Leader election in oriented star graphs

Leader election in a network plays an important role in the area of distributed algorithm design. Structural properties of the network as well as presence of direction on the edges of the network greatly affects the complexity of the leader election problem, which is primarily measured by the message complexity of the protocol. Our purpose in the present article is to adapt the existing distributed match making concepts to design a linear time leader election algorithm for star graphs. Star graphs have been extensively studied as an attractive alternative for the well-known hypercubes for network design. Linear election algorithms for oriented hypercubes is known; no such algorithm exists for oriented star graphs. © 2005 Wiley Periodicals, Inc. NETWORKS, Vol. 45l2r, 169–179 2005

[1]  Paul M. B. Vitányi,et al.  Distributed match-making , 1988, Algorithmica.

[2]  Shmuel Zaks,et al.  Tight lower and upper bounds for some distributed algorithms for a complete network of processors , 1984, PODC '84.

[3]  Derek Allan Holton,et al.  The Petersen graph , 1993, Australian mathematical society lecture series.

[4]  C. Loui Michael,et al.  Election in a complete network with a sense of direction , 1986 .

[5]  Pradip K. Srimani,et al.  Topological properties of star graphs , 1993 .

[6]  Shahram Latifi.  On the Fault-Diameter of the Star Graph , 1993, Inf. Process. Lett..

[7]  Krzysztof Diks,et al.  Broadcasting in Unlabeled Hypercubes with a Linear Number of Messages , 1998, Inf. Process. Lett..

[8]  H. Forde,et al.  Sense of Direction , 1873, Nature.

[9]  Masafumi Yamashita,et al.  Leader Election Problem on Networks in which Processor Identity Numbers Are Not Distinct , 1999, IEEE Trans. Parallel Distributed Syst..

[10]  Pradip K. Srimani,et al.  Super Star: a new optimally fault tolerant network architecture , 1991, [1991] Proceedings. 11th International Conference on Distributed Computing Systems.

[11]  S. Lakshmivarahan,et al.  Symmetry in Interconnection Networks Based on Cayley Graphs of Permutation Groups: A Survey , 1993, Parallel Comput..

[12]  Hans L. Bodlaender,et al.  New Lower Bound Techniques for Distributed Leader Finding and Other Problems on Rings of Processors , 1991, Theor. Comput. Sci..

[13]  Nicola Santoro.  Sense of direction, topological awareness and communication complexity , 1984, SIGA.

[14]  Gerard Tel.  Linear Election in Hypercubes , 1995, Parallel Process. Lett..

[15]  Khaled Day,et al.  A Comparative Study of Topological Properties of Hypercubes and Star Graphs , 1994, IEEE Trans. Parallel Distributed Syst..

[16]  Bernard Mans.  Optimal Distributed Algorithms in Unlabeled Tori and Chordal Rings , 1997, J. Parallel Distributed Comput..

[17]  Sheldon B. Akers,et al.  The Star Graph: An Attractive Alternative to the n-Cube , 1994, ICPP.

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