Efficient collective communication in optical networks

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 multihop 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]  E. Desurvire,et al.  Erbium‐Doped Fiber Amplifiers: Principles and Applications , 1995 .

[2]  Ralf Klasing.  The Relationship Between Gossiping in Vertex-Disjoint Paths Mode and Bisection Width , 1994, MFCS.

[3]  Jean-Claude Bermond,et al.  Large fault-tolerant interconnection networks , 1989, Graphs Comb..

[4]  David W. Krumme,et al.  Gossiping in Minimal Time , 1992, SIAM J. Comput..

[5]  Mario Gerla,et al.  Rooted routing in linear lightwave networks , 1992, [Proceedings] IEEE INFOCOM '92: The Conference on Computer Communications.

[6]  J. E. Midwinter.  Optical Computer Architectures , 1991 .

[7]  Juraj Hromkovic,et al.  Optimal algorithms for dissemination of information in generalized communication modes , 1994, Discret. Appl. Math..

[8]  Guy Kortsarz,et al.  Approximation Algorithms for Minimum Time Broadcast , 1992, ISTCS.

[9]  Andrzej Pelc.  Fault-tolerant broadcasting and gossiping in communication networks , 1996, Networks.

[10]  Eli Upfal,et al.  Efficient routing in all-optical networks , 1994, STOC '94.

[11]  R. Ramaswami,et al.  Multiwavelength lightwave networks for computer communication , 1993, IEEE Communications Magazine.

[12]  Yuval Rabani,et al.  Improved bounds for all optical routing , 1995, SODA '95.

[13]  P.A. Humblet,et al.  Bounds On The Number Of Wavelengths Needed In WDM Networks , 1992, Summer Topical Meeting Digest on Broadband Analog and Digital Optoelectronics, Optical Multiple Access Networks, Integrated Optoelectronics, Smart Pixels.

[14]  David Simchi-Levi,et al.  Routing in a linear lightwave network , 1995, TNET.

[15]  Patrick Solé,et al.  Expanding and Forwarding , 1995, Discret. Appl. Math..

[16]  Peter L. Hammer,et al.  Discrete Applied Mathematics , 1993 .

[17]  R. Ramaswami,et al.  Analysis of optical bus networks using doped-fiber amplifiers , 1990, LEOS Summer Topical on Optical Multiple Access Networks.

[18]  David Hung-Chang Du,et al.  Distributed computing with high-speed optical networks , 1993, Computer.

[19]  N. Alon,et al.  il , , lsoperimetric Inequalities for Graphs , and Superconcentrators , 1985 .

[20]  Paul E. Green,et al.  Optical Networking Update (Invited Paper) , 1996, IEEE J. Sel. Areas Commun..

[21]  Kwok-Wai Cheung,et al.  Acoustooptic Tunable Filters in Narrowband WDM Networks: System Issues and Network Applications , 1990, IEEE J. Sel. Areas Commun..

[22]  Kumar N. Sivarajan,et al.  Design of Logical Topologies for Wavelength-Routed Optical Networks , 1996, IEEE J. Sel. Areas Commun..

[23]  Complexity of the Forwarding Index Problem , 1993, SIAM J. Discret. Math..

[24]  B. Mukherjee,et al.  WDM-based local lightwave networks. I. Single-hop systems , 1992, IEEE Network.

[25]  Biswancrth Mukherjee.  WM-€?ased Local Lightwave Networks , 1992 .

[26]  Sheldon B. Akers,et al.  A Group-Theoretic Model for Symmetric Interconnection Networks , 1989, IEEE Trans. Computers.

[27]  Jaroslav Opatrny,et al.  Forwarding indices of consistent routings and their complexity , 1994, Networks.

[28]  N. Raghavan.  Eecient Routing in All-optical Networks , 1994 .

[29]  Stewart D. Personick,et al.  Review of Fundamentals of Optical Fiber Systems , 1983, IEEE J. Sel. Areas Commun..

[30]  Imrich Chlamtac,et al.  Purely optical networks for terabit communication , 1989, IEEE INFOCOM '89, Proceedings of the Eighth Annual Joint Conference of the IEEE Computer and Communications Societies.

[31]  Ming-Yang Kao,et al.  Optimal Broadcast in All-Port Wormhole-Routed Hypercubes , 1994, ICPP.

