In the paper, we describe a polynomial time algorithm that, for every input graph, either
outputs the minimum bisection of the graph or halts without output. More importantly, we …

In the classic Minimum Bisection problem we are given as input a graph G and an integer k.
The task is to determine whether there is a partition of V (G) into two parts A and B such that …

We describe a new, linear time heuristic for the improvement of graph bisections. The
method is a variant of local search with sophisticated neighborhood relations. It is based on …

A bisection of a graph with n vertices is a partition of its vertices into two sets, each of size
n/2. The bisection cost is the number of edges connecting the two sets. It is known that …

We resolve in the affirmative a question of RB Boppana and T. Bui: whether simulated
annealing can with high probability and in polynomial time, find the optimal bisection of a …

The NP‐hard graph bisection problem is to partition the nodes of an undirected graph into
two equal‐sized groups so as to minimize the number of edges that cross the partition. The …

We resolve in the affirmative a question of Boppana and Bui: whether simulated annealing
can, with high probability and in polynomial time, find the optimal bisection of a random …

In this paper, we compare the performance of two popular graph bisection algorithms. We
also present an empirical study of a new heuristic, first proposed in [B87], that dramatically …

We study the problem of finding the minimum bisection of a graph into two parts of
prescribed sizes. We formulate two lower bounds on the problem by relaxing node-and …

Many divide-and-conquer algorithms on graphs are based on finding a small set of vertices
or edges whose removal divides the graph roughly in half. Most graphs do not have the …