### Table VI. All pairs shortest paths problem (execution times in seconds)

1992

Cited by 27

### Table 4 Maintaining -approximate distances for all-pairs of vertices

"... In PAGE 10: ... Combining the two data-structures _ D; D together as described above, we achieve practically linear update time per edge deletion for maintaining all-pairs approx- imate distances. See the Table4 (please refer to Ta- ble 1, and Table 3 for notations used for the data- structures). This is an improvement over the previous bound of ~ O( n2 pm) on the update time which is ~ O(n1:5) for sparse graphs.... ..."

### Table 3 Maintaining -approximate distances for all-pairs of vertices separated by distance 2 [d; n]

"... In PAGE 10: ... However, it should be noted that the data-structure _ D is more suitable for maintaining -approximate distances for pairs of vertices separated by small distance (refer to Table 1 for dependence of update time on d). Whereas the data-structure D is more suitable for maintaining -approximate distances for pairs of vertices separated by large distances (refer to Table3 for dependence of update time on d). Thus we use both the data- structures simultaneously to achieve better update time as follows.... In PAGE 10: ... Combining the two data-structures _ D; D together as described above, we achieve practically linear update time per edge deletion for maintaining all-pairs approx- imate distances. See the Table 4 (please refer to Ta- ble 1, and Table3 for notations used for the data- structures). This is an improvement over the previous bound of ~ O( n2 pm) on the update time which is ~ O(n1:5) for sparse graphs.... ..."

### Table 1. Output of the Spectral Analysis. Edge connectivity describes the minimum number of edges that can be removed to disconnect the graph. Diameter is the longest shortest path between all pairs of nodes in the graph. Mean distance is the average path length of all unique paths between all pairs of nodes.

"... In PAGE 5: ... Mean distance is the average path length of all unique paths between all pairs of nodes. Table1 indicates that the Philippine AS network has a higher lower bound of edge connectivity, but its upper bound is not that much different from that of Singapore. Japan and Singapore have very similar edge connectivity lower bounds, but Japan has an extremely high edge connectivity upper bound.... ..."

### Table 7: Comparison of four statistical models using Floyd-Warshall all pair shortest path algorithm.

2005

"... In PAGE 14: ... For this purpose we com- pare the length of all paths for an instance with 400 nodes. Table7 provides a summary for the length of the minimal, maximal, and average path. Notice, that all three newly developed models are much more statistically sound.... ..."

Cited by 26

### TABLE VI COMPARISON OF FOUR STATISTICAL MODELS USING FLOYD-WARSHALL ALL PAIR SHORTEST PATH ALGORITHM.

2005

Cited by 26

### Tables 6 and 7 give the total lengths of the all-pairs shortest paths for 4 differently sized sets of data for geometric graphs. For each data size, graphs of increasing density (represented by increasing number of expected number of adjacent edges) are being tested.

### Table 2. Computing all pairs of separations

1997

"... In PAGE 4: ... Our benchmarks include cyclic constraint graphs from [5] and [8] unfolded to varying degrees. These are named hr- n and mr-n in Table2 , where different values of r in- dicate different cyclic graphs, and n denotes the degree of unfolding. The benchmark mcmill was obtained from [7], while diffeq was obtained from an analysis of an asyn- chronous differential equation solver chip [11].... In PAGE 5: ...treat max-only systems in any special way. Table2 also shows the time taken by our algorithm to an- alyze each benchmark. These times are on a MIPS R5000 150 MHz processor with 128 MBytes of main memory, and do not include the time to read in the timing constraint graph and topologically sort the events.... ..."

Cited by 16

### Table 1 Maintaining -approximate distances for all-pairs of vertices separated by distance d

"... In PAGE 10: ... Both these data-structures can be used for maintaining all-pairs approximate distances. However, it should be noted that the data-structure _ D is more suitable for maintaining -approximate distances for pairs of vertices separated by small distance (refer to Table1 for dependence of update time on d). Whereas the data-structure D is more suitable for maintaining -approximate distances for pairs of vertices separated by large distances (refer to Table 3 for dependence of update time on d).... ..."

### Table 1: Heuristics for ESTP. Type classi cation and performance. An \- quot; in- dicates that no or insu cient data is available to give a reliable estimate of reduction over MST and/or running time complexity.

1997

"... In PAGE 16: ...Summary In Table1 we present a summary of heuristics for ESTP, by noting their local search type, average reduction over MST (when available) and running time complexity (when available). The type classi cation descent method in general stands for an iterative best improvement method.... ..."

Cited by 4