## Designing overlay multicast networks for streaming (2003)

### Cached

### Download Links

Venue: | In Proceedings of ACM Symposium on Parallel Algorithms and Architectures |

Citations: | 18 - 4 self |

### BibTeX

@INPROCEEDINGS{Andreev03designingoverlay,

author = {Konstantin Andreev and Bruce M. Maggs and Adam Meyerson and Ramesh K. Sitaraman},

title = {Designing overlay multicast networks for streaming},

booktitle = {In Proceedings of ACM Symposium on Parallel Algorithms and Architectures},

year = {2003},

pages = {149--158}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper we present a polynomial time approximation algorithm for designing a multicast overlay network. The algorithm finds a solution that satisfies capacity and reliability constraints to within a constant factor of optimal, and cost to within a logarithmic factor. The class of networks that our algorithm applies to includes the one used by Akamai Technologies to deliver live media streams over the Internet. In particular, we analyze networks consisting of three stages of nodes. The nodes in the first stage are the sources where live streams originate. A source forwards each of its streams to one or more nodes in the second stage, which are called reflectors. A reflector can split an incoming stream into multiple identical outgoing streams, which are then sent on to nodes in the third and final stage, which are called the sinks. As the packets in a stream travel from one stage to the next, some of them may be lost. The job of a sink is to combine the packets from multiple instances of the same stream (by reordering packets and discarding duplicates) to form a single instance of the stream with minimal loss. We assume that the loss rate between any pair of nodes in the network is known, and that losses between different pairs are independent, but discuss extensions in which some losses may be correlated.

### Citations

1155 | A case for end system multicast
- Chu, Rao, et al.
- 2000
(Show Context)
Citation Context ... however, suffers from the same disruptions and downstream packet loss as the multicast tree approach. Recently promising new approaches have been devolped. One of them is “End System Multicast”(E=-=SM) [3]-=-. In ESM, there is no distinction between clients, reflectors, and servers. Each host participating in the multicast may be called on to play any of these roles simultaneously in order to form a tree.... |

1024 | Multicast routing in a datagram internetwork
- Deering
- 1991
(Show Context)
Citation Context ...eruned as often as needed so that the overlay network adapts to changes in the link failure probabilities or costs. 1.4 Other Approaches One of the oldest alternative approaches is called “multicast=-=” [6]-=-. The goal of multicast is to reduce the total bandwidth consumption required to send the same stream to a large number of hosts. Instead of sending all of the data directly from one server, a multica... |

700 |
Approximation algorithms for combinatorial problems
- Johnson
- 1974
(Show Context)
Citation Context ...er bound of O(log n) with respect to cost for polynomial-time computation (unless NP ⊂ DT IME(n Olog log n )) [21, 8]. A simple greedy algorithm gives a matching upper bound for the set cover proble=-=m [18, 5]-=-. While our problem includes set cover as a special case, the actual problem statement is more general. Our facilities are capacitated (in contrast to the set cover problem where the sets are uncapaci... |

657 | A threshold of ln n for approximating set cover
- Feige
- 1996
(Show Context)
Citation Context ...inequality assumption, the problem is as hard as set cover, giving us an approximation lower bound of O(log n) with respect to cost for polynomial-time computation (unless NP ⊂ DT IME(n Olog log n )=-=) [21, 8]-=-. A simple greedy algorithm gives a matching upper bound for the set cover problem [18, 5]. While our problem includes set cover as a special case, the actual problem statement is more general. Our fa... |

442 |
The complexity of enumeration and reliability problems
- Valiant
- 1979
(Show Context)
Citation Context ...f two edges coming to a node are p1 and p2 respectively then the loss probability of the package at this node is p1p2. Observe that these loss rules are the same as in the network reliability problem =-=[30]-=-, but we also have costs on the edges and multiple commodities. Since our algorithm is reasonably fast it can be reruned as often as needed so that the overlay network adapts to changes in the link fa... |

397 |
MBONE: The multicast backbone,” in
- Eriksson
- 1994
(Show Context)
Citation Context ...t protocols, so as a practical matter it is not possible for a server to rely on multicast alone to deliver its streams. The “mbone” (multicast backbone) network was organized to address this prob=-=lem [7]. Pa-=-rticipants in mbone have installed routers that participate in the multicast protocols. In mbone, packets are sent between multicast routers using unicast “tunnels” through routers that do not par... |

390 |
On the hardness of approximating minimization problems
- Lund, Yannakakis
- 1994
(Show Context)
Citation Context ...inequality assumption, the problem is as hard as set cover, giving us an approximation lower bound of O(log n) with respect to cost for polynomial-time computation (unless NP ⊂ DT IME(n Olog log n )=-=) [21, 8]-=-. A simple greedy algorithm gives a matching upper bound for the set cover problem [18, 5]. While our problem includes set cover as a special case, the actual problem statement is more general. Our fa... |

