### Table 1: Impedances Calculated Using Shortest Paths and Second Shortest Paths Approximation Method

2002

"... In PAGE 7: ... Experimental results show that it is sufficient to consider only the shortest paths and the second shortest paths. Table1 show some data on impedances calculated by using the shortest paths and second shortest paths approximation. The experiment is performed on a power mesh which has the exact structure as shown in Fig.... ..."

Cited by 21

### Table 1. Runtimes of the shortest path benchmark in seconds. \- quot; indicates that the measurements could not be nished within a reasonable period of time. The considered graph consists of a linear chain of nodes. 1 processor 6 processors

"... In PAGE 11: ... Thus, a comparison of the original algorithms and the implementations of the Gamma schemes can only be per- formed with extreme care! We only show the runtimes of the known algorithms in order to give a rough idea, what price we have to pay for the higher level of programming. In the shortest path application (see Table1 and 2), all our techniques improve the runtime of the na} ve implementation enormously. While the complexity of the original Dijkstra-algorithm(with a matrix representation of the graph) is quadratic in the number... ..."

### Table 2: Average Internode Distance: SHORT=Shortest Path Routing, MULT=Multistage Routing, S/M = Ratio of Shortest Path Routing to Multistage Routing

1995

"... In PAGE 8: ...3 Results and Analysis In our experiments, we use the system size 64, 128, and 256 with switch sizes 4, 8, and 16. The average internode distances of single stage networks for shortest path routing and multistage routing are shown in Table2 . The column SHORT and MULT show the average internode distance of shortest path routing and that of multistage routing, re- spectively.... In PAGE 9: ... The improvements varies de- pending on di erent benchmarks. However, we can nd a close relation between the S/M ratios in the Table2 and Table 3. The ratios can not be the same because the read miss latency ratios in Table 3 contain the delay caused by memory access as well as network itself, whereas the S/M ratios in Table 2 re ect only network e ects.... In PAGE 9: ... However, we can nd a close relation between the S/M ratios in the Table 2 and Table 3. The ratios can not be the same because the read miss latency ratios in Table 3 contain the delay caused by memory access as well as network itself, whereas the S/M ratios in Table2 re ect only network e ects. The mem- ory access delay is relatively constant and independent of the routing schemes.... In PAGE 9: ... For example, the S/M ratio of MDG is af- fected the most by the memory access delays. This is the reason why the S/M ratios of MDG and the S/M ratio in Table2 shows bigger di erences than in other benchmarks. MDG has a hot spot memory access pattern so that mem- ory access time is a dominant delay component in read miss latency.... ..."

Cited by 2

### Table 3 Shortest-path running times

"... In PAGE 7: ...1. Shortest-path algorithms We have collected the running times, from [12] in Table3 (the largest problem instances only). 13 Table 4 contains the ranking of the algorithms based on their running times.... ..."

### Table 3 Shortest-path running times

"... In PAGE 7: ...1. Shortest-path algorithms We have collected the running times, from [12] in Table3 (the largest problem instances only). Table 4 contains the ranking of the algorithms based on their running times.... ..."

### TABLE VII PERFORMANCE IMPROVEMENT OF PBR OVER THE SHORTEST PATH ALGORITHM AT VARIOUS POINTS DURING THE RUN OF THE ALGORITHM.

### Table 1: Results with the shortest paths, and 2- and 3- multi- path routes together with the respective single-path routes.

"... In PAGE 5: ...maximumfluxof0:3763 , i.e., the flux corresponding to the outer radial-ring paths at the boundary. The numerical results are given in Table1 , where rows indicated with 1) and 2) correspond to the optimal weights for randomized path selection with the given two and three path sets, respectively, and column multi-path con- tains the corresponding maximum scalar fluxes. However, according to Proposition 1, multi-path routes mp1 and mp2 cannot be an optimal solution to the load balancing problem, and, in particular, the corresponding single-path routes, denoted by sp1 and sp2, obtained using (14) yield a lower maximum scalar packet flux.... In PAGE 5: ... However, according to Proposition 1, multi-path routes mp1 and mp2 cannot be an optimal solution to the load balancing problem, and, in particular, the corresponding single-path routes, denoted by sp1 and sp2, obtained using (14) yield a lower maximum scalar packet flux. This maximum scalar flux can be computed numer- ically and the corresponding results are given in column single- path in Table1 . We note that in both cases combining the multi- path traffic flows to single-path improves the situation considerably, as expected.... In PAGE 6: ...4 0.5 sp1 sp3 mod (r) r modified sp1 sp3 circular (2 path sets) (3 path sets) Figure 5: Resulting scalar flux as a function of distance r from the origin for modified circular paths (see [12]), and the optimal single-path routes sp1 and sp3 (rows 1) and 3) in Table1 ). Three dimensional plots illustrate the same situation.... ..."

### TABLE VII PE a197 RFORMANCE IMPROVEMENT OF PBR OVER THE SHORTEST PATH ALGORITHM AT VARIOUS POINTS DURING THE RUN OF THE ALGORITHM.

2001

Cited by 37

### TABLE VII PE a197 RFORMANCE IMPROVEMENT OF PBR OVER THE SHORTEST PATH ALGORITHM AT VARIOUS POINTS DURING THE RUN OF THE ALGORITHM.

2001

Cited by 37