Graphs are fundamental in computer science, but often challenging to visualize clearly. This thesis addresses the problem of improving the clarity of a specific type of constrained graph using simulated annealing and other techniques while considering time constraints, as the solution is intended for use in interactive software. Various approaches are explored and compared, resulting in a fully implemented algorithm. A key challenge was optimizing the algorithm for efficiency to ensure responsiveness for users, and this thesis discusses the solutions developed to achieve that goal. The implementation is analyzed and discussed in detail, assessing its effectiveness in improving graph clarity under specific constraints. The emphasis is on practical implementation rather than deep theoretical analysis, providing insights into real-world applications and performance optimization.