352 | Distributing streaming media content using cooperative networking
- Wang, Chou
- 2002
(Show Context)
Citation Context ...oups to be formed without any network support for routing protocols and without any other permanent infrastructure dedicated to supporting multicast. Another one is “Cooperative Networking” (CoopN=-=et) [24]-=-. CoopNet is a hybrid between a centralized system as described in our paper and a peer-to-peer system such as ESM. 1.5 Related work Our approach falls into the general class of facility location prob... |

322 | Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and Lagrangian relaxation
- Jain, Vazirani
(Show Context)
Citation Context ...omputer networking. The first approximation algorithm for facility location problems was given by Hochbaum [12] and improved approximatio algorithms havesbeen the subject of numerous papers including =-=[27, 9, 4, 2, 16, 29, 15, 22]. -=-Except for Hochbaum’s result, the papers described above all assume that the weights between reflectors and sinks form a metric (satisfying the symmetry and triangle inequality properties). In our p... |

266 | Approximation algorithms for facility location problems
- Shmoys, Tardos, et al.
- 1997
(Show Context)
Citation Context ...omputer networking. The first approximation algorithm for facility location problems was given by Hochbaum [12] and improved approximatio algorithms havesbeen the subject of numerous papers including =-=[27, 9, 4, 2, 16, 29, 15, 22]. -=-Except for Hochbaum’s result, the papers described above all assume that the weights between reflectors and sinks form a metric (satisfying the symmetry and triangle inequality properties). In our p... |

207 | Improved combinatorial algorithms for facility location and k-median problems
- Charikar, Guha
- 1999
(Show Context)
Citation Context ...omputer networking. The first approximation algorithm for facility location problems was given by Hochbaum [12] and improved approximatio algorithms havesbeen the subject of numerous papers including =-=[27, 9, 4, 2, 16, 29, 15, 22]. -=-Except for Hochbaum’s result, the papers described above all assume that the weights between reflectors and sinks form a metric (satisfying the symmetry and triangle inequality properties). In our p... |

188 | Greedy strikes back: Improved facility location algorithms
- Guha, Khuller
- 1998
(Show Context)
Citation Context |

158 |
An approximation algorithm for the generalized assignment problem
- Shmoys, Tardos
(Show Context)
Citation Context ... along paths since the paths need not be independent in a deeper network). 1.6 Our results Our techniques are based upon linear program rounding, combined with the generalized assignment algorithm of =-=[26]-=-. A direct rounding approach is possible, but would lead to a multicriterion logarithmic approximation. We are forced to lose O(log n) on the cost (due to the set cover lower bounds), but we obtain O(... |

155 |
A greedy heuristic for the set covering problem
- Chvátal
- 1979
(Show Context)
Citation Context ...er bound of O(log n) with respect to cost for polynomial-time computation (unless NP ⊂ DT IME(n Olog log n )) [21, 8]. A simple greedy algorithm gives a matching upper bound for the set cover proble=-=m [18, 5]-=-. While our problem includes set cover as a special case, the actual problem statement is more general. Our facilities are capacitated (in contrast to the set cover problem where the sets are uncapaci... |

119 | A new greedy approach for facility location problems
- Jain, Mahdian, et al.
- 2002
(Show Context)
Citation Context |

111 | Improved approximation algorithms for metric facility location
- Mahdian, Ye, et al.
- 2002
(Show Context)
Citation Context |

80 |
Heuristics for the fixed cost median problem
- Hochbaum
- 1982
(Show Context)
Citation Context ...st. This class of problems has numerous applications in operations research, databases, and computer networking. The first approximation algorithm for facility location problems was given by Hochbaum =-=[12] a-=-nd improved approximatio algorithms havesbeen the subject of numerous papers including [27, 9, 4, 2, 16, 29, 15, 22]. Except for Hochbaum’s result, the papers described above all assume that the wei... |

63 | A randomized fully polynomial time approximation scheme for the all terminal reliability problem
- Karger
(Show Context)
Citation Context ...ork reliability. For general networks Valiant [30] defined the term “network reliability” and proved that computing it is ♯P-complete. Karger showed an FPRAS that approximates the network reliab=-=ility [19]. -=-We consider a three-tiered network because these structures are used in practice (for example in Akamai’s data-distribution network) and because the possible dependencies between paths are greatly r... |

