## Optimal Parallel Algorithms for Path Problems on Planar Graphs

- G. Srikrishna, C. Pandu Rangan
- Theor. Comput. Sci.
- 1995

@inproceedings{Khuller1989ProcessorEP, title={Processor Efficient Parallel Algorithms for the Two Disjoint Paths Problem, and for Finding a Kuratowski Homeomorph}, author={Samir Khuller and Stephen G. Mitchell and Vijay V. Vazirani}, booktitle={FOCS}, year={1989} }

- Published 1989 in FOCS
DOI:10.1109/SFCS.1989.63494

An important step in solvin the general problem is solving the planar case. A pofynomial time a1 orithm for this case was given by Per1 and Shiloach fPS 781. Shiloach [Sh 801 showed how to solve the non-planar case as follows: Find a Kuratowski homeomorphif it is a K3,3 homeomorph, then use it as a high connectivity “switch” to find the two disjoint paths; if it is a K5 homeomorph, use the algorithm of [Wa 68 . Independently, Seymour [Se 801 gave a polynomi a time algorithm for the decision… CONTINUE READING