The effect of girth on the kernelization complexity of Connected Dominating Set

In the Connected Dominating Set problem we are given as input a graph G and a positive integer k, and are asked if there is a set S of at most k vertices of G such that S is a dominating set of G and the subgraph induced by S is connected. This is a basic connectivity problem that is known to be NP-complete, and it has been extensively studied using several algorithmic approaches. In this paper we study the effect of excluding short cycles, as a subgraph, on the kernelization complexity of Connected Dominating Set. Kernelization algorithms are polynomial-time algorithms that take an input and a positive integer k (the parameter) and output an equivalent instance where the size of the new instance and the new parameter are both bounded by some function g(k). The new instance is called a g(k) kernel for the problem. If g(k) is a polynomial in k then we say that the problem admits polynomial kernels. The girth of a graph G is the length of a shortest cycle in G. It turns out that Connect...

• Type: Journal
• Year: 2010
• Where: FSTTCS
• Authors: Neeldhara Misra, Geevarghese Philip, Venkatesh Raman, Saket Saurabh
• Keywords: Connected Dominating Set, Dominating Set, FSTTCS 2010, Positive Integer, Software Engineering