### Table 1: Upper and lower bounds on (Kn) established in this paper.

2000

"... In PAGE 10: ... We have established upper bounds and lower bounds on the geometric thickness of complete graphs. Table1 contains the upper and lower bounds on (Kn)forn 100. Many open questions remain about geometric thickness.... In PAGE 10: .... Find exact values for (Kn) (i.e., remove the gap between upper and lower bounds in Table1... ..."

Cited by 25

### Table 1, upper bound lower bound difference upper bound lower bound difference

### Table 1: Summary of upper and lower bounds according to the value of n in all cases. n Upper bound Lower bound

in Abstract

### Table 1: Upper and lower bounds of linear FD-terms

1994

Cited by 24

### Table 2: The lower/upper bounds for the deterministic/randomized competitiveness of the problem, when parameterized both by ! and .

### Table 1 Parameter Lower Bound Upper Bound Parameter Lower Bound Upper Bound

2006

"... In PAGE 27: ... Summarizing, all the results were found to be very robust under the settings we discussed above, namely 100 distinctly different runs, with profiles based on parameter ranges that were determined by plausibility checks beforehand . In Table1 we list the parameters that have been used for sensitivity and robustness analysis, together with their respective ranges given by upper and lower bounds for their values. For each of the 100 profiles we generated, these parameters were independently, uniformly random drawn between these bounds.... ..."

### Table 1: Summary of Upper and Lower Bounds

2001

"... In PAGE 36: ...an be made as close as desired to m. The theorem follows. 9.1 Summary of upper and lower bounds Table1 summarizes our upper and lower bounds. The rows correspond to the different restrictions on the set A of algorithms, and the columns to the restrictions on the set D of databases and on the aggregation function t.... In PAGE 39: ...2 says that in the case of no wild guesses and a strict aggregation function, TA is tightly instance optimal. In the case of no wild guesses, for which aggregation functions is TA tightly instance optimal?19 What are the possible optimality ratios? For the other cases where we showed instance optimality of one of our algorithms (as shown in Table1 ), is the algorithm in question in fact tightly instance optimal? For cases where our algorithms might turn out not to be tightly instance optimal, what other algorithms are tightly instance optimal? There are several other interesting lines of investigation. One is to find other scenarios where in- stance optimality can yield meaningful results.... ..."

Cited by 231

### Table 1: Summary of Upper and Lower Bounds

2001

"... In PAGE 37: ...an be made as close as desired to m. The theorem follows. 9.1 Summary of upper and lower bounds Table1 summarizes our upper and lower bounds. The rows correspond to the different restrictions on the set A of algorithms, and the columns to the restrictions on the set D of databases and on the aggregation function t.... In PAGE 39: ...2 says that in the case of no wild guesses and a strict aggregation function, TA is tightly instance optimal. In the case of no wild guesses, for which aggregation functions is TA tightly instance optimal?18 What are the possible optimality ratios? For the other cases where we showed instance optimality of one of our algorithms (as shown in Table1 ), is the algorithm in question in fact tightly instance optimal? For cases where our algorithms might turn out not to be tightly instance optimal, what other algorithms are tightly instance optimal? There are several other interesting lines of investigation. One is to find other scenarios where in- stance optimality can yield meaningful results.... ..."

Cited by 231

### Table 1: Summary of Upper and Lower Bounds

"... In PAGE 36: ...an be made as close as desired to m. The theorem follows. 9.1 Summary of upper and lower bounds Table1 summarizes our upper and lower bounds. The rows correspond to the different restrictions on the set A of algorithms, and the columns to the restrictions on the set D of databases and on the aggregation function t.... In PAGE 39: ...2 says that in the case of no wild guesses and a strict aggregation function, TA is tightly instance optimal. In the case of no wild guesses, for which aggregation functions is TA tightly instance optimal?19 What are the possible optimality ratios? For the other cases where we showed instance optimality of one of our algorithms (as shown in Table1 ), is the algorithm in question in fact tightly instance optimal? For cases where our algorithms might turn out not to be tightly instance optimal, what other algorithms are tightly instance optimal? There are several other interesting lines of investigation. One is to find other scenarios where in- stance optimality can yield meaningful results.... ..."