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, bidirectional network containing n-nodes and m-links which uses O(m) messages and which can be completed in O(n) time. Using the ear decomposition, we obtain the following results for a distributed network: 1) The distributed ear decomposition algorithm can be used to test biconnectivity, determine biconnected components, find cutpoints and bridges using O(m) messages in O(n) time. 2) The distributed ear decomposition algorithm can be used to test if a biconnected 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.

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

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

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

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

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

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

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

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

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

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

[11]  Arkady Kanevsky,et al.  Improved Algorithms for Graph Four-Connectivity , 1987, FOCS.

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

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

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

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

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

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

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

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