Minimum Linear Arrangement of Series-Parallel Graphs

We present a factor 14D approximation algorithm for the minimum linear arrangement problem on series-parallel graphs, where D is the maximum degree in the graph. Given a suitable decomposition of the graph, our algorithm runs in time O(|E|) and is very easy to implement. Its divide-andconquer approach allows for an effective parallelization. Note that a suitable decomposition can also be computed in time O(|E| log |E|) (or even O(log |E| log∗ |E|) on an EREW PRAM using O(|E|) processors). For the proof of the approximation ratio, we use a sophisticated charging method that uses techniques similar to amortized analysis in advanced data structures. On general graphs, the minimum linear arrangement problem is known to be NP-hard. To the best of our knowledge, the minimum linear arrangement problem on series-parallel graphs has not been studied before. ∗This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Center “On-The-Fly Computing” (SFB 901). ar X iv :1 41 0. 43 95 v1 [ cs .D M ] 1 6 O ct 2 01 4