### Table 1 - Comparison of representations for shortest path finding

"... In PAGE 6: ...A comparison of representations for shortest path finding is shown in Table1 . As described above, the conventional representation has the possibility of yielding incorrect shortest paths.... ..."

### Table 3. Finding the shortest path in the fuzzy sense.

"... In PAGE 17: ...9. In Table3 , we put the edge weights, ij c , into the correct en- tries of the Table. Next, we calculate f(j) using the same tabular method as in Example 2.... In PAGE 17: ... Similar to Example 2, a row with two or more entries implies an inequality. After searching Table3 for inequalities, we obtain rows i =1,2, and 5, and hence, the following inequalities which satisfy (25): When i =1, 12 c+ ) 2 ( f lt; 13 c+ ) 3 ( f , i.e.... ..."

### 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.... ..."

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

2005

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### Table 2.3, using the expansion corpus do achieve significant improvement over no expansion base- line run using the two relative weight allocation obtained in training. The Wilcoxon Matched-Pairs Signed-Ranks Test was used for statistical significant test, and the p value for the difference between the KITRAN-BASE and KITRAN-WWW-QE@0.7 , and KITRAN-WWW-QE@0.8 are both at 0.00058. However, when the blind relevance feedback based on the top retrieve emails from the email corpus have an appropriate relative weight allocation (say 0.99 for the original query vs 0.5 for the original query), it can produce comparable improvement over the non-expansion base run (KIEVAL- BASE) as the WWW query expansion did. As shown in Table We then examined the effect of query expansion by WWW expansion corpus and that by BRF approach, and found that these two approaches not only achieved similar effect on overall retrieval

"... In PAGE 5: ...2771 0.3242 Table2 : The HARD evaluation results Using CF1, the graphic based clarification forms, actually hurt the performance. Comparing to the retrieval effectiveness of the run HDEVAL, that of HDEVAL-CF1WW decreased about 15% relatively when measured by MAP, and 5.... ..."

### Table 10. The effectiveness of query expansion based on elicited terms Source of query terms R-P P@10 MAP

"... In PAGE 25: ... Table10 compares the effectiveness of the baseline (the run obtained based on the topics title and description) with three other runs: (i) CF_123, obtained by simply using the elicited terms as queries; (ii) title.description.... ..."

### Table 1. Tabular method for finding the shortest path in the crisp case.

"... In PAGE 11: ... First, we put the edge weights from Fig. 3 into the correct entries in Table1 , i.... In PAGE 12: ... We look for inequalities that satisfy (19). Clearly, any row with two or more entries in Table1 entails an inequality. Hence, we get rows i =1,2, and 5 and obtain the following inequalities: when i =1,c12 + f(2) lt; c13 + f(3), i.... In PAGE 13: ... The tabular method for finding the shortest path in a fuzzy network is given in Table 2. Using the same approach as in Table1 , the shortest path in the fuzzy sense obtained from ) 1 ( * f = c12 +f(2) = * 12 c+* 25 c+ ) 5 ( * f = * 12 c+* 25 c+* 58 c+ ) 8 ( * f = * 12 c+* 25 c+* 58 c ,is 1, 2, 5, 8 with length 13.575.... In PAGE 17: ...ries of the Table. Next, we calculate f(j) using the same tabular method as in Example 2. The tabular method for finding the shortest path in the fuzzy sense is shown in Ta- ble 3. Using the same approach as in Table1 , the shortest path based on statistical data obtained from ) 1 ( f = 12 c+ ) 2 ( f = 12 c+25 c+ ) 5 ( f = 12 c+25 c+58 c+ ) 8 ( f = 12 c+25 c+ 58 c , is 1, 2, 5, 8 with length 13.27.... In PAGE 18: ...s constructed, as shown in Fig. 7. The tabular method for finding the shortest path is shown in Table 4. Using the same approach as in Table1 , the shortest path in the fuzzy sense obtained from ) 1 ( o f = o 12 c + ) 2 ( o f = o 12 c+o 25 c+ ) 5 ( o f = o 12 c+o 25 c + o 58 c+ ) 8 ( o f = o 12 c+o 25 c+o 58 c , is 1, 2, 5, 8 with length 13.3855.... ..."

### Table 3: Parallel Shortest Path Algorithm

1997

"... In PAGE 4: ... Our parallel shortest path algorithm uses the SPMD model for which each processor solves the portion of the shortest path tree on its subnetwork for each source. The outline of the algorithm is given in Table3 . Each processor repeatedly solves for shortest paths for its assigned subnetwork.... ..."

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### Table 3: Parallel Shortest Path Algorithm

1997

"... In PAGE 4: ... Our parallel shortest path algorithm uses the SPMD model for which each processor solves the portion of the shortest path tree on its subnetwork for each source. The outline of the algorithm is given in Table3 . Each processor repeatedly solves for shortest paths for its assigned subnetwork.... ..."

Cited by 7