It is known that the bandwidth problem is NP-complete for chordal bipartite graphs, while the problem can be solved in polynomial time for bipartite permutation graphs, which is a subclass of chordal bipartite graphs. This paper shows that the problem is NP-complete even for convex bipartite graphs, a subclass of chordal bipartite graphs and a superclass of bipartite permutation graphs. We provide an O(n)-time, 4-approximation algorithm and an O(n log~2 n)-time, 2-approximation algorithm for convex bipartite graphs with n vertices. For 2-directional orthogonal ray graphs, which is a subclass of chordal bipartite graphs and a superclass of convex bipartite graphs, we provide an O(n~2 log n)-time, 3-approximation algorithm, where n is the number of vertices.
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