all the members are in the multicast tree. A.2 Shortest Path Heuristic ....

....our expected worst Steiner heuristic, often did produce the worst solution; however, it also produced many solutions of surprisingly high quality. D. Degree constrained heuristics easily solved all the dense networks we tested without backtracking. 2. 5 How Bad is the Naive Multicast Routing [13] 2.5.1 Problem definition: There are two types of multicast groups: z Static: once set up, remain unmodified until they are discarded or torn down. z Dynamic: destination nodes which are already part of the group may wish to leave or destination nodes which are not part of the group may ....

M. Doar and I. Leslie, "How Bad is Naive Multicast Routing?", in Proc. of IEEE INFOCOM, San Francisco, CA, pp. 82-89, Apr. 1993.

....problem of routing single multicasts in a network with undirected links. They compared a number of minimum delay and minimum cost algorithms when the link cost and delay weights are the same and derived analytical bounds in cost delay under that assumption. Waxman [11] and later Doar and Leslie [12] studied the problem of dynamically adding and removing destinations on a multicast that had been already routed, also in the context of a single multicast in an undirected network. Waxman studied the RS and KMB heuristics, while Doar and Leslie compared shortest path with KMB for re routing the ....

M. Doar and I. Leslie, "How Bad is Naive Multicast Routing?" IEEE INFOCOM '93, San Francisco, CA, USA, pp 82-9.

....network received approximately the same number of addition and deletion requests. In our simulations, each request was presented to the network only after the previous request was completely serviced. The 50 test graphs were generated to resemble real networks in a manner similar to that of Doar [6]. Each of the 200 nodes is distributed across a Cartesian coordinate plane with minimum and maximum coordinates (0; 0) and (400; 400) creating a forest of 200 nodes spread across this plane. The nodes are then connected by a random spanning tree. This tree is generated by iteratively considering ....

....r is less than a probability function P (x; y) based on the distance between x and y, then the edge is accepted. Each edge s distance is its rectilinear distance. We used the probability function P (x; y) fie Gammad x;y 400ff ; where d x;y is the rectilinear distance between nodes x and y [6]. The parameters ff and fi govern the density of the graph. Increasing ff increases the number of connections to nodes far away and increasing fi increases the number of edges from each node. After some experimentation, we chose ff = 0:10 and fi = 0:20 for generating the graphs used in this ....

M. Doar and I. Leslie. "How bad is naive multicast routing?," in Proc. IEEE INFOCOM, San Francisco, CA, Apr. 1993, pp. 82--89.

....tree by the shortest path between the new member and the multicast tree until all the members are in the multicast tree. We expected this heuristic to give the worst results; as it sometimes does. However, we discovered that it often produces quite respectable results. This matches Doar s results [8]. We treat heuristic Naive as the baseline from which to compare other Steiner heuristics. We describe heuristic Naive as follows. 1. Initialize subtree T to an arbitrary Z node. 2. Connect subtree T with an arbitrary Z node 62 T by the shortest path. 3. If a Z node exists 62 T , go to step 2. ....

....nodes. Likewise, the simulated networks have 10 or 30 of its nodes in the multicast group because multicast applications running on such a WAN are likely to involve only a minority of nodes in the network. The 2000 networks were generated to resemble networks in a manner similar that of Doar [8]. Each of n nodes is distributed across a Cartesian coordinate plane with minimum and maximum coordinates (0; 0) and (2n; 2n) creating a forest of n nodes spread across this plane. In all of our test graphs, the number of nodes n was set at 200. The nodes are then connected by a random spanning ....

[Article contains additional citation context not shown here]

M. Doar and I. Leslie. "How bad is naive multicast routing?," in Proc. IEEE INFOCOM, San Francisco, CA, Apr. 1993, pp. 82--89.

....size (20 to 200 nodes) 0 2 4 6 8 10 12 14 16 18 20 460 480 500 520 540 560 580 600 Number of Edges Percentage of Cases Figure 11: The histogram of the number of edges in the test graphs. The 1000 networks were generated to resemble real networks in a manner similar to that of Doar [5]. Each of the 200 nodes is distributed across a Cartesian coordinate plane with minimum and maximum coordinates (0; 0) and (400; 400) creating a forest of 200 nodes spread across this plane. The nodes are then connected by a random spanning tree. This tree is generated by iteratively considering ....

