## Efficient Collective Communication in Optical Networks (0)

### Cached

### Download Links

- [www.inria.fr]
- [www.dia.unisa.it]
- [www.dia.unisa.it]
- [www.inria.fr]
- DBLP

### Other Repositories/Bibliography

Venue: | In Proc. of ICALP 96 |

Citations: | 51 - 9 self |

### BibTeX

@INPROCEEDINGS{Bermond_efficientcollective,

author = {J.-C. Bermond and L. Gargano and S. Perennes and A. A. Rescigno and U. Vaccaro},

title = {Efficient Collective Communication in Optical Networks},

booktitle = {In Proc. of ICALP 96},

year = {},

pages = {574--585},

publisher = {Springer Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper studies the problems of broadcasting and gossiping in optical networks. In such networks the vast bandwidth available is utilized through wavelength division multiplexing: a single physical optical link can carry several logical signals, provided that they are transmitted on different wavelengths. In this paper we consider both single--hop and multihop optical networks. In single--hop networks the information, once transmitted as light, reaches its destination without being converted to electronic form in between, thus reaching high speed communication. In multi hop networks a packet may have to be routed through a few intermediate nodes before reaching its final destination. In both models, we give efficient broadcasting and gossiping algorithms, in terms of time and number of wavelengths. We consider both networks with arbitrary topologies and particular networks of practical interest. Several of our algorithms exhibit optimal performances. 1 Introduction Motivations. Op...

### Citations

274 |
A survey of gossiping and broadcasting in communication networks
- Hedetniemi, Hedetniemi, et al.
- 1988
(Show Context)
Citation Context ...al relevance in parallel and distributed computation and the related interesting theoretical issues, collective communication problems have been extensively studied in the literature (see the surveys =-=[20, 25, 16]-=-). In this paper we will consider the design of efficient algorithms for two widely used operations: Broadcasting and Gossiping (also called all-to--all broadcasting). Formally the broadcasting and go... |

251 |
A Group-Theoretic Model for Symmetric Interconnection Networks
- Akers, Krishnamurthy
- 1989
(Show Context)
Citation Context ...m ; ffl for any Cayley graph G of degree d wb(G) = d(n \Gamma 1)=de : The last result on Cayley graphs includes, among others, the star interconnection network and the pancake interconnection network =-=[2]-=-. 3.2 Gossiping In this section we study the minimum possible number of wavelengths necessary to perform gossiping in a single--hop network in exactly one round. Lemma 3.2 For each graph G it holds th... |

241 |
An Approximate Max–Flow Min–Cut Theorem for Uniform Multicommodity Flow Problems with Application to Approximation Algorithm
- Leighton, Rao
- 1988
(Show Context)
Citation Context ... = max x2V (G) tb(G; x; w). We denote by tg(G; w) the minimum possible number of rounds necessary to complete the gossiping process using up to w wavelengths per round. The edge--expansion fi(G) of G =-=[27]-=-, (also called isoperimetric number in [32, 43] and conductance in [28]) is the minimum over all subsets of nodes S ae V (G) of size jSjsn=2, of the ratio of the number of edges having exactly one end... |

219 | Routing and Wavelength Assignment in All-Optical Networks - Ramaswami, Sivarajan - 1995 |

204 |
WDM-based Local Lightwave Networks Part I: Single-Hop Systems
- Mukherjee
- 1992
(Show Context)
Citation Context ...be routed trough a few terminal nodes before reaching its final destination. At each terminal node, the packet is converted from light to electronic form and retransmitted on an other wavelength. See =-=[33, 34]-=- for more on these questions. In the present paper we consider both switched single--hop and switched multihop networks. Our results. In this paper we initiate the study of the problem of designing ef... |

156 | Design of logical topologies for wavelength-routed optical networks - Ramaswami, Sivarajan - 1996 |

121 | Efficient Routing in All-Optical Networks
- Raghavan, Upfal
- 1994
(Show Context)
Citation Context ...or more of the output links. Each link is bidirectional and actually consists of a pair of unidirectional links [40]. In this paper we consider switched networks with generalised switches, as done in =-=[1, 5, 10, 39]-=-. In this kind of networks, signals for different requests may travel on a same communication link into a node v (on different wavelengths) and then exit v along different links. Thus the photonic swi... |

107 | Methods and problems of communication in usual networks
- Fraigniaud, Lazard
- 1990
(Show Context)
Citation Context ...al relevance in parallel and distributed computation and the related interesting theoretical issues, collective communication problems have been extensively studied in the literature (see the surveys =-=[20, 25, 16]-=-). In this paper we will consider the design of efficient algorithms for two widely used operations: Broadcasting and Gossiping (also called all-to--all broadcasting). Formally the broadcasting and go... |

