TY - GEN

T1 - Bisections Above Tight Lower Bounds

AU - Mnich, Matthias

AU - Zenklusen, Rico

PY - 2012

Y1 - 2012

N2 - A bisection of a graph is a bipartition of its vertex set in which the number of vertices in the two parts differ by at most one, and the size of the bisection is the number of edges which go across the two parts.every graph with m edges has a bisection of size at least ?m/2 ?, and this bound is sharp for infinitely many graphs. Therefore, gutin and yeo considered the parameterized complexity of deciding whether an input graph with m edges has a bisection of size at least ?m/2 ? + k, where k is the parameter. They showed fixed-parameter tractability of this problem, and gave a kernel with o(k 2) vertices.here, we improve the kernel size to o(k) vertices. Under the exponential time hypothesis, this result is best possible up to constant factors.

AB - A bisection of a graph is a bipartition of its vertex set in which the number of vertices in the two parts differ by at most one, and the size of the bisection is the number of edges which go across the two parts.every graph with m edges has a bisection of size at least ?m/2 ?, and this bound is sharp for infinitely many graphs. Therefore, gutin and yeo considered the parameterized complexity of deciding whether an input graph with m edges has a bisection of size at least ?m/2 ? + k, where k is the parameter. They showed fixed-parameter tractability of this problem, and gave a kernel with o(k 2) vertices.here, we improve the kernel size to o(k) vertices. Under the exponential time hypothesis, this result is best possible up to constant factors.

U2 - 10.1007/978-3-642-34611-8_20

DO - 10.1007/978-3-642-34611-8_20

M3 - Conference article in proceeding

T3 - Lecture Notes in Computer Science

SP - 184

EP - 193

BT - Graph-Theoretic Concepts in Computer Science

PB - Springer

ER -