The maximum linear arrangement problem for trees under projectivity and planarity

A linear arrangement is a mapping π from the n vertices of graph G to distinct consecutive integers. Linear arrangements can be represented by drawing along horizontal line and edges as semicircles above said line. In this setting, length an edge defined absolute value difference between positions its two in arrangement, cost sum all lengths. Here we study variants Maximum Arrangement problem (MaxLA), which consists finding that maximizes cost. planar variant for free trees, have arranged such way there are no crossings. projective rooted root tree cannot covered any edge. paper present algorithms time space solve MaxLA trees. We also prove several properties maximum arrangements, show caterpillar trees maximize over fixed size thereby generalizing previous extremal result on