The maximum independent set problem on layered graphs

The independent set on a graph G = (V, E) is a subset of V such that no two vertices in the subset have an edge between them. The maximum independent set problem on G seeks to identify an independent set with maximum cardinality, i.e. maximum independent set or MIS. The maximum independent set problem on a general graph is known to be NP-complete. On certain classes of graphs MIS can be computed in polynomial time. Such algorithms are known for bipartite graphs, chordal graphs, cycle graphs, comparability graphs, claw-free graphs, interval graphs and circular arc graphs. On trees, the weighted version of this problem can be solved in linear time. In this article we introduce a new type of graph called a layered graph and show that if the number of vertices in a layer is O(log | V |) then the maximum independent set can be computed in