A Fast Multigrid Algorithm for Energy Minimization Under Planar Density Constraints

TL;DR

This paper introduces a linear time multigrid algorithm designed for efficient energy minimization in 2D layout optimization problems with density constraints, applicable to graph visualization tasks.

Contribution

The paper presents a novel linear time multigrid method for solving nonlinear layout optimization problems with density constraints, improving computational efficiency.

Findings

Algorithm demonstrates linear time complexity.

Effective in various graph drawing applications.

Improves space utilization in layout optimization.

Abstract

The two-dimensional layout optimization problem reinforced by the efficient space utilization demand has a wide spectrum of practical applications. Formulating the problem as a nonlinear minimization problem under planar equality and/or inequality density constraints, we present a linear time multigrid algorithm for solving correction to this problem. The method is demonstrated on various graph drawing (visualization) instances.