Abstract
The Minimum Rooted Triplet Inconsistency (MinRTI) problem represents a key computational task in the construction of phylogenetic trees. Inspired by Aho et al’s seminal paper and Bryant’s thesis, we describe an edge-labelled multigraph problem, Minimum Dissolving Graph (MinDG) and show that it is equivalent to MinRTI. We prove that on an n-vertex graph, for every ε > 0, MinDG is hard to approximate within a factor in \(O(2^{\log^{1-\ensuremath{\varepsilon}}n})\), even on trees formed by multi-edges. Via a further reduction, this result applies to MinRTI, resolving the open question of whether there is a sub-linear approximation factor for MinRTI. In addition, we provide polynomial-time algorithms that return optimal solutions when the input multigraph is restricted to a multi-edge path or a simple tree.
Supported in part by an Australian Research Council Future Fellowship and The Melbourne School of Engineering.
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Chester, A., Dondi, R., Wirth, A. (2013). Resolving Rooted Triplet Inconsistency by Dissolving Multigraphs. In: Chan, TH.H., Lau, L.C., Trevisan, L. (eds) Theory and Applications of Models of Computation. TAMC 2013. Lecture Notes in Computer Science, vol 7876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38236-9_24
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DOI: https://doi.org/10.1007/978-3-642-38236-9_24
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