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Counting clique trees and computing perfect elimination schemes in parallel. (English) Zbl 0685.68050
Summary: In a previous result, the authors showed that a clique tree of a chordal graph can be constructed in O(log n) parallel computing time with \(O(n^ 3)\) processors on CRCW PRAM, where n is the number of nodes of the graph. It will be shown that this result can be extended in two ways. First, we show that from the parallel clique tree constructing algorithm we can derive an exact formula of counting clique trees of a labeled connected chordal graph. Next, we show that a perfect elimination scheme of a chordal graph can be computed in O(log n) time with \(O(n^ 2)\) processors on CREW PRAM once a clique tree of the graph is given. This implies that a perfect elimination scheme of a chordal graph can be computed on O(log n) time with \(O(n^ 3)\) processors on CRCW PRAM.

68Q25 Analysis of algorithms and problem complexity
68R10 Graph theory (including graph drawing) in computer science
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
Full Text: DOI
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