### Table 1: Summary of Basic Multiprocessor Scheduling Theorems

1995

"... In PAGE 16: ... The complexity results from deterministic scheduling theory for multiprocessing where tasks are non-preemptive, have a partial order among themselves, have resource constraints (even a single resource constraint), and have a single deadline show that almost all the problems are NP-complete. To delineate the boundary between polynomial and NP-hard problems and to present basic results that every real-time designer should know, we list the following theorems without proof and compare them in Table1 . The metric used in the following theorems is the amount of computation time required for determining a schedule which satis es the partial order and resource constraints, and completes all required processing before a given xed deadline.... ..."

Cited by 94

### Table 2: Performance of Several Multiprocessor Scheduling Algorithms

in Preemptive Scheduling of Periodic Tasks on Multiprocessor: Dynamic Algorithms and Their Performance

1993

"... In PAGE 22: ... Surprisingly, except for RMNF-WC, the dynamic algorithms have the same worst-case performance bounds as their static counterparts using Condition IP. As a summary, the perfor- mance of several scheduling heuristics is presented in Table2 , where ? represents an open prob- lem. Our future work will focus on the investigation of the scheduling heuristics under the neces- sary and sufficient condition -- Condition IFF.... ..."

Cited by 7

### Table 1: The Multiprocessor scheduling: average results for each n over 30 random tests.

"... In PAGE 5: ... We compare the initial solution length (obtained by scheduling permutation de ned with task priorities set by the use of the CP heuristic) and LS obtained schedule to the minimum schedule length obtained by the use of VNS, TS, MLS, and PSGA heuristics. Comparative results are presented in Table1 . The rst column of this table contains the number of tasks in the tasks graphs, the second one the makespan of the best obtained schedule (in average), while in the remining six columns average values of schedule lengths obtained bytheuse of CP constructive heuristic, LS and eachofthenew heuristics are presented.... ..."

### Table 3.2: A list of the best performing agent ordering heuristics in Figure 3.4, with low density meeting scheduling at the top followed by high density meeting scheduling. The p value presented is the paired t-test value when comparing the best heuristic to each of the other heuristics. Bold text indicates statistically significant results (p a115 0.05).

2005

Cited by 2

### Table 3.2: A list of the best performing agent ordering heuristics in Figure 3.4, with low density meeting scheduling at the top followed by high density meeting scheduling. The p value presented is the paired t-test value when comparing the best heuristic to each of the other heuristics. Bold text indicates statistically significant results (p a115 0.05).

2005

### Table3.Schedule length improvement for list scheduling of transformed DAGs

2006

"... In PAGE 15: ... Furthermore, the much tighter lower bound can be used to select DAGs in which additional schedule improvement is possible for more computationally expensive scheduling. Table3 presents the heuristic schedule improvements achieved with graph transformations compared against the schedules produced by list scheduling the original DAGs. The columns Table3.... In PAGE 18: ...ubgraph transformation (column S. Subg. under Sched. improved in Table3 ) which requires much less total computation time. Enumeratively scheduling after the superior subgraph transformation provides further improvement (column S.... ..."

Cited by 3

### Table 5: Deviations of the results obtained from list scheduling with several heuristics from the optimal solution written in percentage of the optimum.

1998

"... In PAGE 28: ...nstructions. This imposes great restrictions on compaction which results in a worse schedule. An optimal schedule was found in only 6 of 30 cases. Table5 shows the deviations from the optimal result. The highest level rst heuristic, which is slightly more costly, yields better schedules than the others heuristics.... ..."

Cited by 5

### Table 5: Deviations of the results obtained from list scheduling with several heuristics from the optimal solution written in percentage of the optimum.

1998

"... In PAGE 27: ...nstructions. This imposes great restrictions on compaction which results in a worse schedule. An optimal schedule was found in only 6 of 30 cases. Table5 shows the deviations from the optimal result. The highest level rst heuristic, which is slightly more costly, yields better schedules than the others heuristics.... ..."

Cited by 5

### Table 5: Deviations of the results obtained from list scheduling with several heuristics from the

in Abstract

1998

"... In PAGE 27: ...nstructions. This imposes great restrictions on compaction which results in a worse schedule. An optimal schedule was found in only 6 of 30 cases. Table5 shows the deviations from the optimal result. The highest level rst heuristic, whichisslightly more costly, yields better schedules than the others heuristics.... ..."

### Table 8: Comparing the register constrained initial MD scheduling algorithm with the pure list scheduling algorithm.

1998

"... In PAGE 11: ... A series of experiments are done to compare our register constraint initial MD scheduling algorithm to the pure list scheduling algorithm without our priority functions. The results (see the Table8 in Section 5) show that, our register constrained initial MD scheduling is able to produce legal schedules with short lengths even when the register constraints are very small, while the pure list scheduling technique can not. Use In nite Impulse Response Filter (IIR) as an example.... In PAGE 18: ... 5 Experimental Results The e ectiveness of MORS to generate the schedule with short length under register constraint has been evaluated by running experiments on a series of DSP lters. Table8 compares the results of our register constrained initial MD scheduling algorithm, de- scribed in Section 3, with the pure list scheduling algorithm. The rst column is the names of lters.... ..."

Cited by 1