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On the Number of 2-Protected Nodes in Tries and Suffix Trees

Jeffrey Gaither 1 Yushi Homma 1 Mark Sellke 1 Mark Daniel Ward 2 
1 Department of mathematics Purdue University
2 Purdue University - Department of Statistics
Abstract : We use probabilistic and combinatorial tools on strings to discover the average number of 2-protected nodes in tries and in suffix trees. Our analysis covers both the uniform and non-uniform cases. For instance, in a uniform trie with $n$ leaves, the number of 2-protected nodes is approximately 0.803$n$, plus small first-order fluctuations. The 2-protected nodes are an emerging way to distinguish the interior of a tree from the fringe.
Keywords : retrieval trees suffix trees Poissonization Mellin transforms pattern matching
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https://hal.inria.fr/hal-01197232
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Jeffrey Gaither, Yushi Homma, Mark Sellke, Mark Daniel Ward. On the Number of 2-Protected Nodes in Tries and Suffix Trees. 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'12), 2012, Montreal, Canada. pp.381-398, ⟨10.46298/dmtcs.3008⟩. ⟨hal-01197232⟩

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