A distributed dual ascent algorithm for Steiner problems in multicast routing

Multicast routing problems are often modeled as Steiner Problems in undirected or directed graphs, the latter case being particularly suitable to cases where most of the traffic has a single source. Sequential Steiner heuristics are not convenient in that context, because one cannot assume that a central node has complete information about the topology and the state of a large wide area network. This article introduces a distributed version of a Dual Ascent primal-dual heuristic, known for its remarkably good practical results, lower and upper bounds, in both undirected and directed Steiner problems. Complexity analysis and experimental results are also presented, showing the efficiency of the proposed algorithm when compared with the best distributed algorithms in the literature. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009

[1]  Gen-Huey Chen,et al.  The steiner problem in distributed computing systems , 1993, Inf. Sci..

[2]  Panos M. Pardalos,et al.  A survey of combinatorial optimization problems in multicast routing , 2005, Comput. Oper. Res..

[3]  David P. Williamson,et al.  Primal-Dual Approximation Algorithms for Integral Flow and Multicut in Trees, with Applications to Matching and Set Cover , 1993, ICALP.

[4]  Renato F. Werneck,et al.  Dual Heuristics on the Exact Solution of Large Steiner Problems , 2001, Electron. Notes Discret. Math..

[5]  Joze Rugelj,et al.  Distributed multicast routing in point-to-point networks , 1997, Comput. Oper. Res..

[6]  Gorazd Kandus,et al.  A note on distributed multicast routing in point-to-point networks , 2001, Comput. Oper. Res..

[7]  Valmir Carneiro Barbosa,et al.  An introduction to distributed algorithms , 1996 .

[8]  Abhishek P. Patil,et al.  Resource Allocation Using Multiple Edge-Sharing Multicast Trees , 2008, IEEE Transactions on Vehicular Technology.

[9]  Richard T. Wong,et al.  A dual ascent approach for steiner tree problems on a directed graph , 1984, Math. Program..

[10]  Anujan Varma,et al.  Distributed algorithms for multicast path setup in data networks , 1996, TNET.

[11]  Renato F. Werneck,et al.  On the Implementation of MST-Based Heuristics for the Steiner Problem in Graphs , 2002, ALENEX.

[12]  Adrian Segall,et al.  Distributed network protocols , 1983, IEEE Trans. Inf. Theory.

[13]  Pierre A. Humblet,et al.  A Distributed Algorithm for Minimum-Weight Spanning Trees , 1983, TOPL.

[14]  Anees Shaikh,et al.  Destination-Driven Routing for Low-Cost Multicast , 1997, IEEE J. Sel. Areas Commun..

[15]  Gurdip Singh,et al.  A Distributed Protocol for Constructing Multicast Trees , 1998, OPODIS.

[16]  Stefan Voß,et al.  Steiner's Problem in Graphs: Heuristic Methods , 1992, Discret. Appl. Math..

[17]  T. Koch,et al.  SteinLib: An Updated Library on Steiner Tree Problems in Graphs , 2001 .

[18]  Siavash Vahdati Daneshmand,et al.  Improved algorithms for the Steiner problem in networks , 2001, Discret. Appl. Math..

[19]  Fabrizio Grandoni,et al.  Primal-dual based distributed algorithms for vertex cover with semi-hard capacities , 2005, PODC '05.

[20]  Gorazd Kandus,et al.  Steiner Tree Based Distributed Multicast Routing in Networks , 2001 .