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We consider the problem of constructing a bipartite graph whose degrees liein prescribed intervals. Necessary and sufficient conditions for the existenceof such graphs are well-known. However, existing realization algorithms sufferfrom large running times. In this paper, we present a realization algorithmthat constructs an appropriate bipartite graph G=(U,V,E) in O(|U| + |V| + |E|)time, which is asymptotically optimal. In addition, we show that our algorithmproduces edge-minimal bipartite graphs and that it can easily be modified toconstruct edge-maximal graphs.

An Optimal Realization Algorithm for Bipartite Graphs with Degrees in Prescribed Intervals