[32]  Luisa Gargano,et al.  Communication Complexity of Fault-Tolerant Information Diffusion , 1998, Theor. Comput. Sci..

[33]  Noga Alon,et al.  lambda1, Isoperimetric inequalities for graphs, and superconcentrators , 1985, J. Comb. Theory, Ser. B.

[34]  W. Mader,et al.  Minimalen-fach kantenzusammenhängende Graphen , 1971 .

[35]  Brian Alspach,et al.  Cayley Graphs with Optimal Fault Tolerance , 1992, IEEE Trans. Computers.

[36]  Arthur L. Liestman,et al.  A survey of gossiping and broadcasting in communication networks , 1988, Networks.

[37]  Frank Thomson Leighton,et al.  An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[38]  Jack J. Dongarra,et al.  Software Libraries for Linear Algebra Computations on High Performance Computers , 1995, SIAM Rev..

[39]  B. Mukherjee,et al.  WDM-based local lightwave networks. II. Multihop systems , 1992, IEEE Network.

[40]  Juraj Hromkovic,et al.  Optimal Algorithms for Broadcast and Gossip in the Edge-Disjoint Path Modes (Extended Abstract) , 1994, SWAT.

[41]  Bojan Mohar,et al.  Isoperimetric numbers of graphs , 1989, J. Comb. Theory, Ser. B.

[42]  Arthur M. Farley.  Minimum-time line broadcast networks , 1980, Networks.

[43]  Luisa Gargano,et al.  Communication complexity of fault-tolerant information diffusion , 1993, Proceedings of 1993 5th IEEE Symposium on Parallel and Distributed Processing.

[44]  R. Ravi,et al.  Rapid rumor ramification: approximating the minimum broadcast time , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[45]  Ouri Wolfson,et al.  The Communication Complexity of Atomic Commitment and of Gossiping , 1991, SIAM J. Comput..

[46]  Geoffrey C. Fox,et al.  Solving problems on concurrent processors: vol. 2 , 1990 .

[47]  G. C. Fox,et al.  Solving Problems on Concurrent Processors , 1988 .

[48]  Pierre A. Humblet,et al.  On the number of wavelengths and switches in all-optical networks , 1994, IEEE Trans. Commun..

[49]  Satish Rao,et al.  Efficient access to optical bandwidth wavelength routing on directed fiber trees, rings, and trees of rings , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[50]  Kumar N. Sivarajan,et al.  Routing and wavelength assignment in all-optical networks , 1995, TNET.

[51]  Marie-Claude Heydemann,et al.  On forwarding indices of networks , 1989, Discret. Appl. Math..

[52]  Juraj Hromkovic,et al.  Optimal Algorithms for Disemination of Information in Generalized Communication Modes , 1992, PARLE.

[53]  Marco Ajmone Marsan,et al.  Topologies for wavelength-routing all-optical networks , 1993, TNET.

[54]  Galen H. Sasaki,et al.  A linear lightwave Benes network , 1993, TNET.

[55]  Juraj Hromkovic,et al.  Optimal Algorithms for Broadcast and Gossip in the Edge-Disjoint Path Modes , 1997, Inf. Comput..

[56]  Christos Kaklamanis,et al.  Efficient Wavelength Routing on Directed Fiber Trees , 1996, ESA.

[57]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[58]  W. Mader.  Minimale n-fach kantenzusammenh angende graphen , 1971 .

[59]  Rajesh K. Pankaj.  Architectures for linear lightwave networks , 1992 .

[60]  Pierre Fraigniaud,et al.  Methods and problems of communication in usual networks , 1994, Discret. Appl. Math..

[61]  Alok Aggarwal,et al.  Efficient routing and scheduling algorithms for optical networks , 1994, SODA '94.

[62]  Andrzej Pelc.  Fault‐tolerant broadcasting and gossiping in communication networks , 1996 .

[63]  Klaus Jansen,et al.  Scheduling of Virtual Connections in Fast Networks , 1996, Universität Trier, Mathematik/Informatik, Forschungsbericht.

[64]  K. Nosu,et al.  Epilog-latest advances in dense WDM technology , 1990 .

[65]  Juraj Hromkovič,et al.  Dissemination of Information in Interconnection Networks (Broadcasting & Gossiping) , 1996 .