NDLI: Cycle Killer...Qu'est-ce que c'est? On the Comparative Approximability of Hybridization Number and Directed Feedback Vertex Set

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Lekić, Nela Linz, Simone Kelk, Steven van Iersel, Leo Scornavacca, Celine Stougie, Leen
Copyright Year	2012
Abstract	We show that the problem of computing the hybridization number of two rooted binary phylogenetic trees on the same set of taxa $X$ has a constant factor polynomial-time approximation if and only if the problem of computing a minimum-size feedback vertex set in a directed graph (DFVS) has a constant factor polynomial-time approximation. The latter problem, which asks for a minimum number of vertices to be removed from a directed graph to transform it into a directed acyclic graph, is one of the problems in Karp's seminal 1972 list of 21 NP-complete problems. Despite considerable attention from the combinatorial optimization community, it remains to this day unknown whether a constant factor polynomial-time approximation exists for DFVS. Our result thus places the (in)approximability of hybridization number in a much broader complexity context, and as a consequence we obtain that it inherits inapproximability results from the problem Vertex Cover. On the positive side, we use results from the DFVS literature to give an $\text{O}( \log r \log \log r)$ approximation for the hybridization number where $r$ is the correct value.
Starting Page	1635
Ending Page	1656
Page Count	22
File Format	PDF
ISSN	08954801
DOI	10.1137/120864350
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	4
Volume Number	26
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2012-11-20
Access Restriction	Subscribed
Subject Keyword	approximation hybridization number directed feedback vertex set Taxonomy, cladistics, statistics Approximation algorithms Directed graphs (digraphs), tournaments Combinatorial optimization phylogenetic networks
Content Type	Text
Resource Type	Article
Subject	Mathematics

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