2006 | OriginalPaper | Chapter
Linear-Time Algorithms for Tree Root Problems
Authors : Maw-Shang Chang, Ming-Tat Ko, Hsueh-I Lu
Published in: Algorithm Theory – SWAT 2006
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
Let
T
be a tree on a set
V
of nodes. The
p-th power
T
p
of
T
is the graph on
V
such that any two nodes
u
and
w
of
V
are adjacent in
T
p
if and only if the distance of
u
and
w
in
T
is at most
p
. Given an
n
-node
m
-edge graph
G
and a positive integer
p
, the
p-th tree root problem
asks for a tree
T
, if any, such that
G
=
T
p
. Given a graph
G
, the
tree root problem
asks for a positive integer
p
and a tree
T
, if any, such that
G
=
T
p
. Kearney and Corneil gave the best previously known algorithms for both problems. Their algorithm for the former (respectively, latter) problem runs in
O
(
n
3
) (respectively,
O
(
n
4
)) time. In this paper, we give
O
(
n
+
m
)-time algorithms for both problems.