Maximum weight independent set in trees

Abstract

Abstract.Computing a maximum independent set, weighted or unweighted, is NP-hard for general as well as planar graphs. However, polynomial time algorithms do exist for solving this problem on special classes of graphs. In this paper we present an efficient algorithm for computing a maximum weight independent set in trees. A divide and conquer approach based on centroid decomposition of trees is used to compute a maximum weight independent set within O(n log n) time, where n is the number of vertices in the tree. We introduce a notion of an aJternating tree which is crucial in obtaining a new independent set from the previous one.

Novel relay node placement algorithms for establishing connected topologies

“…The second step of the OTS-MST algorithm is to find the MWIS from TAG, which is also an NP-Hard problem. However, optimal solution can be found with dynamic programming (DP) if the graph is a tree [25]. The TAG, however, may contain cycles as seen in Figure 6(c).…”

“…After converting TAG to a tree by removing cycles, we can apply DP to find optimal MWIS as presented in [25]. Let G T (V T , E T ) be the triangular adjacency tree of Γ mst .…”