TITLE:
An Algorithm for the Feedback Vertex Set Problem on a Normal Helly Circular-Arc Graph
AUTHORS:
Hirotoshi Honma, Yoko Nakajima, Atsushi Sasaki
KEYWORDS:
Design and Analysis of Algorithms, Feedback Vertex Set, Normal Helly Circular-Arc Graphs, Intersection Graphs
JOURNAL NAME:
Journal of Computer and Communications,
Vol.4 No.8,
June
27,
2016
ABSTRACT: The feedback vertex set (FVS) problem is to
find the set of vertices of minimum cardinality whose removal renders the graph
acyclic. The FVS problem has applications in several areas such as
combinatorial circuit design, synchronous systems, computer systems, and
very-large-scale integration (VLSI) circuits. The FVS problem is known to be
NP-hard for simple graphs, but polynomi-al-time algorithms have been found for
special classes of graphs. The intersection graph of a collection of arcs on a
circle is called a circular-arc graph. A normal Helly circular-arc graph is a
proper subclass of the set of circular-arc graphs. In this paper, we present an
algorithm that takes time to solve the FVS problem in a normal Helly
circular-arc graph with n vertices and m edges.