2 research outputs found
Algorithms for the minimum non-separating path and the balanced connected bipartition problems on grid graphs (With erratum)
For given a pair of nodes in a graph, the minimum non-separating path problem
looks for a minimum weight path between the two nodes such that the remaining
graph after removing the path is still connected. The balanced connected
bipartition (BCP) problem looks for a way to bipartition a graph into two
connected subgraphs with their weights as equal as possible. In this paper we
present an algorithm in time for finding a minimum weight
non-separating path between two given nodes in a grid graph of nodes with
positive weight. This result leads to a 5/4-approximation algorithm for the
BCP problem on grid graphs, which is the currently best ratio achieved in
polynomial time. We also developed an exact algorithm for the BCP problem
on grid graphs. Based on the exact algorithm and a rounding technique, we show
an approximation scheme, which is a fully polynomial time approximation scheme
for fixed number of rows.Comment: With erratu