Abstract
The linear time serial algorithm for planarity testing of [LEC-67] uses the linear time serial algorithm of [ET-76] for st-numbering. This st-numbering algorithm is based on depth-first search (DFS). A known conjecture states that DFS, which is a key technique in designing serial algorithms, is not amenable to poly-log time parallelism using "around linearly" (or even polynomially) many processors. The first contribution of this paper is a general method for searching efficiently in parallel undirected graphs, called ear-decomposition search (EDS).
The second contribution demonstrates the applicability of this search method. We present an efficient parallel algorithm for st-numbering in a biconnected graph. The algorithm is quite subtle and runs in logarithmic time using a linear number of processors on a concurrent-read concurrent-write (CRCW) PRAM. An efficient parallel algorithm for the problem did not exist before. It was not even known to be in NC.
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The research of this author was supported by NSF grant NSF-DCR-8318874 and ONR grant N00014-85-K-0046.
The research of these authors was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U. S. Department of Energy under contract number DE-AC02-76ER03077.
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© 1986 Springer-Verlag Berlin Heidelberg
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Maon, Y., Schieber, B., Vishkin, U. (1986). Parallel ear decomposition search (EDS) and st-numbering in graphs. In: Makedon, F., Mehlhorn, K., Papatheodorou, T., Spirakis, P. (eds) VLSI Algorithms and Architectures. AWOC 1986. Lecture Notes in Computer Science, vol 227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16766-8_4
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DOI: https://doi.org/10.1007/3-540-16766-8_4
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