Convex Recoloring Revisited: Complexity and Exact Algorithms

We take a new look at the convex path recoloring (CPR), convex tree recoloring (CTR), and convex leaf recoloring (CLR) problems through the eyes of the independent set problem. This connection allows us to give a complete characterization of the complexity of all these problems in terms of the number of occurrences of each color in the input instance, and consequently, to present simpler NP-hardness proofs for them than those given earlier. For example, we show that the CLR problem on instances in which the number of leaves of each color is at most 3, is solvable in polynomial time, by reducing it to the independent set problem on chordal graphs, and becomes NP-complete on instances in which the number of leaves of each color is at most 4. This connection also allows us to develop improved exact algorithms for the problems under consideration. For instance, we show that the CPR problem on instances in which the number of vertices of each color is at most 2, denoted 2-CPR, proved to be...

• Type: Conference
• Year: 2009
• Where: COCOON
• Authors: Iyad A. Kanj, Dieter Kratsch
• Keywords: COCOON 2009, Combinatorics, Exact Algorithms, Independent Set Problem, Polynomial Time