Abstract
In this paper we consider the minimum feedback vertex set problem in graphs, i.e., the problem of finding a minimal cardinality subset of the vertices, whose removal makes a graph acyclic. The problem is \({\cal NP}\)-hard for general topologies, but optimal and near-optimal solutions have been provided for particular networks. We improve the upper bounds of [11] both for the two-dimensional mesh of trees, and for the pyramid networks. We also present upper and lower bounds for other topologies: the higher-dimensional meshes of trees, and the trees of meshes networks. For the two-dimensional meshes of trees the results are optimal; for the higher-dimensional meshes of trees and the tree of meshes the results are asymptotically optimal. For the pyramid networks, the presented upper bound almost matches the lower bound of [11].
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call