In this paper, we study the approximability and the computational complexity of the Maximum Happy Set problem (MaxHS for short) on graph classes: For an undirected graph \(G = (V, E)\) and a subset \(S\subseteq V\) of vertices, a vertex v is happy if v and all its neighbors are in S; otherwise unhappy. Given a graph G and an integer k, the goal of MaxHS is to find a subset S of k vertices such that the number of happy vertices is maximized. MaxHS is known to be NP-hard even for bipartite graphs and cubic (i.e., 3-regular) graphs. As for the approximability, it is known that there is a polynomial-time \((2\Delta +1)\) -approximation algorithm for MaxHS on graphs with maximum degree \(\Delta \) , and furthermore the approximation ratio can be improved to \(\Delta \) if \(\Delta \) is a constant. In this paper, we first design a polynomial-time 2-approximation algorithm for MaxHS on cubic graphs. We then design an exact algorithm for MaxHS on n-vertex convex bipartite graphs, which runs in \(O(n^2 + k^3 n)\) time.