Computing the metric dimension for chain graphs

• We show how to compute the metric dimension of bipartite chain graphs.
• Our algorithm works in linear time even on compact representations.
• We also conclude combinatorial results for simple chain graphs.
• Our order-theoretic arguments may be useful for other problems, as well.
• We indicate this for some variants of metric dimension.

The metric dimension of a graph G is the smallest size of a set R of vertices that can distinguish each vertex pair of G by the shortest-path distance to some vertex in R. Computing the metric dimension is NP-hard, even when restricting inputs to bipartite graphs. We present a linear-time algorithm for computing the metric dimension for chain graphs, which are bipartite graphs whose vertices can be ordered by neighborhood inclusion.