### Table 1. Current bounds for algorithms scheduling jobs one by one with no constraints.

"... In PAGE 10: ... The analysis of all these algorithms is relatively complicated. The current state of our knowledge is summarized in Table1 . For comparison we include also the competitive ratio of List Scheduling.... In PAGE 14: ... It essentially tries to preserve the invariant above, with some special considerations for large jobs. Thus, in this model both deterministic and randomized cases are completely solved, giving the same bounds as the randomized lower bounds in Table1 . More- over, we know that randomization does not help.... In PAGE 17: ... Joel Wein observed that for preemptive open shop scheduling there exists a 2-competitive algorithm for arbitrary m. Gerhard Woeginger and the author ob- served that the randomized lower bound from the basic model which approaches e=(e ? 1) 1:5819 (see Table1 ) can be modi ed to work for open shop, too. 4.... ..."

### Table 3. Density estimation techniques in multi-objective evolutionary algorithms and operators used in this study.

2001

"... In PAGE 11: ... Many advanced multi-objective evolutionary algorithms use some form of density dependent selection. Furthermore, nearly all techniques can be expressed in terms of density estimation, a classification is given in Table3 . We will make use of this as a further step towards a common framework of evolutionary multi-objective optimizers, and present the relevant enhancement of the unified model.... ..."

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### Table 3. Density estimation techniques in multi-objective evolutionary algorithms and operators used in this study.

2001

"... In PAGE 11: ... Many advanced multi-objective evolutionary algorithms use some form of density dependent selection. Furthermore, nearly all techniques can be expressed in terms of density estimation, a classification is given in Table3 . We will make use of this as a further step towards a common framework of evolutionary multi-objective optimizers, and present the relevant enhancement of the unified model.... ..."

Cited by 20

### Table 2. Job scheduling.

"... In PAGE 8: ... As with the heat equation, the dimension of the global grid of n x n cells is n = qm, where q is the dimension of the mesh of processors. Table2 shows the execution time T(n, p) in seconds on a q x q mesh of p processors, p = q * q, the processor efficiency E(n, p) = T(n, 1)/(p*T(n, p)) and the speedup S(n, p) = p * E(n, p).... ..."

### Table 2. Job scheduling.

"... In PAGE 8: ... As with the heat equation, the dimension of the global grid of n x n cells is n = qm, where q is the dimension of the mesh of processors. Table2 shows the execution time T(n, p) in seconds on a q x q mesh of p processors, p = q * q, the processor efficiency E(n, p) = T(n, 1)/(p*T(n, p)) and the speedup S(n, p) = p * E(n, p).... ..."

### Table 2. Behaviour of Scheduling Algorithms for various scenarios on the Grid.

2000

"... In PAGE 7: ... Note that for this value, the deadline of 990 seconds is infeasible, and the deadline of 1980 seconds is the optimal deadline plus 10%. Table2 shows a summary of results for each combination of scheduling algorithm, deadline and budget, and the resulting percentage of completed jobs, the total running time, and the final cost. The jobs marked infeasible have no scheduling solution that enables 100% completion of jobs.... ..."

Cited by 64

### Table 2. Behaviour of Scheduling Algorithms for various scenarios on the Grid.

2000

"... In PAGE 7: ... Note that for this value, the deadline of 990 seconds is infeasible, and the deadline of 1980 seconds is the optimal deadline plus 10%. Table2 shows a summary of results for each combination of scheduling algorithm, deadline and budget, and the resulting percentage of completed jobs, the total running time, and the final cost. The jobs marked infeasible have no scheduling solution that enables 100% completion of jobs.... ..."

Cited by 64

### Table 2. Behaviour of Scheduling Algorithms for various scenarios on the Grid.

2000

"... In PAGE 7: ...Computational Power Grids for Parameter Sweep Applications 7 Table2 shows summary of results of the combinations of algorithm, deadline and budget, and the resulting percentage of completed jobs, the total running time, and the final cost. The jobs marked infeasible have no scheduling solution that would enable 100% completion of jobs.... ..."

Cited by 64

### Table 2. Job Shop Scheduling Results with the BAS and the Petri Net algorithms.

2006

"... In PAGE 10: ...the Petri-Net models consisted of 220 places and 200 transitions. A summary of the results is shown in Table2 . Notice that both algorithms show competitive results in terms of solution quality and CPU times.... ..."

### Table 1: Performance Measures for Job-shop Scheduling and Control

2001

"... In PAGE 2: ... Our distributed, evolutionary approach to scheduling avoids these problems by removing the requirement for a truly optimal solution, requiring instead only a towards-optimal (but practical and useful) solution. The goal is to optimize (often) conflicting local and global performance measures (French, 1983), as outlined in columns one and two of Table1 . A secondary goal is to minimize the variance in the global stability measures in column three, in order to maximize the stability of the system.... ..."

Cited by 1