Linear Time LexDFS on Cocomparability Graphs

Lexicographic depth first search (LexDFS) is a graph search protocol which has already proved to be a powerful tool on cocomparability graphs, a subfamily of perfect graphs. Cocomparability graphs have been well studied through their complements (comparability graphs) and their corresponding posets. Recently however LexDFS has led to a number of elegant near linear time algorithms on cocomparability graphs when used as a preprocessing step; therefore dispensing with the complement/poset computation of the graph. The nonlinearity of some of these results is a consequence of the preprocessing step. In this talk, we will present the first linear time algorithm to compute a LexDFS ordering of a cocomparability graph, therefore helping achieve linear time algorithms on this graph class. Additionally, if the input graph is a comparability graph, we also show how to slightly modify our algorithm to compute the desired ordering for the cocomparability graph in linear time.