An efficient algorithm for label updating in 2PM model to avoid a moving object

In this paper, we present a simple and fast algorithm for updating labels of a set of points in presence of a moving point-shaped object. The labels are assumed to be axis parallel, unit length, square shaped, each attached exclusively to a point on one of its horizontal (vertical) edges, denoted by 2PM model. The updated labeling should include all labels, avoid the moving point with largest possible label length. We allow flip and resize operations on labels for updating a labeling. The known algorithm for this problem, where labels may be attached to their corresponding points on the middle of any edges, the 4PM model, uses O(n2) preprocessing time and O(n) space to update the labeling in O(lg n + k) time, where k is the number of update operations (Rostamabadi and Ghodsi, CCCG’04). In this paper, we present a simpler and more efficient algorithm that uses O(n lg n) time and O(n) space for preprocessing with simplified data structures and updates the labeling with the same time bound.

An Efficient Algorithm for Label Updating in 2PM Model to Avoid a Moving Object

In this paper, we present a simple and fast algorithm for updating labels of a set of points in presence of a moving point-shaped object. The labels are assumed to be axis parallel, unit length, square shaped, each attached exclusively to a point on one of its horizontal (vertical) edges, denoted by 2PM model. The updated labeling should include all labels, avoid the moving point with largest possible label length. We allow flip and resize operations on labels for updating a labeling. The known algorithm for this problem, where labels may be attached to their corresponding points on the middle of any edges, the 4PM model, uses O(n 2) preprocessing time and O(n) space to update the labeling in O(lg n + k) time, where k is the number of update operations (Rostamabadi and Ghodsi, CCCG’04). In this paper, we present a simpler and more efficient algorithm that uses O(n lg n) time and O(n) space for preprocessing with simplified data structures and updates the labeling with the same time bound.