Fig. 2

A diagram of a graph containing two embedded threads. The graph consists of nodes with sides \(\{1, 2, 3, \ldots , 10\}\), connected by edges {2, 5}, {4, 5}, {6, 7}, {6, 9}, {8, 8}, and {10, 9}. Note that, once again, odd numbers are used for left sides and even numbers are used for right sides. As in Fig. 1, nodes are represented by rectangles, and thread orientations running from node to node are represented by dashed lines. The actual edges connecting the nodes are omitted for clarity; only the thread orientations are shown. Because each side’s B[] array defines a separate permutation, each node is divided into two parts by a central double yellow line (like on a road). The top half of each node shows visits to the node’s right side, while the bottom half shows visits to the node’s left side. Within the appropriate half of each node, the B[] array entries for the entry side are shown. The special 0 value is used to indicate that a thread stops and does not continue on to another node. When moving from the entry side to the exit side of a node, threads cross over each other so that they become sorted, stably, by the side of their next visit. Threads’ order of arrival at a node is determined by the relative order of the edges incident on the side they arrive at, which is in turn determined by the ordering of the sides on the other ends of the edges. The threads shown here are [1, 2, 5, 6, 9, 10, 9, 10] and [3, 4, 5, 6, 7, 8, 8, 7]. See Table 1 for a tabular representation of this example.