@inbook {IOPORT.06102420, author = {Di Giacomo, Emilio and Didimo, Walter and Liotta, Giuseppe and Montecchiani, Fabrizio}, title = {$h$-quasi planar drawings of bounded treewidth graphs in linear area.}, year = {2012}, booktitle = {Graph-theoretic concepts in computer science. 38th international workshop, WG 2012, Jerusalem, Israel, June 26--28, 2012. Revised selcted papers}, isbn = {978-3-642-34610-1}, pages = {91-102}, publisher = {Berlin: Springer}, doi = {10.1007/978-3-642-34611-8_12}, abstract = {Summary: We study the problem of computing $h$-quasi planar drawings in linear area; in an $h$-quasi planar drawing the number of mutually crossing edges is at most $h - 1$. We prove that every $n$-vertex partial $k$-tree admits a straight-line $h$-quasi planar drawing in $O(n)$ area, where $h$ depends on $k$ but not on $n$. For specific sub-families of partial $k$-trees, we present ad-hoc algorithms that compute $h$-quasi planar drawings in linear area, such that $h$ is significantly reduced with respect to the general result. Finally, we compare the notion of $h$-quasi planarity with the notion of $h$-planarity, where each edge is allowed to be crossed at most $h$ times.}, identifier = {06102420}, }