Advertisement
Published in:
2009 | OriginalPaper | Chapter
Covering a Tree by a Forest
Authors : Fanica Gavril, Alon Itai
Published in: Graph Theory, Computational Intelligence and Thought
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
Consider a tree
T
and a forest
F
. The paper discusses the following new problems: The
Forest vertex-cover problem (FVC)
: cover the vertices of
T
by a minimum number of copies of trees of
F
, such that every vertex of
T
is covered exactly once. The
Forest edge-cover problem (FEC)
: cover the edges of
T
by a minimum number of copies of trees of
F
, such that every edge of
T
is covered exactly once. For a solution to always exist, we assume that
F
contains a one vertex (one edge) tree.
Two versions of Problem FVC are considered: ordered covers (OFVC), and unordered covers (UFVC). Three versions of Problem FEC are considered: ordered covers (OFEC), unordered covers (UFEC) and consecutive covers (CFEC). We describe polynomial time algorithms for Problems OFVC, UFVC and CFEC, and prove that Problems OFEC and UFEC are NP-complete.