---
res:
bibo_abstract:
- "We are given a set T = {T 1 ,T 2 , . . .,T k } of rooted binary trees, each T
i leaf-labeled by a subset L(Ti)⊂{1,2,...,n} . If T is a tree on {1,2, . . .,n
}, we let T|L denote the minimal subtree of T induced by the nodes of L and all
their ancestors. The consensus tree problem asks whether there exists a tree T
* such that, for every i , T∗|L(Ti) is homeomorphic to T i .\r\n\r\nWe present
algorithms which test if a given set of trees has a consensus tree and if so,
construct one. The deterministic algorithm takes time min{O(N n 1/2 ), O(N+ n
2 log n )}, where N=∑i|Ti| , and uses linear space. The randomized algorithm takes
time O(N log3 n) and uses linear space. The previous best for this problem was
a 1981 O(Nn) algorithm by Aho et al. Our faster deterministic algorithm uses a
new efficient algorithm for the following interesting dynamic graph problem: Given
a graph G with n nodes and m edges and a sequence of b batches of one or more
edge deletions, then, after each batch, either find a new component that has just
been created or determine that there is no such component. For this problem, we
have a simple algorithm with running time O(n 2 log n + b 0 min{n 2 , m log n
}), where b 0 is the number of batches which do not result in a new component.
For our particular application, b0≤1 . If all edges are deleted, then the best
previously known deterministic algorithm requires time O(mn−−√) to solve this
problem. We also present two applications of these consensus tree algorithms which
solve other problems in computational evolutionary biology.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Monika H
foaf_name: Henzinger, Monika H
foaf_surname: Henzinger
foaf_workInfoHomepage: http://www.librecat.org/personId=540c9bbd-f2de-11ec-812d-d04a5be85630
orcid: 0000-0002-5008-6530
- foaf_Person:
foaf_givenName: V.
foaf_name: King, V.
foaf_surname: King
- foaf_Person:
foaf_givenName: T.
foaf_name: Warnow, T.
foaf_surname: Warnow
bibo_doi: 10.1007/pl00009268
bibo_volume: 24
dct_date: 1999^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0178-4617
- http://id.crossref.org/issn/1432-0541
dct_language: eng
dct_publisher: Springer Nature@
dct_subject:
- Algorithms
- Data structures
- Evolutionary biology
- Theory of databases
dct_title: Constructing a tree from homeomorphic subtrees, with applications to
computational evolutionary biology@
...