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Abstract:
In this paper we study a few
important tree optimization problems with
applications to computational biology.
These problems ask for trees that are consistent with an
as large part of the given data as possible.
We show that the maximum homeomorphic agreement
subtree problem cannot be approximated within a factor of
$N^{\epsilon}$, where $N$ is the input size, for any $0 \leq \epsilon
< \frac{1}{18}$ in polynomial time, unless P=NP. On the other hand,
we present an $O(N\log N)$-time heuristic for the restriction of this
problem to instances with $O(1)$ trees of height $O(1)$,
yielding solutions within a constant factor of the optimum.
We prove that the maximum inferred consensus tree
problem is NP-complete and we provide a simple fast heuristic
for it, yielding solutions within one third of the optimum.
We also present a more specialized polynomial-time heuristic
for the maximum inferred local consensus tree problem.
