### Table 1. Trade-offs between N and the total solution time on the SPACE-960-r MINLP

"... In PAGE 11: ... Experimentally, we have observed a convex relationship between N and the total solution time. We illustrate this observation in Table1 for various values of N on the SPACE-960-r MINLP from the MacMINLP library [12]. It shows the average time to solve a subproblem, the total time to solve N subproblems in one iteration, the number of iterations needed to resolve the inconsistent global constraints, and the overall time to solve the problem.... In PAGE 12: ...013 0.015 close to the optimal value (as illustrated in Table1 ). Next, we reduce N by half (Line 8) and repeat the process.... In PAGE 12: ... As a result, we only evaluate one subproblem in each iteration of Figure 7 in order to estimate Tp(N) (Line 4). For the SPACE-960-r MINLP in Table1 , we set N to 480, 240, 120, 60, 30, 15. We stop at N = 15 and report N = 30 when overall time starts to increase.... ..."

### Table 1: Time and space comparisons for working

1991

"... In PAGE 12: ... We compare the non magic sets evaluation with magic sets evaluations for queries (of the form working(X), with X bound to a constant) at di erent depths down the tree. Table1 gives the evaluation times (seconds of real time), and maximum space requirements (number of tuples) | including space for old copies of relations, and the \deltas quot; used by the di erential techniques.... ..."

Cited by 35

### Table 1: Time and space comparisons for working()

1995

"... In PAGE 32: ... We compare the non magic sets evaluation with magic sets evaluations for queries (of the form working(X), with X bound to a constant) at di erent depths down the tree. Table1 gives the evaluation times (seconds of real time), and maximumspace requirements (number of tuples) | including space for old copies of relations, and the \deltas quot; used by the di erential techniques. Explicitly computing and storing the complement of false facts may be thought to take up too much space.... ..."

Cited by 29

### Table 1: Time and space comparisons for working()

1995

"... In PAGE 41: ... We compare the non magic sets evaluation with magic sets evaluations for queries (of the form working(X), with X bound to a constant) at di erent depths down the tree. Table1 gives the evaluation times (seconds of real time), and maximumspace requirements (number of tuples) | including space for old copies of relations, and the \deltas quot; used by the di erential techniques. Explicitly computing and storing the complement of false facts may be thought to take up too much space.... ..."

Cited by 29

### Table 1. Time and space requirements for generating schedules.

"... In PAGE 5: ... In addition we experiment with using breadth-first (BFS), depth-first search strategy (DFS), or depth-first search in combination with bit-state hashing (BSH) [6]8. In Table1 we present the time (in seconds) and space (in MB) consumed by UPPAAL version 3.0.... In PAGE 5: ... The positions marked with - indicate that the execution requires more than 256MB of memory, two hours of execution time, or that a suitable hash table size has not found10. As can be seen in Table1 , the use of guides allows us to generate schedules for 35 batches using 250 MB and 3.5 min- utes, whereas no schedule can be generated for three batches when no guides are used.... ..."

### Table 1. Time and space requirements for generating schedules.

"... In PAGE 5: ... In addition we experiment with using breadth-first (BFS), depth-first search strategy (DFS), or depth-first search in combination with bit-state hashing (BSH) [6]8. In Table1 we present the time (in seconds) and space (in MB) consumed by UPPAAL version 3.0.... In PAGE 5: ... The positions marked with - indicate that the execution requires more than 256MB of memory, two hours of execution time, or that a suitable hash table size has not found10. As can be seen in Table1 , the use of guides allows us to generate schedules for 35 batches using 250 MB and 3.5 min- utes, whereas no schedule can be generated for three batches when no guides are used.... ..."

### Table 1. Time and space requirements for generating schedules.

"... In PAGE 5: ... In addi- tion we experiment with using breadth-first (BFS), depth-first search strategy (DFS), or depth-first search in combination with bit-state hashing (BSH) [6]8. In Table1 we present the time (in seconds) and space (in MB) consumed by UPPAAL version 3.0.... In PAGE 5: ... The positions marked with - indicate that the execution requires more than 256MB of memory, two hours of execution time, or that a suitable hash table size was not found10. As can be seen in Table1 , the use of guides allows us to generate schedules for 35 batches using 250 MB and 3.5 minutes, whereas no schedule can be generated for 3 batches when no guides are used.... ..."

### Table 1: Summary of Results Problem Previous results (time, space) Our results (time, space)

"... In PAGE 14: ...unctions. An optimality algorithm for monotone linear systems appears in Section 5. We show that this algorithm can work with some non-linear constraints, and we generalize the algorithm to monotone weight functions as well. Table1 summarizes the results for 2VIP systems. 2 Feasibility Algorithm Given a 2VIP system, we are interested in developing an algorithm which nds a feasible solution, if such a solution exists.... ..."

### Table 9: Excitation periods of three reversals for 0.8 cm window size, 1.2 cm window size. Periods T0,1 and T1,3 of both window sizes were evaluated from profiles extracted from the time-space plots at the reversal position: 0.1 cm. T0,2 for 0.8 cm and 1.2 cm window sizes were evaluated from profiles extracted from the time-space plots at the reversal positions: 0.7 cm and 1.1 cm, respectively. Medium with 8 mM PG (the reference solution mixture). The bold numbers are the values for medium with 11 mM PG (the solution mixture III).

2004

"... In PAGE 78: ...ropagating to the left and at a location around 0.15 cm for those propagating to the right. The dependence of the excitation periods on the voltages applied to the system in the case of three reversals, is shown in Fig. 32 (see also Table9 ). The definition of period T0,1 is different from the definition of periods T0,2 , T1,3, and T2,4 since T0,1 is the period between the first wave passing from the left to the right and the first reversed wave passing from the right to the left, while other periods are measured between reversed waves propagating in the same direction.... In PAGE 79: ... ( m i n ) U (V) Figure 32: Excitation periods Texc. as a function of the applied voltage U plotted from the data in Table9 for the medium with 8 mM PG.... ..."

### Table 6. Waiting Time Spacings under different traffic loading distributions (ri;i+1 = 1:1).

2000

"... In PAGE 6: ... In all the cases con- sidered, the system utilization is = 0:9. The results are shown in Table6 . We can observe that under different traf- fic distributions, our proposed algorithm is highly effective in achieving the specified waiting time ratios.... ..."

Cited by 10