3 research outputs found
Tree Drawings Revisited
We make progress on a number of open problems concerning the area requirement for drawing trees on a grid. We prove that
1) every tree of size n (with arbitrarily large degree) has a straight-line drawing with area n2^{O(sqrt{log log n log log log n})}, improving the longstanding O(n log n) bound;
2) every tree of size n (with arbitrarily large degree) has a straight-line upward drawing with area n sqrt{log n}(log log n)^{O(1)}, improving the longstanding O(n log n) bound;
3) every binary tree of size n has a straight-line orthogonal drawing with area n2^{O(log^*n)}, improving the previous O(n log log n) bound by Shin, Kim, and Chwa (1996) and Chan, Goodrich, Kosaraju, and Tamassia (1996);
4) every binary tree of size n has a straight-line order-preserving drawing with area n2^{O(log^*n)}, improving the previous O(n log log n) bound by Garg and Rusu (2003);
5) every binary tree of size n has a straight-line orthogonal order-preserving drawing with area n2^{O(sqrt{log n})}, improving the O(n^{3/2}) previous bound by Frati (2007)