Parameterized Complexity of Independence and Domination on Geometric Graphs
نویسنده
چکیده
We investigate the parameterized complexity of Maximum Independent Set and Dominating Set restricted to certain geometric graphs. We show that Dominating Set is W[1]-hard for the intersection graphs of unit squares, unit disks, and line segments. For Maximum Independent Set, we show that the problem is W[1]-complete for unit segments, but fixed-parameter tractable if the segments are axis-parallel.
منابع مشابه
Complexity and approximation ratio of semitotal domination in graphs
A set $S subseteq V(G)$ is a semitotal dominating set of a graph $G$ if it is a dominating set of $G$ andevery vertex in $S$ is within distance 2 of another vertex of $S$. Thesemitotal domination number $gamma_{t2}(G)$ is the minimumcardinality of a semitotal dominating set of $G$.We show that the semitotal domination problem isAPX-complete for bounded-degree graphs, and the semitotal dominatio...
متن کاملCoverings, matchings and paired domination in fuzzy graphs using strong arcs
The concepts of covering and matching in fuzzy graphs using strong arcs are introduced and obtained the relationship between them analogous to Gallai’s results in graphs. The notion of paired domination in fuzzy graphs using strong arcs is also studied. The strong paired domination number γspr of complete fuzzy graph and complete bipartite fuzzy graph is determined and obtained bounds for the s...
متن کاملROMAN DOMINATION: A Parameterized Perspective
We analyze the graph-theoretic formalization of Roman domination, dating back to the military strategy of Emperor Constantine, from a parameterized perspective. More specifically, we prove that this problem is W[2]-complete for general graphs. However, parameterized algorithms are presented for graphs of bounded treewidth and for planar graphs. Moreover, it is shown that a parametric dual of Ro...
متن کاملA General Data Reduction Scheme for Domination in Graphs
Data reduction by polynomial-time preprocessing is a core concept of (parameterized) complexity analysis in solving NP-hard problems. Its practical usefulness is confirmed by experimental work. Here, generalizing and extending previous work, we present a set of data reduction preprocessing rules on the way to compute optimal dominating sets in graphs. In this way, we arrive at the novel notion ...
متن کاملk-Efficient partitions of graphs
A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...
متن کامل