 
Summary: Fast algorithms for computing the
Tripartitionbased Distance between
Phylogenetic Networks
Nguyen Bao Nguyen, C. Thach Nguyen, and WingKin Sung
National University of Singapore, 3 Science Drive 2, Singapore 117543. Email:
{baonguyen, thachnguyen, dcsswk}@nus.edu.sg
Abstract. Consider two phylogenetic networks N and N
of size n. The
tripartitionbased distance finds the proportion of tripartitions which
are not shared by N and N
. This distance is proposed by Moret et
al (2004) and is a generalization of RobinsonFoulds distance, which is
orginally used to compare two phylogenetic trees. This paper gives an
O(min{kn log n, n log n + hn})time algorithm to compute this distance,
where h is the number of hybrid nodes in N and N
while k is the max
imum number of hybrid nodes among all biconnected components in N
and N
. Note that k << h << n in a phylogenetic network. In addition,
we propose algorithms for comparing galledtrees, which are an impor
