An optimal distributed ear decomposition algorithm with applications to biconnectivity and outerplanarity testing

We present an asynchronous distributed algorithm to determine an ear decomposition of an arbitrary, connected, bi-directional network containing n-nodes and m-links using O(m) messages and O(n) time. Using the ear decomposition we obtain the following results: 1. The distributed ear decomposition algorithm can be used to test biconnectivity, determine biconnected components, find outpoints and bridges using O(m) messages in O(n) time. 2. The distributed ear decomposition algorithm can be used to test if a network is outerplanar using O(n) messages in O(n) time and if the network is outerplanar the embedding is also given using the same message and time complexity.<<ETX>>

[1]  K. V. S. Ramarao,et al.  Distributed Algorithms for Network Recognition Problems , 1989, IEEE Trans. Computers.

[2]  Israel Cidon.  Yet Another Distributed Depth-First-Search Algorithm , 1988, Inf. Process. Lett..

[3]  S. Venkatesan,et al.  On Finding and Updating Shortest Paths Distributively , 1992, J. Algorithms.

[4]  Donald S. Fussell,et al.  Finding Triconnected Components by Local Replacements , 1989, ICALP.

[5]  Baruch Awerbuch,et al.  A New Distributed Depth-First-Search Algorithm , 1985, Inf. Process. Lett..

[6]  S. Sitharama Iyengar,et al.  An Optimal Distributed Algorithm for Recognizing Mesh-Connected Networks , 1993, Theor. Comput. Sci..

[7]  Vijaya Ramachandran.  Parallel Open Ear Decomposition with Applications to Graph Biconnectivity and Triconnectivity , 1993 .

[8]  Gary L. Miller,et al.  A new graphy triconnectivity algorithm and its parallelization , 1987, STOC.

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

[10]  Gary L. Miller,et al.  A new graph triconnectivity algorithm and its parallelization , 1992, Comb..

[11]  Frank Harary,et al.  Graph Theory , 2016 .

[12]  Greg N. Frederickson,et al.  Space-Efficient and Fault-Tolerant Message Routing in Outerplanar Networks , 1988, IEEE Trans. Computers.

[13]  Walter Hohberg,et al.  How to Find Biconnected Components in Distributed Networks , 1990, J. Parallel Distributed Comput..

[14]  Uzi Vishkin,et al.  Efficient Parallel Triconnectivity in Logarithmic Time , 1988, AWOC.

[15]  Willy Zwaenepoel,et al.  Distributed process groups in the V Kernel , 1985, TOCS.

[16]  S. Sitharama Iyengar,et al.  An Efficient Distributed Depth-First-Search Algorithm , 1989, Inf. Process. Lett..

[17]  Greg N. Frederickson,et al.  A new approach to all pairs shortest paths in planar graphs , 1987, STOC.

[18]  Arkady Kanevsky,et al.  Improved algorithms for graph four-connectivity , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[19]  Krishnaiyan Thulasiraman,et al.  A Time-Optimal Message-Efficient Distributed Algorithm for Depth-First-Search , 1987, Inf. Process. Lett..

[20]  Leslie Lamport,et al.  Using Time Instead of Timeout for Fault-Tolerant Distributed Systems. , 1984, TOPL.

[21]  Vijaya Ramachandran,et al.  Planarity Testing in Parallel , 1994, J. Comput. Syst. Sci..

[22]  Edsger W. Dijkstra,et al.  Self-stabilizing systems in spite of distributed control , 1974, CACM.

[23]  Scott Shenker,et al.  Epidemic algorithms for replicated database maintenance , 1988, OPSR.

[24]  H. Whitney.  Non-Separable and Planar Graphs. , 1931, Proceedings of the National Academy of Sciences of the United States of America.