Computer Science – Data Structures and Algorithms
Scientific paper
2010-05-17
Computer Science
Data Structures and Algorithms
Scientific paper
In a graph $G=(V,E)$, a bisection $(X,Y)$ is a partition of $V$ into sets $X$ and $Y$ such that $|X|\le |Y|\le |X|+1$. The size of $(X,Y)$ is the number of edges between $X$ and $Y$. In the Max Bisection problem we are given a graph $G=(V,E)$ and are required to find a bisection of maximum size. It is not hard to see that $\lceil |E|/2 \rceil$ is a tight lower bound on the maximum size of a bisection of $G$. We study parameterized complexity of the following parameterized problem called Max Bisection above Tight Lower Bound (Max-Bisec-ATLB): decide whether a graph $G=(V,E)$ has a bisection of size at least $\lceil |E|/2 \rceil+k,$ where $k$ is the parameter. We show that this parameterized problem has a kernel with $O(k^2)$ vertices and $O(k^3)$ edges, i.e., every instance of Max-Bisec-ATLB is equivalent to an instance of Max-Bisec-ATLB on a graph with at most $O(k^2)$ vertices and $O(k^3)$ edges.
Gutin Gregory
Yeo Anders
No associations
LandOfFree
Note on Maximal Bisection above Tight Lower Bound 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 Note on Maximal Bisection above Tight Lower Bound, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Note on Maximal Bisection above Tight Lower Bound will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-297918