Strongly Chordal and Chordal Bipartite Graphs Are Sandwich Monotone

Heggernes, Pinar; Mancini, Federico; Papadopoulos, Charis; Sritharan, R.

doi:10.1007/978-3-642-02882-3_40

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Graph Sandwich1

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2012

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“…They provided efficient algorithms when G 1 or G 2 is chordal, where "efficient" means that it runs in polynomial time in the input size and linear time in the output size. Their approach was generalized by Heggernes et al [5] to all sandwich-monotone graph classes. In this respect, this paper gives another example of efficient graph sandwich enumeration algorithms.…”

Section: Graph Sandwichmentioning

confidence: 99%

Efficient Enumeration of the Directed Binary Perfect Phylogenies from Incomplete Data

Kiyomi

Okamoto

Saitoh

2012

Experimental Algorithms

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We study a character-based phylogeny reconstruction problem when an incomplete set of data is given. More specifically, we consider the situation under the directed perfect phylogeny assumption with binary characters in which for some species the states of some characters are missing. Our main object is to give an efficient algorithm to enumerate (or list) all perfect phylogenies that can be obtained when the missing entries are completed. While a simple branch-and-bound algorithm (B&B) shows a theoretically good performance, we propose another approach based on a zero-suppressed binary decision diagram (ZDD). Experimental results on randomly generated data exhibit that the ZDD approach outperforms B&B. We also prove that counting the number of phylogenetic trees consistent with a given data is #P-complete, thus providing an evidence that an efficient random sampling seems hard.

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Section: Graph Sandwichmentioning

confidence: 99%