We consider the tree consensus problem, an important problem in bioinformatics.  ]  Gawrychowski, Landau, Sung, and Weimann [ICALP'18] devise a greedy algorithm that runs in time O(n^{1.5}\log n) based on micro-macro decomposition . We give a faster algorithm  that runs in time O(n\log n). Our key ingredient is a bipartition compatibility criteria based on amortized-time leaf counters  ]  .
We consider the tree consensus problem, an important problem in bioinformatics. Given a rooted tree t and another tree T, one would like to incorporate compatible information from T to t. This problem is a subproblem in the tree refinement problem called the RF-Optimal Tree Refinement Problem defined by in Christensen, Molloy, Vachaspati and Warnow WABI'19] who employ the greedy algorithm by Gawrychowski, Landau, Sung, and Weimann [ICALP'18] that runs in time O(n^{1.5}\log n) . We give a faster algorithm for this problem that runs in time O(n\log n). Our key ingredient is a bipartition compatibility criteria based on amortized-time leaf counters . While this is an improvement, the fastest solution is an algorithm by Jansson, Shen, and Sung JACM'16] which runs in time O(n) .
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Given a rooted tree t and another tree T, one would like to incorporate compatible information from T to t. This problem is a subproblem in the tree refinement problem called the RF-Optimal Tree Refinement Problem defined by in Christensen, Molloy, Vachaspati and Warnow
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WABI'19
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who employ the greedy algorithm by
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devise a greedy algorithm
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based on micro-macro decomposition
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for this problem
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. While this is an improvement, the fastest solution is an algorithm by Jansson, Shen, and Sung
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JACM'16
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which runs in time O(n)