Finding lowest common ancestors in parallel

Journal Article · Fri Aug 01 04:00:00 EDT 1986 · IEEE Trans. Comput.; (United States)

DOI:https://doi.org/10.1109/TC.1986.1676830· OSTI ID:5364487

Tsin, Y H

Two parallel algorithms for finding the lowest common ancestors of a set of vertex pairs Q (the query set) in a directed tree are presented. With all the overheads taken into account, these algorithms take O(((n + absolute value of Q)/p) log/sub 2/n) and O(n/sup 2//p + log/sub 2/n) time, respectively, with p(>0) processors (n is the size of the tree). These results are better than the best known result in that the first achieves the O(log/sub 2/n) time bound with only n + absolute value of Q processors which the second reduces the number of processors used by a factor of log/sub 2/n which is optimal for large query sets when 0 < p less than or equal to n/sup 2//log/sub 2/n. The computer model the authors use here is the PRAM which is an SIMD model allowing read but not write conflicts. The results also imply the following improvements: the processor bound for finding a set of fundamental cycles in an undirected graph is improved by a factor of log/sub 2/n and the result is optimal for dense graphs; the implementations of some other sequential and parallel algorithms are also simplified.

• Research Organization: Dept. of Computer Science, Memorial Univ. of Newfoundland, St. John's, Newfoundland A1C 5S7
• OSTI ID: 5364487
• Journal Information: IEEE Trans. Comput.; (United States), Journal Name: IEEE Trans. Comput.; (United States) Vol. C-35:8; ISSN ITCOB
• Country of Publication: United States
• Language: English

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99 GENERAL AND MISCELLANEOUS
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