3,116 research outputs found
A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest
We give a 2-approximation algorithm for the Maximum Agreement Forest problem
on two rooted binary trees. This NP-hard problem has been studied extensively
in the past two decades, since it can be used to compute the Subtree
Prune-and-Regraft (SPR) distance between two phylogenetic trees. Our result
improves on the very recent 2.5-approximation algorithm due to Shi, Feng, You
and Wang (2015). Our algorithm is the first approximation algorithm for this
problem that uses LP duality in its analysis
A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest
We give a 2-approximation algorithm for the Maximum Agreement Forest problem
on two rooted binary trees. This NP-hard problem has been studied extensively
in the past two decades, since it can be used to compute the rooted Subtree
Prune-and-Regraft (rSPR) distance between two phylogenetic trees. Our algorithm
is combinatorial and its running time is quadratic in the input size. To prove
the approximation guarantee, we construct a feasible dual solution for a novel
linear programming formulation. In addition, we show this linear program is
stronger than previously known formulations, and we give a compact formulation,
showing that it can be solved in polynomial tim
A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest
We give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the rooted Subtree Prune-and-Regraft (rSPR) distance between two phylogenetic trees. Our algorithm is combinatorial and its running time is quadratic in the input size. To prove the approximation guarantee, we construct a feasible dual solution for a novel linear programming formulation. In addition, we show this linear program is stronger than previously known formulations, and we give a compact formulation, showing that it can be solved in polynomial tim
Learning High-Dimensional Markov Forest Distributions: Analysis of Error Rates
The problem of learning forest-structured discrete graphical models from
i.i.d. samples is considered. An algorithm based on pruning of the Chow-Liu
tree through adaptive thresholding is proposed. It is shown that this algorithm
is both structurally consistent and risk consistent and the error probability
of structure learning decays faster than any polynomial in the number of
samples under fixed model size. For the high-dimensional scenario where the
size of the model d and the number of edges k scale with the number of samples
n, sufficient conditions on (n,d,k) are given for the algorithm to satisfy
structural and risk consistencies. In addition, the extremal structures for
learning are identified; we prove that the independent (resp. tree) model is
the hardest (resp. easiest) to learn using the proposed algorithm in terms of
error rates for structure learning.Comment: Accepted to the Journal of Machine Learning Research (Feb 2011
A Fixed Parameter Tractable Approximation Scheme for the Optimal Cut Graph of a Surface
Given a graph cellularly embedded on a surface of genus , a
cut graph is a subgraph of such that cutting along yields a
topological disk. We provide a fixed parameter tractable approximation scheme
for the problem of computing the shortest cut graph, that is, for any
, we show how to compute a approximation of
the shortest cut graph in time .
Our techniques first rely on the computation of a spanner for the problem
using the technique of brick decompositions, to reduce the problem to the case
of bounded tree-width. Then, to solve the bounded tree-width case, we introduce
a variant of the surface-cut decomposition of Ru\'e, Sau and Thilikos, which
may be of independent interest
Better Practical Algorithms for rSPR Distance and Hybridization Number
The problem of computing the rSPR distance of two phylogenetic trees (denoted by RDC) is NP-hard and so is the problem of computing the hybridization number of two phylogenetic trees (denoted by HNC). Since they are important problems in phylogenetics, they have been studied extensively in the literature. Indeed, quite a number of exact or approximation algorithms have been designed and implemented for them. In this paper, we design and implement one exact algorithm for HNC and several approximation algorithms for RDC and HNC. Our experimental results show that the resulting exact program is much faster (namely, more than 80 times faster for the easiest dataset used in the experiments) than the previous best and its superiority in speed becomes even more significant for more difficult instances. Moreover, the resulting approximation programs output much better results than the previous bests; indeed, the outputs are always nearly optimal and often optimal. Of particular interest is the usage of the Monte Carlo tree search (MCTS) method in the design of our approximation algorithms. Our experimental results show that with MCTS, we can often solve HNC exactly within short time
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