The topo-geometric detour router is an autorouter intended for single layer or multi layer printed circuit boards with variable network widths and clearances.
The algorithm presented in this paper is neither a pure topological autorouter nor a pure geometric autorouter: it is a combination. It uses topology to make high level decisions about the structure of solution but uses geometry after each decision to ensure routability of the board. On the topology side the main idea is to do a path search on a tree of decisions instead of doing the search in geometric space. In turn this reduces the geometric problem to find the two possible detour path around an obstacle.
While the two aspects of the routing, topology and geometry, are running in parallel, they are independent in the sense that the algorithm for each aspect can be replaced without affecting the other aspect.