100 | Dissemination of information in interconnection networks (broadcasting & gossiping
- Hromkovič, Klasing, et al.
- 1996
(Show Context)
Citation Context ...al relevance in parallel and distributed computation and the related interesting theoretical issues, collective communication problems have been extensively studied in the literature (see the surveys =-=[20, 25, 16]-=-). In this paper we will consider the design of efficient algorithms for two widely used operations: Broadcasting and Gossiping (also called all-to--all broadcasting). Formally the broadcasting and go... |

81 |
Multi-wavelength lightwave networks
- Ramaswami
- 1993
(Show Context)
Citation Context ...ned separate wavelengths. The major applications for such networks are video conferencing, scientific visualisation and realtime medical imaging, high--speed super-computing and distributed computing =-=[18, 40, 44]-=-. We refer to the books of Green [18] and McAulay [30] for a presentation of the physical theory and applications of this emerging technology. In order to state the new algorithmic issues and challeng... |

81 | Graph problems arising from wavelength-routing in all-optical networks - Beauquier, Bermond, et al. - 1997 |

80 |
Isoperimetric numbers of graphs
- Mohar
- 1989
(Show Context)
Citation Context ...(G; w) the minimum possible number of rounds necessary to complete the gossiping process using up to w wavelengths per round. The edge--expansion fi(G) of G [27], (also called isoperimetric number in =-=[32, 43]-=- and conductance in [28]) is the minimum over all subsets of nodes S ae V (G) of size jSjsn=2, of the ratio of the number of edges having exactly one endpoint in S to the size of S. A graph G is said ... |

79 | Efficient routing and scheduling algorithms for optical networks
- Aggarwal, Bar-Noy, et al.
- 1994
(Show Context)
Citation Context ...mponents, hence it is reliable and easy to operate. However, switchless networks suffer of severe limitations that make problematic their extension to wide area networks. Indeed it has been proven in =-=[1]-=- that switchless networks require a large number of wavelengths to support even simple traffic patterns. Other drawbacks of switchless networks are discussed in [40]. Therefore, optical switches are r... |

67 |
1, isoperimetric inequalities for graphs, and superconcentrators
- Alon, Milman
- 1985
(Show Context)
Citation Context ...he Laplacian of a graph with adjacency matrix A and degree function d(\Delta) is the n \Theta n matrix with entries d(x)ffi x;y \Gamma A x;y , where ffi x;y is the Kronecker symbol, from Lemma 2.1 of =-=[3]-=-, Theorem 4.2 of [32], Lemma 3.2, Theorem 3.2, and formulae (1), (3) of the present paper we get: Theorem 3.3 Letsbe the second smallest eigenvalue of the Laplacian associated to G. We have wg(G) =\Om... |

67 | Software Libraries for Linear Algebra Computations on High Performance Computers
- Dongarra, Walker
- 1995
(Show Context)
Citation Context ... one of the most important issues in multiprocessor systems. The need for collective communication arises in many problems of parallel and distributed computing including many scientific computations =-=[9, 12, 15]-=- and database management [17, 45]. Due to the considerable practical relevance in parallel and distributed computation and the related interesting theoretical issues, collective communication problems... |

60 | Optical networking update - Green - 1996 |

50 | Scheduling of virtual connections in fast networks - Erlebach, Jansen - 1996 |

46 | Gossiping in minimal time - Krumme, Cybenko, et al. - 1992 |

43 |
On forwarding indices of networks
- Heydemann, Meyer, et al.
- 1989
(Show Context)
Citation Context ... from x to y. Given a routing R for the graph G, the load of an edge e 2 E(G), denoted by load(R; e), is the number of paths of R going through e in either directions. The edge--forwarding index of G =-=[21]-=-, denoted by (G), is the minimum over all routings R for G of the maximum over all the edges of G of the load posed by the routing R on the edge, that is, (G) = minR max e2E(G) load(R; e): It is known... |

41 | Erbium-Doped Fiber Amplifiers, Principles and Applications - Desurvire - 1994 |

39 |
Fault-tolerant broadcasting and gossiping in communication networks, Département d’Informatique, Université du Québec à
- Pelc
- 1996
(Show Context)
Citation Context ...sustained throughput at high data rates is subsequently available [39]. Still distributed algorithms are worth investigating. ffl We did not consider fault tolerant issues here. See the recent survey =-=[36]-=- for an account of the vast literature on fault--tolerance in traditional networks. ffl Some of our results are susceptible of improvements. In particular, we ask the following question: Is the lower ... |

38 | K.: Algorithms for Routing in a Linear Lightwave Network - Bala, Stern, et al. - 1991 |

