Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Approximating the maximally balanced connected partition problem in graphs
Information Processing Letters
Journal of the ACM (JACM)
Graph Connectivity After Path Removal
Combinatorica
A weaker version of Lovász' path removal conjecture
Journal of Combinatorial Theory Series B
Lowest common ancestors in trees and directed acyclic graphs
Journal of Algorithms
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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 (BCP2) 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 O(NlogN) for finding a minimum weight non-separating path between two given nodes in a grid graph of N nodes with positive weight. This result leads to a 5/4-approximation algorithm for the BCP2 problem on grid graphs, which is the currently best ratio achieved in polynomial time. We also developed an exact algorithm for the BCP2 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.