The article explores how to organize a graph's vertices on a line to minimize the total sum of the right ends of edges. By focusing on graphs with few cycles, the researchers found that placing dense subgraphs early can help finish edges quickly. They compared the objective function to a scenario where each vertex is the right end of one edge, revealing deviations described as "charges" that can form "dipoles". This approach led to the development of polynomial algorithms and NP-completeness results for specific cases, as well as FPT results.