Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing the blocks of a quasi-median graph   Quasi-median graphs are a tool commonly used by evolutionary biologists to
visualise the evolution of molecular sequences. As with any graph, a
quasi-median graph can contain cut vertices, that is, vertices whose removal
disconnect the graph. These vertices induce a decomposition of the graph into
blocks, that is, maximal subgraphs which do not contain any cut vertices. Here
we show that the special structure of quasi-median graphs can be used to
compute their blocks without having to compute the whole graph. In particular
we present an algorithm that, for a collection of $n$ aligned sequences of
length $m$, can compute the blocks of the associated quasi-median graph
together with the information required to correctly connect these blocks
together in run time $\mathcal O(n^2m^2)$, independent of the size of the
sequence alphabet. Our primary motivation for presenting this algorithm is the
fact that the quasi-median graph associated to a sequence alignment must
contain all most parsimonious trees for the alignment, and therefore
precomputing the blocks of the graph has the potential to help speed up any
method for computing such trees.

25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th