A Generalization of Nemhauser and Trotter's Local Optimization Theorem

Details A Generalization of Nemhauser and Trotter's Local Optimization Theorem A Generalization of Nemhauser and Trotter's Local Optimization Theorem

2009-02-12

arxiv.org/abs/0902.2149v1

26th International Symposium on Theoretical Aspects of Computer Science STACS 2009 (2009) 409-420

Computer Science

Computational Complexity

Scientific paper

The Nemhauser-Trotter local optimization theorem applies to the NP-hard Vertex Cover problem and has applications in approximation as well as parameterized algorithmics. We present a framework that generalizes Nemhauser and Trotter's result to vertex deletion and graph packing problems, introducing novel algorithmic strategies based on purely combinatorial arguments (not referring to linear programming as the Nemhauser-Trotter result originally did). We exhibit our framework using a generalization of Vertex Cover, called Bounded- Degree Deletion, that has promise to become an important tool in the analysis of gene and other biological networks. For some fixed d \geq 0, Bounded-Degree Deletion asks to delete as few vertices as possible from a graph in order to transform it into a graph with maximum vertex degree at most d. Vertex Cover is the special case of d = 0. Our generalization of the Nemhauser-Trotter theorem implies that Bounded-Degree Deletion has a problem kernel with a linear number of vertices for every constant d. We also outline an application of our extremal combinatorial approach to the problem of packing stars with a bounded number of leaves. Finally, charting the border between (parameterized) tractability and intractability for Bounded-Degree Deletion, we provide a W[2]-hardness result for Bounded-Degree Deletion in case of unbounded d-values.

Affiliated with

Also associated with

No associations

Rating

A Generalization of Nemhauser and Trotter's Local Optimization Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Generalization of Nemhauser and Trotter's Local Optimization Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Generalization of Nemhauser and Trotter's Local Optimization Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-556731