Introduction This paper presents a new description of the maximum parsimony criterion. In particular, this paper demonstrates a new mathematical equivalence between Fitch parsimony as well as selection of certain types of consensus trees. The link between parsimony and consensus is intended to contribute to the discussion on parsimony as well as consensus and total evidence. A link between pars...

Proof. The proof is similar to the one in (Beygelzimer et al., 2008), which is based on defining the overall-regret of any subtree. The key change in our proof is to define the path-regret of any subtree to be the total regret of the nodes on the ideal path of the subtree. The induction step follows similarly from the proof in (Beygelzimer et al., 2008) by considering two cases: one for the ide...

Di erent phylogenetic trees for the same group of species are often produced either by procedures that use diverse optimality criteria [16] or from di erent genes [12] in the study of molecular evolution. Comparing these trees to nd their similarities and dissimilarities (i.e. distance) is thus an important issue in computational molecular biology. Several distance metrics including the nearest...

Given two trees (a target T and a pattern P ) and a natural number w, window embedded subtree problems consist in deciding whether P occurs as an embedded subtree of T and/or finding the number of size (at most) w windows of T which contain pattern P as an embedded subtree. P is an embedded subtree of T if P can be obtained by deleting some nodes from T (if a node v is deleted, all edges adjace...

Subtree filament graphs are the intersection graphs of subtree filaments in a tree. This class of graphs contains subtree overlap graphs, interval filament graphs, chordal graphs, circle graphs, circular-arc graphs, cocomparability graphs, and polygon-circle graphs. In this paper we show that, for circle graphs, the clique cover problem is NP-complete and the h-clique cover problem for fixed h ...

Given a tree containing n vertices, consider the sum of the distance between all vertices and a k-leaf-subtree (subtree which contains exactly k leaves). A k-tree-core is a k-leaf-subtree which minimizes the sum of the distances. In this paper, we propose a linear time algorithm for nding a k-tree-core for a given k.

In this article, we propose fast subtree kernels on graphs. On graphs with n nodes and m edges and maximum degree d, these kernels comparing subtrees of height h can be computed in O(mh), whereas the classic subtree kernel by Ramon & Gärtner scales as O(n4h). Key to this efficiency is the observation that the Weisfeiler-Lehman test of isomorphism from graph theory elegantly computes a subtree k...

Proof. The proof is similar to the one in (Beygelzimer et al., 2008), which is based on defining the overallregret of any subtree. The key change in our proof is to define the path-regret of any subtree to be the total regret of the nodes on the ideal path of the subtree. The induction step follows similarly from the proof in (Beygelzimer et al., 2008) by considering two cases: one for the idea...

We show that for every positive integer d, every downwards closed subtree T of d without terminal nodes and every finite weakly embedded subtree A of T there is a finite list of equivalence relations on Em(T ) with the property that for every other equivalence relation E on Em(T ) there is a strongly embedded subtree S ⊆ T of height ω, such that E Em(S) is equal to one of the equivalence relati...