Capacitated b-Edge Dominating Set and Related Problems
نویسندگان
چکیده
In this paper, we discuss the approximability of the capacitated b-edge dominating set problem, which generalizes the edge dominating set problem by introducing capacities and demands on the edges. We present an approximation algorithm for this problem and show that it achieves a factor of 8/3 for general graphs and a factor of 2 for bipartite graphs. Moreover, we discuss the relationships of the edge dominating set problem and the vertex cover problem. The results show, that improving the approximation factor beyond 8/3 using our approach of adding valid inequalities to a natural linear programming relaxation is as hard as improving the approximation factor for vertex cover beyond 2.
منابع مشابه
Technical Report TR - 2006 - 009 Capacitated b - Edge Dominating Set and Related Problems
In this paper, we discuss the approximability of the capacitated b-edge dominating set problem, which generalizes the edge dominating set problem by introducing capacities and demands on the edges. We present an approximation algorithm for this problem and show that it achieves a factor of 8/3 for general graphs and a factor of 2 for bipartite graphs. Moreover, we discuss the relationships of t...
متن کاملApproximability of the capacitated b-edge dominating set problem
In this paper, we discuss the approximability of the capacitated b-edge dominating set problem, which generalizes the edge dominating set problem by introducing capacities and demands on the edges. We present an approximation algorithm for this problem and show that it achieves a factor of 8/3 for general graphs and a factor of 2 for bipartite graphs. Moreover, we discuss the relationships of t...
متن کاملCapacitated Domination and Covering: A Parameterized Perspective
Capacitated versions of Vertex Cover and Dominating Set have been studied intensively in terms of polynomial time approximation algorithms. Although the problems Dominating Set and Vertex Cover have been subjected to considerable scrutiny in the parameterized complexity world, this is not true for their capacitated versions. Here we make an attempt to understand the behavior of the problems Cap...
متن کاملPlanar Capacitated Dominating Set Is W[1]-Hard
Given a graph G together with a capacity function c : V (G) → N, we call S ⊆ V (G) a capacitated dominating set if there exists a mapping f : (V (G) \ S) → S which maps every vertex in (V (G) \S) to one of its neighbors such that the total number of vertices mapped by f to any vertex v ∈ S does not exceed c(v). In the Planar Capacitated Dominating Set problem we are given a planar graph G, a ca...
متن کاملBeyond O*(2^n) in domination-type problems
In this paper we provide algorithms faster thanO(2) for several NP-complete dominationtype problems. More precisely, we provide: • an algorithm for CAPACITATED DOMINATING SET that solves it in O(1.89), • a branch-and-reducealgorithm solving LARGEST IRREDUNDANT SET inO(1.9657) time, • and a simple iterative-DFS algorithm for SMALLEST INCLUSION-MAXIMAL IRREDUNDANT SET that solves it in O(1.999956...
متن کامل