### Table 4: Time (msec) required to find the base plan for Blocksworld problems with 5 and 8 blocks.

"... In PAGE 10: ... We refer the reader to the paper by Younes and Simmons (2003) for a thorough description of these heuristics as well as experimental results with other domains. We depict the results of our experiments with the Blocksworld problems in the first and third lines of Table4 (the second and fourth lines in Tables 4 and 5 will be explained later).... In PAGE 11: ... We modified the best working strategies, namely variants of mc and mw, and implemented the delay of separable threats (in Table 3 these are shown with the dsep suffix.) We show the planning times for the experiments with and without dsep in Table 5 (we repeat the columns from Table4 for comparison). The results show that time improvement can be seen for the 5-blocks problem.... ..."

### Table 1: Summary of theoretical results for D-SEPs. The last two columns show the time complexity of nding the optimal policy for a D-SEP with N participants. In general, this problem is EXPTIME-hard but if the utility function is K-partitionable then the problem is polynomial time in N. Adding restrictions on how often the manager may send suggestions makes the problem even more tractable. Note that the size of the optimal policy is nite and must be computed only once, even though the execution of a SEP may be in nite (e.g., with AnyUnlimited ).

"... In PAGE 7: ... Thus, the optimal policy may be computed via a depth- rst search over the graph in total time O(N3K). 2 Table1 summarizes the results presented above as well as a few other interesting cases ( Immediate and Synchronous ). These results rely on two key optimizations.... ..."

### Table 1: Summary of theoretical results for D-SEPs. The last two columns show the time complexity of nding the optimal policy for a D-SEP with N participants. In general, this problem is EXPTIME-hard but if the utility function is K-partitionable then the problem is polynomial time in N. Adding restrictions on how often the manager may send suggestions makes the problem even more tractable. Note that the size of the optimal policy is nite and must be computed only once, even though the execution of a SEP may be in nite (e.g., with AnyUnlimited ).

"... In PAGE 7: ... Thus, the optimal policy may be computed via a depth- rst search over the graph in total time O(N3K). 2 Table1 summarizes the results presented above as well as a few other interesting cases ( Immediate and Synchronous ). These results rely on two key optimizations.... ..."

### Table 5.5 Performance on small test problems.

1998

Cited by 44

### Table 6: Comparison with aperture photometry

"... In PAGE 13: ...perture data for 5 of our galaxies. On the average, our magnitudes are 0.145 mag brighter in J and 0.061 in K. Table6 gives the di erences (literature magnitudes minus ours) for the 5 galaxies. The di erences are larger than expected from the scatter in the standard stars, and consistent with the surface brightness comparisons.... ..."

### Table 1 Summary of theoretical results for D-SEPs. The last two columns show the time complex- ity of nding the optimal policy for a D-SEP with N participants. In general, this problem is EXPTIME-hard but if the utility function is K-partitionable then the problem is polyno- mial time in N. (An MDP can be solved in time guaranteed to be polynomial in the number of states, though the polynomial has high degree). Adding restrictions on how often the manager may send suggestions makes the problem even more tractable. Note that the size of the optimal policy is nite and must be computed only once, even though the execution of a SEP may be in nite (e.g., with AnyUnlimited ).

2004

"... In PAGE 20: ... (If the system can send at most L suggestions to any participant, then the total time needed is O(N(2L+1)K).) 2 Table1 summarizes the results presented above as well as a few other interest- ing cases ( Immediate and Synchronous ). These results rely on two key opti- mizations.... ..."

Cited by 3

### Table 1 Summary of theoretical results for D-SEPs. The last two columns show the time complex- ity of nding the optimal policy for a D-SEP with N participants. In general, this problem is EXPTIME-hard but if the utility function is K-partitionable then the problem is polyno- mial time in N. (An MDP can be solved in time guaranteed to be polynomial in the number of states, though the polynomial has high degree). Adding restrictions on how often the manager may send suggestions makes the problem even more tractable. Note that the size of the optimal policy is nite and must be computed only once, even though the execution of a SEP may be in nite (e.g., with AnyUnlimited ).

2004

"... In PAGE 20: ... (If the system can send at most L suggestions to any participant, then the total time needed is O(N(2L+1)K).) 2 Table1 summarizes the results presented above as well as a few other interest- ing cases ( Immediate and Synchronous ). These results rely on two key opti- mizations.... ..."

Cited by 3

### TABLE I ABBREVIATIONSUSED IN THE PAPER

1998

Cited by 66

### Table 1: Summary of papers

"... In PAGE 3: ...Table 1: Summary of papers 2 Review of accepted papers Table1 summarizes the different methods used in the six papers presented in the workshop and the problem for which they have been applied. As one can notice, there is a interesting selection of graphical models, as there is a wide variety of them.... ..."

### TABLE III NOTATIONS IN THIS PAPER

2003

Cited by 29