Listing All st-Orientations

See examples in Fig. 1(b). Many graph algorithms use an st-orientation. For instance, graph drawing algorithms [3], [4], [17], [19], [22], routing algorithms [1], [13] and partitioning algorithms [14]. Given a biconnected graph G and its two vertices s and t, one can find an st-orientation of G in O(m + n) time [5], [6], [22]. Note that if G is not biconnected then G may have no st-orientation. Generating all objects with some property without duplications has many applications, including unbiased statistical analysis [12]. A lot of algorithms to solve these problems are known [2], [11], [12], [15], [23]. See textbooks [8]– [10], [20], [21]. To solve these all-graph-generation problems some types of algorithms are known. Classical method algorithms [8] first generate all the graphs with a given property allowing duplications, but output each graph exactly once when the graph has generated for the first time. Thus this method requires quite a huge space to store a list of graphs that have already been output. Furthermore, checking whether each graph has already been output requires a lot of time. Orderly method algorithms [8] need not store the list,