Efficient Parallel Algorithms for some Tree Layout Problems

The minimum cut and minimum length linear arrangement problems usually occur in solving wiring problems and have a lot in common with job sequencing questions. Both problems are NP-complete for general graphs and in P for trees. We present here two algorithms in NC. The first solves the minimum length linear arrangement problem for unrooted trees in $O(\log^2 n)$ time and $O(n^2 3^{\log n})$ CREW PRAM processors. The second algorithm solves the minimum cut arrangement for unrooted trees of maximum degree $d$ in $O(d \log^2 n)$ time and $O(n^2 /\log n)$ CREW PRAM processors.