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Generating Linear Extensions Fast
"... One of the most important sets associated with a poset P is its set of linear extensions, E(P) . "ExtensionFast.html" 87 lines, 2635 characters One of the most important sets associated with a poset P is its set of linear extensions, E(P) . In this paper, we present an algorithm to generat ..."
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Cited by 48 (6 self)
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One of the most important sets associated with a poset P is its set of linear extensions, E(P) . "ExtensionFast.html" 87 lines, 2635 characters One of the most important sets associated with a poset P is its set of linear extensions, E(P) . In this paper, we present an algorithm to generate all of the linear extensions of a poset in constant amortized time; that is, in time O(e(P)) , where e ( P ) =  E(P) . The fastest previously known algorithm for generating the linear extensions of a poset runs in time O(n e(P)) , where n is the number of elements of the poset. Our algorithm is the first constant amortized time algorithm for generating a ``naturally defined'' class of combinatorial objects for which the corresponding counting problem is #Pcomplete. Furthermore, we show that linear extensions can be generated in constant amortized time where each extension differs from its predecessor by one or two adjacent transpositions. The algorithm is practical and can be modified to efficiently count linear extensions, and to compute P(x < y) , for all pairs x,y , in time O( n^2 + e ( P )).
Shortest Walks in Almost ClawFree Graphs
, 1993
"... There have been many results concerning clawfree graphs and hamiltonicity. Recently, Jackson and Wormald have obtained more general results on walks in clawfree graphs. In this paper, we consider the family of almost clawfree graphs that contains the previous one, and give some results on walk ..."
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Cited by 1 (1 self)
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There have been many results concerning clawfree graphs and hamiltonicity. Recently, Jackson and Wormald have obtained more general results on walks in clawfree graphs. In this paper, we consider the family of almost clawfree graphs that contains the previous one, and give some results on walks, especially on shortest covering walks visiting only once some given vertices.