### Table 5. Evaluation of the MARS Algorithm based on 12 nouns, 1 verb, 1 adjective in LDOCE. Word Pos #Senses #Done #Correct Prec

### Table 2.4: Summary of Computational Results Using Lower Bound Based Branching Rules. From the tables we make the following observations: It is in general too costly to perform 10 dual simplex pivots on all fractional vari- ables. Strong branching can be highly e ective on some problems, but the e ectiveness is impacted greatly by the ability to select a suitable subset of variables on which to perform a number of dual simplex pivots. 11

1999

Cited by 33

### Table 1: Lower bounds for randomized algorithms.

"... In PAGE 8: ... For n = 15 and s = 1 + i=100 for i = 1; : : : ; 99, we have calculated the optimal values of this linear program by using CPLEX. We display the actual lower bounds in Table1 . The value c(i) is a lower bound for any randomized online algorithm at speed s = 1 + i=100.... ..."

### Table 4. Asymptotic lower bounds for online simplex range searching.

1999

"... In PAGE 28: ... Erickson apos;s techniques also imply nontrivial lower bounds for online and o ine halfspace emptiness searching, but with a few exceptions, these are quite weak. Table4 summarizes the best known lower bounds for online simplex and related queries, and Table 5 summarizes the best known lower bounds for o ine range searching. Lower bounds for emptiness problems apply to counting and reporting problems as well.... ..."

Cited by 205

### Table 5. Asymptotic lower bounds for o ine simplex range searching.

### Table 4. Asymptotic lower bounds for online simplex range searching using O(m) space.

1999

"... In PAGE 31: ... Erickson apos;s techniques also imply nontrivial lower bounds for online and o ine halfspace emptiness searching, but with a few exceptions, these are quite weak. Table4 summarizes the best known lower bounds for online simplex queries, and Table 5 summarizes the best known lower bounds for o ine simplex range searching. Lower bounds for emptiness problems apply to counting and reporting problems as well.... ..."

Cited by 205

### Table 1. Runtime in seconds for 100; 000 random points in dimension d: pivoting (solid line) and move-to-front (dotted line) (left). Runtime in seconds on regular d-simplex in dimension d (right).

1999

"... In PAGE 12: ... I have tested the algorithm on random point sets up to di- mension 30 to evaluate the speed of the method, in particular with respect to the relation between the pivoting and the move-to-front variant. Table1 (left) shows the respective runtimes for 100; 000 points randomly chosen in the d-dimensional unit cube, in logarithmic scale (averaged over 100 runs). All runtimes (excluding the time for generating and storing the points) have been obtained on a SUN Ultra-Sparc II (248 MHz), compiling with the GNU C++-Compiler g++ Version 2.... In PAGE 12: ... In this case, the number of support points is d. Table1 (right) shows... ..."

Cited by 15

### Table 1. Runtime in seconds for 100; 000 random points in dimension d: pivoting (solid line) and move-to-front (dotted line) (left). Runtime in seconds on regular d-simplex in dimension d (right).

1999

"... In PAGE 12: ... I have tested the algorithm on random point sets up to di- mension 30 to evaluate the speed of the method, in particular with respect to the relation between the pivoting and the move-to-front variant. Table1 (left) shows the respective runtimes for 100; 000 points randomly chosen in the d-dimensional unit cube, in logarithmic scale (averaged over 100 runs). All runtimes (excluding the time for generating and storing the points) have been obtained on a SUN Ultra-Sparc II (248 MHz), compiling with the GNU C++-Compiler g++ Version 2.... In PAGE 12: ... In this case, the number of support points is d. Table1 (right) shows... ..."

Cited by 15