### Table 1. Output of k-shortest paths computation for k=3 Shortest path Total weight Path

"... In PAGE 2: ... If the directed graph in Fig. 1 is taken as an input, the output of the k-shortest path computation is listed in Table1 . In this table, as an example, the parameter of k is 4, meaning that the output of the computation consists of the first shortest path, the second shortest path, the third shortest path, and the fourth shortest path.... In PAGE 3: ... DNA sequence design and synthesis Consider a directed graph and the output of the shortest path computation as shown in Fig. 1 and Table1 respectively. Let n be the total number of nodes in the graph.... ..."

### Table 3 Performance of Shortest Path Search

"... In PAGE 2: ... This allows us to test if a general link classification model could be obtained to apply to unseen Websites. We build different versions of weighted directed graphs using each of the three types of classifiers and compare the performances of the algorithms on the different graphs Table3 and 4. As can be seen from the results, the SPS and DMST algorithms using weighted graph models outperform the simple BFS significantly.... ..."

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### Table 1: Output of the k-shortest path computation, for N = 4

"... In PAGE 2: ... In this graph, the vertex V1 is assigned as a source point whereas the vertex V5 is assigned as a destination point. If the directed graph in Figure 1 is taken as an input, the output of the k-shortest path computation is listed in Table1 . In this table, as an example, the parameter of k is 4, meaning that the output of the computation consists of the first, second, third, and fourth shortest path.... ..."

### Table 2. Shortest Path Table

"... In PAGE 5: ... 3. Graph representation for function (6) Table2 summarizes the SP of this graph. NP, NN, SSP, and MNNAP are summarized in Table 3.... ..."

### Table 1 Comple xity results on characterization of shortest-path IRSs

"... In PAGE 3: ... A summary of these and other results can be found in [9]. For general graphs, existing comple xity results for the weighted/unweighted models and various IRS variants are summarized in Table1 , where an entry for any of the single-path IRS or global compactness refers to both the strict and non-strict versions of the problem; an entry for the all-shortest-path IRS of edge compactness refers to both the linear and non-linear versions of the problem; NPC denotes an NP-complete problem. All the problems related to single-shortest-path IRS are known to be NP-complete.... ..."

### Table 3. Generated paths and each path costs k-shortest path method The proposed method Paths

"... In PAGE 9: ... from the k-shortest algorithm are concentrated, but the paths from the proposed method are scattered over the whole network. Table3 summarizes the values of path cost and links on the path. The first two paths have the same values of path costs for all method, but the rest three path costs of the proposed algorithm are higher than those of k-shortest path one because it generates the paths in order of degree of path overlap, not in order of path costs.... In PAGE 10: ... prohibitions at node 11, node 14 and node 23 exist, with the value of 50% of path overlap. Table 4 demonstrates that five dissimilar paths are also generated, and that last 2 paths are different from those of paths in Table3 due to turning restrictions. We note here that the 5th path has U-turn movement at node 24 because of left-turn prohibition at node 23.... ..."

### Table 8: Average Shortest Path for the wordnets

2007

"... In PAGE 37: ... Further, the shortest lengths between all pairs in the graph are averaged to produce the average length for the graph. The results are summarised in Table8 . The average length is fairly small for graphs of these sizes.... ..."

### Table 5: Average Shortest Path for the wordnets

"... In PAGE 6: ... Further, the shortest lengths between all pairs in the graph are averaged to produce the average length for the graph. The results are summarised in Table5 . The average length is fairly small for graphs of these sizes.... ..."

### Table 5: Average Shortest Path for the wordnets

"... In PAGE 6: ... Further, the shortest lengths between all pairs in the graph are averaged to produce the average length for the graph. The results are summarised in Table5 . The average length is fairly small for graphs of these sizes.... ..."

### Table 4.8: Output of the k-shortest paths computation

2006