1.5-Approximation for Treewidth of Graphs Excluding a Graph with One Crossing as a Minor
نویسندگان
چکیده
We give polynomial-time constant-factor approximation algorithms for the treewidth and branchwidth of any H-minor-free graph for a given graph H with crossing number at most 1. The approximation factors are 1.5 for treewidth and 2.25 for branchwidth. In particular, our result directly applies to classes of nonplanar graphs such as K5-minorfree graphs and K3,3-minor-free graphs. Along the way, we present a polynomial-time algorithm to decompose H-minor-free graphs into planar graphs and graphs of treewidth at most cH (a constant dependent on H) using clique sums. This result has several applications in designing fully polynomial-time approximation schemes and fixed-parameter algorithms for many NP-complete problems on these graphs.
منابع مشابه
-Approximation for Treewidth of Graphs Excluding a Graph with One Crossing as a Minor
We give polynomial-time constant-factor approximation algorithms for the treewidth and branchwidth of any H-minor-free graph for a given graph H with crossing number at most 1. The approximation factors are 1.5 for treewidth and 2.25 for branchwidth. In particular, our result directly applies to classes of nonplanar graphs such as K5-minorfree graphs and K3,3-minor-free graphs. Along the way, w...
متن کاملApproximation algorithms for classes of graphs excluding single-crossing graphs as minors
Many problems that are intractable for general graphs allow polynomial-time solutions for structured classes of graphs, such as planar graphs and graphs of bounded treewidth. In this paper, we demonstrate structural properties of larger classes of graphs and show how to exploit the properties to obtain algorithms. The classes considered are those formed by excluding as a minor a graph that can ...
متن کاملFast approximation schemes for K minor free or K minor free graphs
As the class of graphs of bounded treewidth is of limited size we need to solve NP hard problems for wider classes of graphs than this class Eppstein introduced a new concept which can be considered as a generalization of bounded treewidth A graph G has locally bounded treewidth if for each vertex v of G the treewidth of the subgraph of G induced on all vertices of distance at most r from v is ...
متن کاملFast approximation schemes for K3, 3-minor-free or K5-minor-free graphs
As the class of graphs of bounded treewidth is of limited size, we need to solve NP-hard problems for wider classes of graphs than this class. Eppstein introduced a new concept which can be considered as a generalization of bounded treewidth. A graph G has locally bounded treewidth if for each vertex v of G, the treewidth of the subgraph of G induced on all vertices of distance at most r from v...
متن کاملBidimensional Parameters and Local Treewidth
For several graph theoretic parameters such as vertex cover and dominating set, it is known that if their values are bounded by k then the treewidth of the graph is bounded by some function of k. This fact is used as the main tool for the design of several fixed-parameter algorithms on minor-closed graph classes such as planar graphs, single-crossing-minor-free graphs, and graphs of bounded gen...
متن کامل