### Table 1. Comparison of the weighted path length of optimal and nearly optimal multiway trees

### Table 1. Comparison of the weighted path length of optimal and nearly optimal multiway trees

### TABLE 38.3. Binary vs. Multi-way Splits Binary Multi-way Gain

1997

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### Table 3b. Solution Statistics for Model 2 (Minimization)

1999

"... In PAGE 4: ...6 Table 2. Problem Statistics Model 1 Model 2 Pt Rows Cols 0/1 Vars Rows Cols 0/1 Vars 1 4398 4568 4568 4398 4568 170 2 4546 4738 4738 4546 4738 192 3 3030 3128 3128 3030 3128 98 4 2774 2921 2921 2774 2921 147 5 5732 5957 5957 5732 5957 225 6 5728 5978 5978 5728 5978 250 7 2538 2658 2658 2538 2658 120 8 3506 3695 3695 3506 3695 189 9 2616 2777 2777 2616 2777 161 10 1680 1758 1758 1680 1758 78 11 5628 5848 5848 5628 5848 220 12 3484 3644 3644 3484 3644 160 13 3700 3833 3833 3700 3833 133 14 4220 4436 4436 4220 4436 216 15 2234 2330 2330 2234 2330 96 16 3823 3949 3949 3823 3949 126 17 4222 4362 4362 4222 4362 140 18 2612 2747 2747 2612 2747 135 19 2400 2484 2484 2400 2484 84 20 2298 2406 2406 2298 2406 108 Table3 a. Solution Statistics for Model 1 (Maximization) Pt Initial First Heuristic Best Best LP Obj.... In PAGE 5: ...) list the elapsed time when the heuristic procedure is first called and the objective value corresponding to the feasible integer solution returned by the heuristic. For Table3 a, the columns Best LP Obj. and Best IP Obj.... In PAGE 5: ... report, respectively, the LP objective bound corresponding to the best node in the remaining branch-and-bound tree and the incumbent objective value corresponding to the best integer feasible solution upon termination of the solution process (10,000 CPU seconds). In Table3 b, the columns Optimal IP Obj., bb nodes, and Elapsed Time report, respectively, the optimal IP objective value, the total number of branch-and-bound tree nodes solved, and the total elapsed time for the solution process.... ..."

### TABLE III Average update performance of multiway range trees.

2001

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### TABLE III Average update performance of multiway range trees.

2001

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### Table 3. Comparison between Tree Splitting and PV Splitting for Various Processor Tree Con gurationsa (L, F) Tree splitting PV splitting

1982

"... In PAGE 21: ... Tree splitting and PV splitting have been compared by simulation. Results are given in Table3 a and b. All searches were carried out on trees of depth 4 and width 24.... ..."

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### Table 3: Average prediction accuracies (with standard deviations) of the decision trees ob- tained using the di erent splitting strategies and evaluation functions. Binary Greedy Optimal

1999

"... In PAGE 29: ... Recall that in binary partitioning IG and BGlog coincide. Table3 records the average prediction accuracies (with standard deviations) that were obtained when the trees were not required to be reduced; i.e.... In PAGE 30: ...30 Table 4: Statistically signi cant di erences in the prediction accuracies of Table3 when comparing the evaluation functions within splitting strategies. Binary Greedy Optimal Diff.... In PAGE 30: ... GR ++ 8 5 11 + 2 3 3 16 17 10 ? 2 3 1 ?? 2 2 5 the di erences in average accuracy are relatively consistently either in favor or against GR throughout the strategies. The only outstanding value di erence in Table3 is the di erence on the domain Sonar. In this example set there are only few duplicate values, which appears to be an impairing factor for the GR function.... In PAGE 30: ... These results indicate that the choice of the numerical attribute evaluation function has an e ect on the prediction accuracy of the resulting decision tree, no matter which splitting strategy is used. The results in Table3 also seem to indicate that the choice of partitioning strategy has only a marginal e ect on the outcome of induction. In order to test this hy- pothesis statistically, we also paired the results obtained by all the three strategies with each other according to the evaluation function that was used.... In PAGE 31: ...31 Table 5: Statistically signi cant di erences in the prediction accuracies of Table3 when comparing the splitting strategies without changing the evaluation function. GR BGlog Diff.... ..."

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### Table 3. Average prediction accuracies (with standard deviations) of the decision trees obtained using the di erent splitting strategies and evaluation functions. Binary Greedy Optimal

"... In PAGE 30: ... Recall that in binary partitioning IG and BGlog coincide. Table3 records the average prediction accuracies (with standard deviations) that were obtained when the trees were not required to be reduced; i.e.... In PAGE 30: ... In individual domains the di erences in average accuracy are relatively consistently either in favor or against GR throughout the strategies. The only outstanding value di erence in Table3 is the di erence on the domain Sonar. In this example set there are only few duplicate values, which appears to be an impairing factor for the GR function.... In PAGE 30: ... These results indicate that the choice of the numerical attribute evaluation func- tion has an e ect on the prediction accuracy of the resulting decision tree, no matter which splitting strategy is used. The results in Table3 also seem to indicate that... In PAGE 31: ...Table 4. Statistically signi cant di erences in the prediction accuracies of Table3 when comparing the evaluation functions within splitting strategies. Binary Greedy Optimal Diff.... In PAGE 32: .... ELOMAA AND J. ROUSU Table 5. Statistically signi cant di erences in the prediction accuracies of Table3 when comparing the splitting strategies without changing the evaluation function. GR BGlog Diff.... ..."

### Table 1 summarizes the symbols and definitions introduced in this section. In the sequel we show how they can be applied for multiway spatial joins.

1999

"... In PAGE 3: ...CostWQ(Ri,q) number of node accesses for a window query q on Ri CostRJ(Ri,Rj) number of node accesses for a spatial join between two R-trees Ri and Rj Table1 Table of symbols 3. MULTIWAY SPATIAL JOINS A multiway spatial join can be represented by a graph Q where Q[i][j] denotes the join condition between Ri and Rj.... ..."

Cited by 31