37 |
Improved bounds for all optical routing
- Aumann, Rabani
- 1995
(Show Context)
Citation Context ...or more of the output links. Each link is bidirectional and actually consists of a pair of unidirectional links [40]. In this paper we consider switched networks with generalised switches, as done in =-=[1, 5, 10, 39]-=-. In this kind of networks, signals for different requests may travel on a same communication link into a node v (on different wavelengths) and then exit v along different links. Thus the photonic swi... |

37 |
Combinatorial Problems and Exercises, 2nd edition
- Lovasz
- 1993
(Show Context)
Citation Context ...number of rounds necessary to complete the gossiping process using up to w wavelengths per round. The edge--expansion fi(G) of G [27], (also called isoperimetric number in [32, 43] and conductance in =-=[28]-=-) is the minimum over all subsets of nodes S ae V (G) of size jSjsn=2, of the ratio of the number of edges having exactly one endpoint in S to the size of S. A graph G is said k--edge--connected if k ... |

34 |
Architectures for Linear Lightwave Networks
- Pankaj
- 1992
(Show Context)
Citation Context ...as been recently considered in [1, 5, 31, 39]. Above papers contain also efficient algorithms for routing in networks of practical interest. Routing in hypercube based networks has been considered by =-=[5, 35, 39]-=-. Lower bounds on the number of wavelengths necessary for routing permutations have been given in [35, 6, 38]. Gossiping in broadcast-- and--select optical networks has been considered in [1]. Other w... |

30 |
Optical Computer Architectures
- MCAULAY
- 1991
(Show Context)
Citation Context ...orks are video conferencing, scientific visualisation and realtime medical imaging, high--speed super-computing and distributed computing [18, 40, 44]. We refer to the books of Green [18] and McAulay =-=[30]-=- for a presentation of the physical theory and applications of this emerging technology. In order to state the new algorithmic issues and challenges concerning data communication in optical networks, ... |

29 | On the number of wavelengths and switches in all-optical networks - Barry, Humblet - 1993 |

29 | Purely optical networks for terabit communication - Chlamtac, Ganz, et al. - 1989 |

28 | Topologies for wavelength–routing all-optical networks - MARSAN, BIANCO, et al. - 1993 |

27 |
Minimum-time line broadcast networks, Networks 10
- Farley
- 1980
(Show Context)
Citation Context ...lengths necessary for routing permutations have been given in [35, 6, 38]. Gossiping in broadcast-- and--select optical networks has been considered in [1]. Other work related to ours is contained in =-=[13, 23, 14, 24, 25]-=-. In these papers the problem of designing efficient broadcasting and gossiping algorithms in traditional networks has been considered under the assumption that data exchange can take place through ed... |

26 | Approximation algorithms for minimum time broadcast
- Kortsarz, Peleg
- 1992
(Show Context)
Citation Context ...f the quantities wb(G; t), wg(G; t), tb(G; w), tg(G; w) deserves to be investigated. It is likely that for some of them it is NP--hard. In this view, approximation algorithms in the sense of [41] and =-=[19]-=- could be interesting to design. ffl Our algorithm require a centralised control. This seems not to be a severe limitation in that the major applications for optical networks require connections that ... |

24 | Efficient wavelength routing on directed fiber trees - Kaklamanis, Persiano - 1996 |

21 |
Optimal Broadcast in All-Port Wormhole-Routed Hypercubes
- Ho, Kao
- 1995
(Show Context)
Citation Context ...lengths necessary for routing permutations have been given in [35, 6, 38]. Gossiping in broadcast-- and--select optical networks has been considered in [1]. Other work related to ours is contained in =-=[13, 23, 14, 24, 25]-=-. In these papers the problem of designing efficient broadcasting and gossiping algorithms in traditional networks has been considered under the assumption that data exchange can take place through ed... |

21 |
Distributed computing with high-speed optical networks
- Vitter, Du
- 1993
(Show Context)
Citation Context ...ned separate wavelengths. The major applications for such networks are video conferencing, scientific visualisation and realtime medical imaging, high--speed super-computing and distributed computing =-=[18, 40, 44]-=-. We refer to the books of Green [18] and McAulay [30] for a presentation of the physical theory and applications of this emerging technology. In order to state the new algorithmic issues and challeng... |

19 |
Minimale n-fach kantenzusammenhängende Graphen
- Mader
- 1971
(Show Context)
Citation Context ...gives the exact value of the number of wavelengths necessary to broadcast in one round in various classes of important networks. Notice that every vertex transitive graph is maximally edge--connected =-=[29]-=-. In particular we have ffl for the d-dimensional hypercube H d wb(H d ) = l (2 d \Gamma 1)=d m ; ffl for the r \Theta s mesh M r;s wb(M r;s ) = d(rs \Gamma 1)=2e ; ffl for the d dimensional torus C d... |

