An efficient algorithm for Mixed domination on Generalized Series-Parallel Graphs

An Efficient Algorithm for Mixed Domination on Generalized Series-Parallel Graphs

A mixed dominating set S of a graph G = (V,E) is a subset S ⊆ V ∪ E such that each element v ∈ (V ∪ E) \ S is adjacent or incident to at least one element in S. The mixed domination number γm(G) of a graph G is the minimum cardinality among all mixed dominating sets in G. The problem of finding γm(G) is know to be NP-complete. In this paper, we present an explicit polynomial-time algorithm to c...

Mixed Domination in Trees: A Parallel Algorithm

A set of vertices S in a graph G = (V;E) is called a dominating set of G if every vertex in the set (V n S) is adjacent to some vertex in S. For arbitrary graphs, the problem of computing smallest dominating set is NP-complete [3]. A slightly more general version of this problem is called \mixed domination" problem [1]. In this paper we present new parallel NC algorithm to nd smallest mixed dom...

Parallel Decomposition of Generalized Series-Parallel Graphs

Received July 17, 1997; accepted May 1, 1998. Communicated by Wen-Lian Hsu. *A preliminary version of this paper appeared in the proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA’97) Las Vegas, Nevada, pp. 890-896, 1997. Research supported in part by NSC under Grant 83-0408-E-008-004. JOURNAL OF INFORMATION SCIENCE AND ENGINEER...

Space Efficient Algorithms for Series-Parallel Graphs

The subclass of directed series-parallel graphs plays an important role in computer science. To determine whether a graph is series-parallel is a well studied problem in algorithmic graph theory. Fast sequential and parallel algorithms for this problem have been developed in a sequence of papers. For series-parallel graphs methods are also known to solve the reachability and the decomposition p...

Circuit Covers in Series-Parallel Mixed Graphs