Abstract: We consider the problem of placing labels of the points
on a plane. For each point, its position, the size of its label and a
priority are given. Moreover, several candidates of its label positions
are prespecified, and each of such label positions is assigned a
priority. The objective of our problem is to maximize the total sum
of priorities of placed labels and their points. By refining a labeling
algorithm that can use these priorities, we propose a new heuristic
algorithm which is more suitable for treating the assigned priorities.
Abstract: Some fast exact algorithms for the maximum weight clique problem have been proposed. Östergard’s algorithm is one of them. Kumlander says his algorithm is faster than it. But we confirmed that the straightforwardly implemented Kumlander’s algorithm is slower than O¨ sterga˚rd’s algorithm. We propose some improvements on Kumlander’s algorithm.