18 | Large fault-tolerant interconnection networks - Bermond, Homobono, et al. - 1989 |

17 |
A Linear Lightwave Benes Network
- Pieris, Sasaki
- 1993
(Show Context)
Citation Context ...networks of practical interest. Routing in hypercube based networks has been considered by [5, 35, 39]. Lower bounds on the number of wavelengths necessary for routing permutations have been given in =-=[35, 6, 38]-=-. Gossiping in broadcast-- and--select optical networks has been considered in [1]. Other work related to ours is contained in [13, 23, 14, 24, 25]. In these papers the problem of designing efficient ... |

16 | Optimal Algorithms for Dissemination of Information in Generalized Communication Networks
- Feldmann, Hromkovic, et al.
- 1992
(Show Context)
Citation Context ...lengths necessary for routing permutations have been given in [35, 6, 38]. Gossiping in broadcast-- and--select optical networks has been considered in [1]. Other work related to ours is contained in =-=[13, 23, 14, 24, 25]-=-. In these papers the problem of designing efficient broadcasting and gossiping algorithms in traditional networks has been considered under the assumption that data exchange can take place through ed... |

12 |
Complexity of the forwarding index problem
- Saad
- 1993
(Show Context)
Citation Context ...nd an edge between any two paths sharing an edge in the same direction, is (G)=2--vertex colorable. We also notice that the problem of determining the edge--forwarding index of a graph is NP-complete =-=[42]-=-. In the rest of this section we will put in relation the minimum possible number of wavelengths necessary to perform gossiping in G in one round with the edge--expansion of G. From Lemma 3.2 and (1) ... |

10 | Cayley graphs with optimal fault tolerance - Alspach - 1992 |

10 |
The communication complexity of atomic commitment and of gossiping
- Wolfson, Segall
- 1991
(Show Context)
Citation Context ... multiprocessor systems. The need for collective communication arises in many problems of parallel and distributed computing including many scientific computations [9, 12, 15] and database management =-=[17, 45]-=-. Due to the considerable practical relevance in parallel and distributed computation and the related interesting theoretical issues, collective communication problems have been extensively studied in... |

9 | E.Lazard, Methods and problems of communication in usual networks - Fraignaud - 1994 |

8 | H.: Optimal algorithms for broadcast and gossip in the edge-disjoint path modes - Hromkovič, Klasing, et al. - 1997 |

7 | Forwarding indices of consistent routings and their complexity - Heydemann, Meyer, et al. - 1994 |

7 |
Expanding and forwarding
- SOLÉ
- 1995
(Show Context)
Citation Context ...(G; w) the minimum possible number of rounds necessary to complete the gossiping process using up to w wavelengths per round. The edge--expansion fi(G) of G [27], (also called isoperimetric number in =-=[32, 43]-=- and conductance in [28]) is the minimum over all subsets of nodes S ae V (G) of size jSjsn=2, of the ratio of the number of edges having exactly one endpoint in S to the size of S. A graph G is said ... |

6 |
Optimal algorithms for broadcast and gossip in the edge-disjoint path modes
- Hromkovi, Klasing, et al.
- 1997
(Show Context)
Citation Context |

5 |
Bounds on the Number of Wavelengths Needed
- Barry, Humblet
- 1992
(Show Context)
Citation Context ...networks of practical interest. Routing in hypercube based networks has been considered by [5, 35, 39]. Lower bounds on the number of wavelengths necessary for routing permutations have been given in =-=[35, 6, 38]-=-. Gossiping in broadcast-- and--select optical networks has been considered in [1]. Other work related to ours is contained in [13, 23, 14, 24, 25]. In these papers the problem of designing efficient ... |

5 | Review of fundamentals of optical fiber systems - Personick - 1983 |

5 |
Rapid rumour ramification: Approximating the minimum broadcasting time
- Ravi
- 1994
(Show Context)
Citation Context ...plexity of the quantities wb(G; t), wg(G; t), tb(G; w), tg(G; w) deserves to be investigated. It is likely that for some of them it is NP--hard. In this view, approximation algorithms in the sense of =-=[41]-=- and [19] could be interesting to design. ffl Our algorithm require a centralised control. This seems not to be a severe limitation in that the major applications for optical networks require connecti... |

4 |
Accousto-optic tunable filters in narrowband WDM networks
- CHENG
- 1990
(Show Context)
Citation Context ...or more of the output links. Each link is bidirectional and actually consists of a pair of unidirectional links [40]. In this paper we consider switched networks with generalised switches, as done in =-=[1, 5, 10, 39]-=-. In this kind of networks, signals for different requests may travel on a same communication link into a node v (on different wavelengths) and then exit v along different links. Thus the photonic swi... |