### Table 4.1 contains time complexity and memory overhead for the different versions of the polynomial expansion algorithm described above. Included are also the case three-dimensional data with full certainty. This case will be used in an experiment in section 6.1.2.

2001

Cited by 15

### Table 2. Performance of PRAD under different test conditions. All values are averaged over 100 runs. The columns represent the complexity of the function, the amount of noise, and the average error, polynomial degree, and time in milliseconds.

### Table 1. Complexity of problems on the Horn difference 1 n 2 ( 1; 2 and are Horn)

"... In PAGE 2: ... This alternative has also been studied repeatedly, since it offers advantages to formula-based representation in certain cases; see [13,10, 4] for more details. Our results on the complexity of these issues are summarized in Table1 , which gives a complete picture of the tractability/intractability frontier of these problems. The table also shows results on the Horn envelope [11, 12] of the difference, i.... In PAGE 10: ... Our results imply polynomial time algorithms in some cases, but a complete picture remains to be drawn. Another issue is a more accurate account of the complexity of the polynomial cases in Table1 . Under formula-based representation, all these problems are complete for P under logspace reductions; this is an easy con- sequence of the fact that deciding the satisfiability of a Horn CNF is complete for P under logspace reductions.... ..."

### Table 1 Time complexity

2006

"... In PAGE 17: ... The number of mappings is bounded by size(G)size(Q) and testing is obviously polynomial in the size of Q and G. It follows that all NP-complete problems in Table1 are polynomial for data complexity. They remain NP-complete for query complexity (one obtains the H-coloring problem [28]).... ..."

Cited by 2

### Table 2. Speedup in Worst-Case Execution Time for Optimized Virtual Table Algorithm

"... In PAGE 5: ... However, for the OVTA, the optimiza- tion over VTA depends completely on the characteristics of the generator polynomial chosen. Table2 shows the improvement over the VTA for several different polyno- mials (refer to Section 4 for a description of CRC32sub8 and CRC32sub16) . Note that for the particular CRC24 and CRC32 polynomials we used for our experiments, the OVTA has no improvement at all over the VTA.... ..."

### Table 1 Complexity of the global (left) and modular (right) algorithms The polynomial complexity bound must be compared to usual learning algo-

"... In PAGE 13: ...2 Complexity analysis The correction of the learning algorithm has been proved in previous sections. Complexity of the di erent steps is summarized in Table1 for both global and modular algorithms. The values of the most time-consuming steps are related to the complexity of matrix computations which is bounded by O((NPNO)3).... ..."

### Table 1 Time complexities of the different PNN variants.

"... In PAGE 7: ... Thus, the proposed algorithm takes O@(N2M)log N#5O(N log N2M log N)5O(N log N) time in total, assuming that M!N. The time complexities of the PNN method both in vector quantization and in thresholding are summarized in Table1 . The time com- plexities of the LMQ ~for thresholding! and the GLA ~for vector quantization! are shown in Table 2 for comparison.... In PAGE 11: ...9 by the PNN1LMQ, and 42.1 by the optimal method for Medi- cal 4 ~ Table1 1!. The reduction in the MSE, on the other hand, can be as much as 66% from that of the LMQ: MSE values 32.... In PAGE 11: ...4 versus 94.1 for Medical 3 ~ Table1 0!. This cor- responds to 4.... In PAGE 11: ... It is also noted that the combination of PNN1LMQ could be even faster than the LMQ alone. This is because the PNN can provide better initial thresholding, and thus, the LMQ uses less iterations ~ Table1 2!. We would also like to note that the run times are so small that the implemen- tation details and system level details, such as memory caching, can affect the time measurement.... ..."

### Table 1: Time complexity for different phases

Cited by 1