....is accepted. Each edge s distance is its rectilinear distance plus a small constant. This distance is also the time it takes for a message to traverse this edge. We used the probability function P (x; y) fie Gammad x;y 2ffn ; where d x;y is the rectilinear distance between nodes x and y [5]. The parameters ff and fi govern the density of the graph. Increasing ff increases the number of connections to nodes far away and increasing fi increases the number of edges from each node. After some experimentation, we chose ff = 0:10 and fi = 0:20 for generating the graphs used in this ....

M. Doar and I. Leslie. "How bad is naive multicast routing?," in Proc. IEEE INFOCOM, San Francisco, CA, Apr. 1993, pp. 82--89.

....comparisons. It supplies many of the basic graph manipulation routines common to the heuristics simulated such as adding edges, deleting edges, and computing shortest paths. 1.1. 1 Network Model The random networks used in simulations were generated in a manner similar to that described by Doar [13]. The nodes are distributed across a Cartesian coordinate plane with minimum and maximum coordinates (0; 0) and (400; 400) creating a forest of 200 nodes spread across this plane. The nodes are then connected by a random spanning tree. This tree is generated by iteratively considering a random ....

....(0,2n) Distribute network nodes. 0,0) 2n,0) 0,2n) Generate random spanning tree. 0,0) 2n,0) 0,2n) Add redundant edges. Figure 1.2: Generating random network topologies. probability function P (x; y) fie Gammad x;y 2ffn ; where d x;y is the rectilinear distance between nodes x and y [13]. The parameters ff and fi govern the density of the graph. Increasing ff increases the number of connections to nodes far away and increasing fi increases the number of edges from each node. After some experimentation, the graphs in this simulation were generated using ff = 0:10 and fi = 0:20. ....

[Article contains additional citation context not shown here]

M. Doar and I. Leslie. "How bad is naive multicast routing?," in Proc. IEEEINFOCOM, San Francisco, CA, Apr. 1993, pp. 82--89.

....tree by the shortest path between the new member and the multicast tree until all the members are in the multicast tree. We expected this heuristic to give the worst results; as it sometimes does. However, we discovered that it often produces quite respectable results. This matches Doar s results [6]. We treat heuristic Naive as the baseline from which to compare other Steiner heuristics. A.2 Shortest Path Heuristic (SPH) The shortest path heuristic [16] produces surprisingly good results and has many variants. SPH initializes the multicast tree to an arbitrary multicast member. It then joins ....

....nodes. Likewise, the simulated networks have 10 or 30 of its nodes in the multicast group because multicast applications running on such a WAN are likely to involve only a minority of nodes in the network. The 2000 networks were generated to resemble networks in a manner similar that of Doar [6]. Each of n nodes is distributed across a Cartesian coordinate plane with minimum and maximum coordinates (0; 0) and (2n; 2n) creating a forest of n nodes spread across this plane. In all of our test graphs, the number of nodes n was set at 200. The nodes are then connected by a random spanning ....

[Article contains additional citation context not shown here]

M. Doar and I. Leslie. "How bad is naive multicast routing?", in Proc. IEEE INFOCOM, San Francisco, CA, Apr. 1993, pp. 82--89.

....the problem of locating the multicast server or the core in a shared tree. This is an area that is ignored by the Internet community. ffl Provides a consistent set of membership information to all endpoints for the purpose of establishing virtual circuits. We have also identified Naive Routeing [7] to be the prime candidate for multicast routeing due to its properties of simplicity and easy integration with unicast routeing with acceptable performance. 13 3 5 Access Control Access control is an area that has been very much ignored in conventional multicast mechanisms, such as IP ....

M. Doar and I. Leslie, "How bad is naive multicast routing ?," in Procceding of Infocomm 93: Proceedings of the Tenth Annual Joint Conference of the IEEE Computer and Communications Societies, 1993.

.... routes and network overhead caused by control packets [6] Another paper investigates the performance influence of different multicast delivery trees and multicast routing algorithms based upon a graph theoretic approach [18] Other papers investigate general effects of multicast tree selection [1][8][17] In this paper we investigate the performance of a real protocol implementation (IP multicast) in real time multimedia applications. The results of our studies may easily be generalized to other connectionless, network layer multicast protocols. This paper is organized as follows: Section 2 ....

Doar, M., Leslie, I., "How Bad is Naive Multicast Routing?", IEEE INFOCOM '93, pp. 82-89, 1993

....network received approximately the same number of addition and deletion requests. In our simulations, each request was presented to the network only after the previous request was completely serviced. The 50 test graphs were generated to resemble real networks in a manner similar to that of Doar [9]. Each of the 200 nodes is distributed across a Cartesian coordinate plane with minimum and maximum coordinates (0; 0) and (400; 400) creating a forest of 200 nodes spread across this plane. The nodes are then connected by a random spanning tree. This tree is generated by iteratively considering ....

