15,043 research outputs found
A Branch-and-Reduce Algorithm for Finding a Minimum Independent Dominating Set
An independent dominating set D of a graph G = (V,E) is a subset of vertices
such that every vertex in V \ D has at least one neighbor in D and D is an
independent set, i.e. no two vertices of D are adjacent in G. Finding a minimum
independent dominating set in a graph is an NP-hard problem. Whereas it is hard
to cope with this problem using parameterized and approximation algorithms,
there is a simple exact O(1.4423^n)-time algorithm solving the problem by
enumerating all maximal independent sets. In this paper we improve the latter
result, providing the first non trivial algorithm computing a minimum
independent dominating set of a graph in time O(1.3569^n). Furthermore, we give
a lower bound of \Omega(1.3247^n) on the worst-case running time of this
algorithm, showing that the running time analysis is almost tight.Comment: Full version. A preliminary version appeared in the proceedings of WG
200
Fast algorithms for min independent dominating set
We first devise a branching algorithm that computes a minimum independent
dominating set on any graph with running time O*(2^0.424n) and polynomial
space. This improves the O*(2^0.441n) result by (S. Gaspers and M. Liedloff, A
branch-and-reduce algorithm for finding a minimum independent dominating set in
graphs, Proc. WG'06). We then show that, for every r>3, it is possible to
compute an r-((r-1)/r)log_2(r)-approximate solution for min independent
dominating set within time O*(2^(nlog_2(r)/r))
(Total) Vector Domination for Graphs with Bounded Branchwidth
Given a graph of order and an -dimensional non-negative
vector , called demand vector, the vector domination
(resp., total vector domination) is the problem of finding a minimum
such that every vertex in (resp., in ) has
at least neighbors in . The (total) vector domination is a
generalization of many dominating set type problems, e.g., the dominating set
problem, the -tuple dominating set problem (this is different from the
solution size), and so on, and its approximability and inapproximability have
been studied under this general framework. In this paper, we show that a
(total) vector domination of graphs with bounded branchwidth can be solved in
polynomial time. This implies that the problem is polynomially solvable also
for graphs with bounded treewidth. Consequently, the (total) vector domination
problem for a planar graph is subexponential fixed-parameter tractable with
respectto , where is the size of solution.Comment: 16 page
- …