Checking Phylogenetic Decisiveness in Theory and in Practice

Parvini, Ghazaleh; Braught, Katherine; Fernández-Baca, David

doi:10.1007/978-3-030-57821-3_17

Cited by 4 publications

(3 citation statements)

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“…References [9,6] formulate the question of determining whether such data suffices to reconstruct a unique tree as a combinatorial problem, termed "decisiveness." The decisiveness problem is equivalent to the complement of the no-rainbow 4-coloring problem [5].…”

Section: Introductionmentioning

confidence: 99%

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Exact Algorithms for No-Rainbow Coloring and Phylogenetic Decisiveness

Parvini¹,

Fernández-Baca²

2021

Preprint

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The input to the no-rainbow hypergraph coloring problem is a hypergraph where every hyperedge has nodes. The question is whether there exists ancoloring of the nodes of such that all colors are used and there is no rainbow hyperedge -i.e., no hyperedge uses all colors. The no-rainbow hypergraph -coloring problem is known to be NP-complete for ≥ 3. The special case of = 4 is the complement of the phylogenetic decisiveness problem. Here we present a deterministic algorithm that solves the no-rainbow -coloring problem in * (( − 1) ( −1) / ) time and a randomized algorithm that solves the problem in * (( 2 ) ) time.The * -notation is a variant of -notation that ignores polynomial factors [3].

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Section: Introductionmentioning

confidence: 99%

“…In [5] we presented exact algorithms for no-rainbow -coloring for = 3 and = 4, that run in time * (1.89 ) and * (2.81 ) time, respectively . Here we present more efficient randomized and deterministic algorithms based on local search.…”

Section: Introductionmentioning

confidence: 99%

Exact Algorithms for No-Rainbow Coloring and Phylogenetic Decisiveness

Parvini¹,

Fernández-Baca²

2021

Preprint

Self Cite

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show abstract

“…Suppose n ≥ n + 2. H admits a no-rainbow 4-coloring if and only if H admits a no-rainbow r-coloring for some r ∈ {2, 3, 4}(17).Proof. (If ) Suppose H = ( X, E) admits a no-rainbow r-coloring c for some r ∈ {2, 3, 4}.…”

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confidence: 99%