Divide-and-conquer algorithms for graph-layout problems

Tutte introduced a decomposition of 2-connected graphs which has widely been used in solving various graph-theoretic problems. In this paper, we extend it to a class of graph-layout problems, namely, determining the bandwidth, cutwidth, and pagenumber of graphs. In particular, we present linear-time algorithms for testing and, if so, constructing linear layouts of 2-edge-connected bandwidth-2 and cut-width-3 graphs. We also present a simple linear-time algorithm for embedding series-parallel graphs in two pages. The interesting feature of these algorithms is that they use a divide-and-conquer paradigm with Tutte decomposition of 2-connected graphs as a common framework; thus, they are different from the previously known algorithms. Moreover, since Tutte decomposition can be computed efficiently in parallel, all three proposed algorithms parallelize naturally.