Evolutionary Approaches To Minimizing Network Coding Resources

We wish to minimize the resources used for network coding while achieving the desired throughput in a multicast scenario. We employ evolutionary approaches, based on a genetic algorithm, that avoid the computational complexity that makes the problem NP-hard. Our experiments show great improvements over the sub-optimal solutions of prior methods. Our new algorithms improve over our previously proposed algorithm in three ways. First, whereas the previous algorithm can be applied only to acyclic networks, our new method works also with networks with cycles. Second, we enrich the set of components used in the genetic algorithm, which improves the performance. Third, we develop a novel distributed framework. Combining distributed random network coding with our distributed optimization yields a network coding protocol where the resources used for coding are optimized in the setup phase by running our evolutionary algorithm at each node of the network. We demonstrate the effectiveness of our approach by carrying out simulations on a number of different sets of network topologies.

[1]  Moshe Sidi,et al.  Topological design of local-area networks using genetic algorithms , 1996, TNET.

[2]  Ratul Mahajan,et al.  Measuring ISP topologies with Rocketfuel , 2004, IEEE/ACM Transactions on Networking.

[3]  Dorothea Heiss-Czedik,et al.  An Introduction to Genetic Algorithms. , 1997, Artificial Life.

[4]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[5]  Christina Fragouli,et al.  Information flow decomposition for network coding , 2006, IEEE Transactions on Information Theory.

[6]  David E. Goldberg,et al.  The Gambler's Ruin Problem, Genetic Algorithms, and the Sizing of Populations , 1999, Evolutionary Computation.

[7]  R. Gary Parker,et al.  On multiple steiner subgraph problems , 1986, Networks.

[8]  Muriel Médard,et al.  Genetic Representations for Evolutionary Minimization of Network Coding Resources , 2007, EvoWorkshops.

[9]  R. Koetter,et al.  The benefits of coding over routing in a randomized setting , 2003, IEEE International Symposium on Information Theory, 2003. Proceedings..

[10]  Rudolf Ahlswede,et al.  Network information flow , 2000, IEEE Trans. Inf. Theory.

[11]  Peter Sanders,et al.  Polynomial time algorithms for multicast network code construction , 2005, IEEE Transactions on Information Theory.

[12]  Tracey Ho,et al.  Network Coding with a Cost Criterion , 2004 .

[13]  E. Cantu-Paz,et al.  The Gambler's Ruin Problem, Genetic Algorithms, and the Sizing of Populations , 1997, Evolutionary Computation.

[14]  Meir Feder,et al.  Efficient network codes for cyclic networks , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[15]  Lalit M. Patnaik,et al.  Genetic algorithms: a survey , 1994, Computer.

[16]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[17]  Michael Langberg,et al.  The encoding complexity of network coding , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[18]  Muriel Médard,et al.  An algebraic approach to network coding , 2003, TNET.

[19]  Guy Melançon,et al.  Generating connected acyclic digraphs uniformly at random , 2004, Inf. Process. Lett..

[20]  Don Coppersmith,et al.  Matrix multiplication via arithmetic progressions , 1987, STOC.

[21]  Yunnan Wu,et al.  Minimum-energy multicast in mobile ad hoc networks using network coding , 2004, Information Theory Workshop.

[22]  Muriel Medard,et al.  On Randomized Network Coding , 2003 .

[23]  Ralf Koetter,et al.  Minimal network coding for multicast , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[24]  Don Coppersmith,et al.  Matrix multiplication via arithmetic progressions , 1987, STOC.

[25]  Alice E. Smith,et al.  Efficient optimization of all-terminal reliable networks, using an evolutionary approach , 1997 .

[26]  Tracey Ho,et al.  A Random Linear Network Coding Approach to Multicast , 2006, IEEE Transactions on Information Theory.

[27]  M. Médard,et al.  On Minimizing Network Coding Resources : An Evolutionary Approach , 2005 .

[28]  R. Koetter,et al.  Distributed Asynchronous Algorithms for Multicast Network Coding , 2005 .