Incremental algorithms for the maximum internal spanning tree problem

The maximum internal spanning tree (MIST) problem is utilized to determine a in graph G, with the number of possible vertices. incremental (IMIST) version MIST whose feasible solutions are edge-sequences e1, e2, …, en−1 such that first k edges form trees for all ∈ [n − 1]. A solution’s quality measured using $${\text{max}_{k \in - 1]}}\frac{{\text{opt}(G,k)}}{{\left| {\text{In}({T_k})} \right|}}$$ lower being better. Here, opt(G, k) denotes vertices which has largest vertices, and ∣In(Tk)∣ comprising edges. We obtained an IMIST algorithm competitive ratio 2, followed by 12/7-competitive based on approximation MIST.