Journal ArticleDOI
Steiner trees, connected domination and strongly chordal graphs
Reads0
Chats0
TLDR
A polynomial algorithm and a min-max theorem for the cardinality Steiner problem in strongly chordal graphs and a polynometric algorithm for the weighted connected dominating set problem in series-parallel graphs are given.Abstract:
We consider Steiner tree problems and connected dominating set problems for several classes of graphs. We give a polynomial algorithm and a min-max theorem for the cardinality Steiner problem in strongly chordal graphs and a polynomial algorithm for the weighted connected dominating set problem in series-parallel graphs. We establish simple direct transformations between Steiner problems and connected domination problems for several classes of graphs and establish related NP-completeness results.read more
Citations
More filters
Journal ArticleDOI
The NP-completeness column: An ongoing guide
TL;DR: This is the fourteenth edition of a quarterly column that provides continuing coverage of new developments in the theory of NP-completeness, and readers who have results they would like mentioned (NP-hardness, PSPACE- hardness, polynomialtime-solvability, etc.), or open problems they wouldlike publicized, should send them to David S. Johnson.
Journal ArticleDOI
Steiner problem in networks: a survey
TL;DR: The problem of determining a minimum cost connected network G that spans a given subset of vertices is known in the literature as the Steiner problem in networks and exact algorithms and heuristics are surveyed.
Journal ArticleDOI
Approximation Algorithms for Connected Dominating Sets
Sudipto Guha,Samir Khuller +1 more
TL;DR: In this paper, a polynomial time algorithm with a (c+1) H(Δ) +c-1 approximation factor was proposed, where c is the Steiner approximation ratio.
Journal ArticleDOI
Steiner tree problems
Frank K. Hwang,Dana Richards +1 more
TL;DR: A survey up to 1989 on the Steiner tree problems which include the four important cases of euclidean, rectilinear, graphic, phylogenetic and some of their generalizations.
Book ChapterDOI
Approximation Algorithms for Connected Dominating Sets
Sudipto Guha,Samir Khuller +1 more
TL;DR: This work focuses on the question of finding a connected dominating set of minimum size, where the graph induced by vertices in the dominating set is required to be connected.
References
More filters
Reducibility Among Combinatorial Problems.
TL;DR: Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
Journal ArticleDOI
The Rectilinear Steiner Tree Problem is $NP$-Complete
TL;DR: The problem of determining the minimum length of an optimum rectilinear Steiner tree for a set A of points in the plane is shown to be NP-complete and the emphasis of the literature on heuristics and special case algorithms is well justified.
Journal ArticleDOI
Topology of series-parallel networks
TL;DR: The series-parallel connection is a simple type of electric network termed a series parallel connection which occurs frequently in both theoretical and applied electrical engineering as mentioned in this paper, where the joint resistance is easily evaluated by the following two rules due to Ohm: 0 s.
Journal ArticleDOI
Triangulated graphs and the elimination process
TL;DR: In this paper, a triangulated graph is defined as a graph in which for every cycle of length l > 3, there is an edge joining two nonconsecutive vertices.