Tree inclusions in windows and slices
A labelled tree P is an embedded subtree of a labelled tree T if P can be obtained by deleting some nodes from T : if a node v is deleted, all edges adjacent to v are also deleted and replaced by edges going from the parent of v (if it exists) to the children of v . Deciding whether P is an embedded...
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| Veröffentlicht in: | Journal of mathematical sciences (New York, N.Y.) N.Y.), 2009-05, Vol.158 (5), p.623-632 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | A labelled tree
P
is an embedded subtree of a labelled tree
T
if
P
can be obtained by deleting some nodes from
T
: if a node
v
is deleted, all edges adjacent to
v
are also deleted and replaced by edges going from the parent of
v
(if it exists) to the children of
v
. Deciding whether
P
is an embedded subtree of
T
is known to be NP-complete. Given two trees (a target
T
and a pattern
P
) and a natural number
w
, we address two problems: 1) counting the number of windows of
T
having height exactly
w
and containing the pattern
P
as an embedded subtree, and 2) counting the number of slices of
T
having height exactly
w
and containing the pattern
P
as an embedded subtree. Our algorithms run in time
O
(|
T
|(
w
−
h
(
P
)+2)
4|
P
|
), where |
T
| (respectively, |
P
|) is the size of
T
(respectively,
P
), and
h
(
P
) is the height of
P
. Bibliography: 10 titles. |
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| ISSN: | 1072-3374 1573-8795 |
| DOI: | 10.1007/s10958-009-9401-7 |