60 | Approximation algorithms for data placement in arbitrary networks
- Baev, Rajaraman
- 2001
(Show Context)
Citation Context ...ommodate capacitated sets, but our problem additionally requires an assignment of both commodities to reflectors and reflectors to sinks. Similar two-level assignments have been considered previously =-=[20, 1, 23, 11]-=-, but again the earlier work assumed that the points were located in a metric space. The greedy approach may not work for multiple commodities, as the coverage no longer increases concavely as reflect... |

58 |
Probabilistic Analysis of Algorithms
- Hofri
- 1987
(Show Context)
Citation Context ...on the capacity and probabilities by accepting a larger constant multiplier to the cost. Our algorithm is randomized, and the randomized rounding makes use of Chernoff bounds as extended by Hoeffding =-=[13, 14]-=-. 1.7 Outline of the paper The remainder of this paper is organized as follows. In Section 2 we formalize the problem. In Section 3 we describe the randomized rounding procedure which is the first sta... |

55 | Placement algorithms for hierarchical cooperative caching
- Korupolu, Plaxton, et al.
(Show Context)
Citation Context ...ommodate capacitated sets, but our problem additionally requires an assignment of both commodities to reflectors and reflectors to sinks. Similar two-level assignments have been considered previously =-=[20, 1, 23, 11]-=-, but again the earlier work assumed that the points were located in a metric space. The greedy approach may not work for multiple commodities, as the coverage no longer increases concavely as reflect... |

47 | A constant-factor approximation algorithm for packet routing, and balancing local vs. global criteria
- Srinivasan, Teo
- 1997
(Show Context)
Citation Context ... rounding for only some linear program variables and completing the rounding procedure by using a modified version of generalized assignment. In Section 6 we use a technique due to Srinivasan and Teo =-=[28]-=- to tackle some extensions of this problem. The constants can be traded off in a manner typical for multicriterion approximations, allowing us to improve the constants on the capacity and probabilitie... |

45 | Facility location with nonuniform hard capacities
- Pal, Tardos, et al.
(Show Context)
Citation Context ... is more general. Our facilities are capacitated (in contrast to the set cover problem where the sets are uncapacitated). Capacitated facility location (with “hard” capacities) has been considered=-= by [25]-=-, but the local search algorithm provided depends heavily upon the use of an underlying metric space. The standard greedy approach for the set cover problem can be extended to accommodate capacitated ... |

17 |
An approximation algorithm for the fault tolerant metric facility location problem,” in Approximation Algorithms for Combinatorial Optimization
- Jain, Vazirani
- 2000
(Show Context)
Citation Context ...s work in set cover and facility location, where the goal is to cover each customer with exactly one reflector. Several earlier papers have considered the problem of facility location with redundancy =-=[17, 10]-=-. Unlike our results, each of the previous papers assumes an underlying metric, and it is also assumed that the coverage provided by each facility is equivalent (whereas in our problem the coverage pr... |

11 | Web caching using access statistics
- Meyerson, Munagala, et al.
- 2001
(Show Context)
Citation Context ...ommodate capacitated sets, but our problem additionally requires an assignment of both commodities to reflectors and reflectors to sinks. Similar two-level assignments have been considered previously =-=[20, 1, 23, 11]-=-, but again the earlier work assumed that the points were located in a metric space. The greedy approach may not work for multiple commodities, as the coverage no longer increases concavely as reflect... |

9 | Improved algorithms for fault tolerant facility location
- Guha, Meyerson, et al.
- 2001
(Show Context)
Citation Context ...s work in set cover and facility location, where the goal is to cover each customer with exactly one reflector. Several earlier papers have considered the problem of facility location with redundancy =-=[17, 10]-=-. Unlike our results, each of the previous papers assumes an underlying metric, and it is also assumed that the coverage provided by each facility is equivalent (whereas in our problem the coverage pr... |

9 |
An 1.582-approximation algorithm for the metric uncapacitated facility location problem.” to appear
- Sviridenko
- 2002
(Show Context)
Citation Context |

8 | Improved algorithms for the data placement problem
- Guha, Munagala
- 2002
(Show Context)
Citation Context |

4 |
Improved algorithms for uncapacitated facility location problem
- Chudak
- 1998
(Show Context)
Citation Context |

1 |
Probability inequalities for sums
- Hoeffding
- 1963
(Show Context)
Citation Context ...on the capacity and probabilities by accepting a larger constant multiplier to the cost. Our algorithm is randomized, and the randomized rounding makes use of Chernoff bounds as extended by Hoeffding =-=[13, 14]-=-. 1.7 Outline of the paper The remainder of this paper is organized as follows. In Section 2 we formalize the problem. In Section 3 we describe the randomized rounding procedure which is the first sta... |