....r is less than a probability function P (x; y) based on the distance between x and y, then the edge is accepted. Each edge s distance is its rectilinear distance. We used the probability function P (x; y) fie Gammad x;y 400ff ; where d x;y is the rectilinear distance between nodes x and y [9]. The parameters ff and fi govern the density of the graph. Increasing ff increases the number of connections to nodes far away and increasing fi increases the number of edges from each node. After some experimentation, we chose ff = 0:10 and fi = 0:20 for generating the graphs used in this ....

M. Doar and I. Leslie. "How bad is naive multicast routing?", in Proc. IEEE INFOCOM, San Francisco, CA, Apr. 1993, pp. 82--89.

....a destination node; it may be useful to provide finer control over revisions to destination cost estimates to change the characteristics of the tree. Also, we do not address the issue of dynamic groups where members may join and leave. It is possible, however, to use either the na ive approach [30] adding shortest paths to new nodes or the recently proposed ARIES algorithm [31] which selectively repairs parts of the tree after a given number of membership changes. Additional goals include the development of an actual protocol using DDMC. It would be beneficial to incorporate it into a ....

M. Doar and I. Leslie, "How bad is na ive multicast routing?," in IEEE INFOCOM, (San Francisco, California), pp. 82--89, March 1993.

....nodes. Likewise, the simulated networks have 10 or 30 of its nodes in the multicast group because multicast applications running on such a WAN are likely to involve only a minority of nodes in the network. The 2000 networks were generated to resemble networks in a manner similar to that of Doar [11]. Each of the n nodes is distributed across a Cartesian coordinate plane with minimum and maximum coordinates (0; 0) and (2n; 2n) creating a forest of n nodes spread across this plane. In all of our test graphs, the number of nodes n was set at 200. The nodes are then connected by a random ....

....4 6 8 10 12 14 16 18 20 460 480 500 520 540 560 580 600 Number of Edges Percentage of Cases Figure 15: The histogram of the number of edges in the test graphs. the probability function P (x; y) fie Gammad x;y 2ffn ; where d x;y is the rectilinear distance between nodes x and y [11]. The parameters ff and fi govern the density of the graph. Increasing ff increases the number of connections to nodes far away and increasing fi increases the number of edges from each node. After some experimentation, we chose ff = 0:10 and fi = 0:20 for generating the graphs used in this ....

M. Doar and I. Leslie. "How bad is naive multicast routing?," in Proc. IEEE INFOCOM, San Francisco, CA, Apr. 1993, pp. 82--89.

....the heuristics; they should not be many hops longer than the shortest path. 4.2. 1 Topology We generated various large topologies using the Georgia Tech ITM topology generator [ZCB96, CZ] We used one flat random network of 100 nodes (Figure 9a) using the Doar Leslie edge connection method [DL93] to generate edges that mostly connect nodes near each other. The average degree of connectivity for this network is 4.26. We also created transit stub topologies, which consist of a backbone network and connected stub networks, with each sub network generated randomly. Figure 9b shows a ....

Matthew Doar and Ian Leslie. "How Bad Is Naive Multicast Routing?". In IEEE INFOCOM, 1993.

....network received approximately the same number of addition and deletion requests. In our simulations, each request was presented to the network only after the previous request was completely serviced. The 50 test graphs were generated to resemble real networks in a manner similar to that of Doar [7]. Each of the 200 nodes is distributed across a Cartesian coordinate plane with minimum and maximum coordinates (0; 0) and (400; 400) creating a forest of 200 nodes spread across this plane. The nodes are then connected by a random spanning tree. This tree is generated by iteratively considering ....

....r is less than a probability function P (x; y) based on the distance between x and y, then the edge is accepted. Each edge s distance is its rectilinear distance. We used the probability function P (x; y) fie Gammad x;y 400ff ; where dx;y is the rectilinear distance between nodes x and y [7]. The parameters ff and fi govern the density of the graph. Increasing ff increases the number of connections to nodes far away and increasing fi increases the number of edges from each node. After some experimentation, we chose ff = 0:10 and fi = 0:20 for generating the graphs used in this ....

M. Doar and I. Leslie. "How bad is naive multicast routing?", in Proc. IEEE INFOCOM, San Francisco, CA, Apr. 1993, pp. 82--89.

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