"... In PAGE 19: ... Perform the next iteration of the do loop beginning on Line (4) until all tasks have been mapped. Table3 shows a scenario in which the Sufferage will outperform the Min-min. Table 3 shows the expected execution time values for four tasks on four machines (all initially idle).... In PAGE 19: ... Table 3 shows a scenario in which the Sufferage will outperform the Min-min. Table3 shows the expected execution time values for four tasks on four machines (all initially idle). In this case, the Min- min heuristic gives a makespan of 93 and the Sufferage heuristic gives a makespan of 78.... In PAGE 21: ...apping event without actually beginning execution (i.e., the task is starving for a machine). This impacts the response time the user sees (this is examined as a sharing penalty in [17]). 0 0 t on m t on m 3 1 t on m 2 1 t on m 2 3 t on m 3 0 t on m 0 1 t on m 2 1 t on m 3 2 using Sufferage using Min-min Figure 3: An example scenario (based on Table3 ) where the Sufferage gives a shorter makespan than the Min-min (bar heights are proportional to task execution times). To reduce starvation, aging schemes are implemented.... ..."

"... In PAGE 9: ...1 seconds up to 5 minutes (3000 tness evaluations). The results concerning the random graphs are summarized in Table3 ; again, the stochastic approaches were aborted after 3000 tness evaluations.7 Interest- ingly, for these graphs APGAN only in 15% of all cases is better than Monte Carlo and only on in two cases better than the Evolutionary Algorithm.... In PAGE 9: ...84% of the costs achieved by the Monte Carlo simulation). Hill Climbing, however, might be an alternative to the evolutionary approach; the results shown in Table3 might suggest a superiority of Hill Climbing, but re- garding the absolute bu er costs this hypothesis could not be con rmed (the costs achieved by the Evolutionary Algorithm deviate from the costs produced by Hill Climbing by a factor of 0.19% in average).... ..."

"... In PAGE 9: ...1 seconds up to 5 minutes (3000 tness evaluations). The results concerning the random graphs are summarized in Table3 ; again, the stochastic approaches were aborted after 3000 tness evaluations.7 Interest- ingly, for these graphs APGAN only in 15% of all cases is better than Monte Carlo and only on in two cases better than the Evolutionary Algorithm.... In PAGE 9: ...84% of the costs achieved by the Monte Carlo simulation). Hill Climbing, however, might be an alternative to the evolutionary approach; the results shown in Table3 might suggest a superiority of Hill Climbing, but re- garding the absolute bu er costs this hypothesis could not be con rmed (the costs achieved by the Evolutionary Algorithm deviate from the costs produced by Hill Climbing by a factor of 0.19% in average).... ..."

"... In PAGE 9: ...1 seconds up to 5 minutes (3000 tness evaluations). The results concerning the random graphs are summarized in Table3 ; again, the stochastic approaches were aborted after 3000 tness evaluations.7 Interest- ingly, for these graphs APGAN only in 15% of all cases is better than Monte Carlo and only on in two cases better than the Evolutionary Algorithm.... In PAGE 9: ...84% of the costs achieved by the Monte Carlo simulation). Hill Climbing, however, might be an alternative to the evolutionary approach; the results shown in Table3 might suggest a superiority of Hill Climbing, but re- garding the absolute bu er costs this hypothesis could not be con rmed (the costs achieved by the Evolutionary Algorithm deviate from the costs produced by Hill Climbing by a factor of 0.19% in average).... ..."

"... In PAGE 13: ...Table2 shows the percentage of test- runs in which the algorithm outperformed all the heuristics. Further discussion and an example on which the heuristics fail appear in the thesis.... ..."

"... In PAGE 12: ... For the trees randomly obtained as above, we ran Algorithm 1 and each heuristic described in Section 3. Table1 tells for how many of the random trees (of depth d and k different alignments) none of the heuristics matched the optimal solution obtained by Algorithm 1. Note that as the size of the tree grows, the percentage of trees in which Algorithm 1 outperformed all of the heuristics grows rapidly.... ..."