### Table 1. Worst-case complexities and the nature of the conditions in dominance. (Only node dominance can be used in solving (1) with general constraints.)

"... In PAGE 2: ... The complexity to find the optimal bundle is a72a74a73 a51 a75 a63 a75 a64a13a76 , which is polynomial in a75 a63 a75 . Table1 summa- rizes the complexities and the types of condition involved. When general constraints a45 a11 a13a15a14 a16a37a43 are present in (1), the Principle of Optimality cannot be applied to partial bundles because a dominated partial bundle may satisfy a general constraint that spans beyond the current stage, whereas a dominating partial bundle may not.... In PAGE 3: ... It then applies path dominance on the a75 a78 a26 a2a79a1a0 a2 a33 a75 a4a3 a75 a78 a26 a80a79a38a33 a75 pairs across adjacent stages in or- der to identify the best bundle. This leads to a worst- case complexity of a72 a6a5 a51 a75 a63 a75 a35 a8a7 a18 a61 a57 a53 a21 a57 a75 a78 a26 a10a9 a33 a75 a11a3 a75 a78 a26 a12a9 a35 a2 a33 a75 a13 (third column in Table1 ), which is better than the worst- case complexity when path dominance is applied alone. Note that node dominance, when applied in conjunction with path dominance, is necessary as well as sufficient be- cause dominating bundles involving dominating nodes sat- isfy the Principle of Optimality.... In PAGE 3: ... Hence, node dominance is only necessary but no longer sufficient for feasibility. Further, to find the optimal bundle, one needs to enumer- ate all possible combinations of bundles of a75 a78 a26 a2a79a38a33 a75 nodes in stage a28 a16 a36a48a30a50a49a47a49a50a49a23a30a52a51 , leading to a worst-case complexity of a72 a14a5 a51 a75 a63 a75 a16a15 a18 a53 a21 a57 a75 a78 a26 a12a9 a33 a75 a13 (last column in Table1 ). Here, we assume a worst-case complexity of a75 a63 a75 in stage a28 for finding one of the a78 a26 a80a79a38a33 nodes in an enumerated bundle.... In PAGE 6: ... Further, (18) and (20) refer to conditions on the gen- eral constraints that must be satisfied. c) As is discussed in Section 1, the use of node domi- nance helps reduce the search complexity from a72 a73 a75 a63 a75 a18 a76 to a72 a5 a51 a75 a63 a75 a15 a18 a53 a21 a57 a75 a78 a26 a10a9 a33 a75 a13 ( Table1 ). As a75 a78 a26 a12a9 a33 a75 , the number of points in a63 of stage a55 that are feasible and are local mini- mum of a0 a39 , is much smaller than a75 a63 a75 , node dominance helps reduce the base of the exponential complexity to a much smaller value.... ..."

### Table 3.8: Object-Flow analysis constraint templates corresponding to pure atomic expressions in Java.

in Approved by:

2002

### Table 1. Topological temporal relations between two pure intervals

"... In PAGE 3: ... Then events have thirteen possible qual- itative relations. The relations that are shown in Table1 capture the qualitative aspect of event pairs as before, meets, overlaps, starts, finishes, during, and equal, in terms of constraints on the end points of the constituent temporal intervals. These basic temporal relations have their corresponding converse relations, with equal being self-converse.... In PAGE 5: ...e., relations defined in Table1 ). The strategy for finding this subgraph follows the principles of logical consistency in a graph [14].... ..."

### Table9.Different definitions of coverage constraints

"... In PAGE 46: ... This is one of the reasons why pure cyclical schedules are generally not workable. In Table9 , we have grouped the approaches... ..."

### Table 2: Optimal Bonus Pools and Compensation with Dominant Strategy Implemen- tation

2006

"... In PAGE 23: ...nant strategy equilibrium is a bonus pool that is proper almost everywhere, with the one possible exception being the case where all four metrics record their lowest realization. Table2 shows the optimal bonus pool arrangements under the same assumptions as in Table 1, but with the addition of the constraint that the high efiort level has to be implemented as a dominant strategy. The main result of interest from Table 2 is that sllll 1 + sllll 2 = 46:62 lt; 55:65 = wll; while every one of the 15 other signal vector realizations results in a proper bonus pool.... ..."

### 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

### Table 2. Comparison of the feasible region of LP-QDMC and single QDMC strategy.

1980

Cited by 1

### Tableau 2 illustrates local restricted cumulativity. When the weaker constraints C and D are simul- taneously violated, their joint effect can be stronger than their linear sum. As a result, to- gether they are able to override the immediately dominating constraint B. This type of cumulativ- ity is similar to the effects of local conjunction. The result is a conjoined constraint C amp;D, which is ranked immediately above constraint B in the hierarchy.

### Table 8: Minimum-Expected-Shortfall Hedging Portfolios with Three Dominant Assets

2005

"... In PAGE 21: ... For all cases, the obtained optimal strikes of the hedging portfolio increases with maturity and decreases with strike of the basket option. For minimum-expected-shortfall hedging portfolio, two constraints are provided on the hedging cost and the numerical results are given in Table8 , respectively. The first one is HP7, the hedging cost of the static super-hedging portfolio on all 7 underlying assets.... ..."

### Table 6: The tc; ts; and tw co cients for the three schemes (one iteration of set training regime of BP) We note from table 6 that the coe cient of tc is identical for the three schemes. The coe cient of ts is smallest for the pure partitioning scheme and is largest for the pure checkerboarding scheme. Furthermore, note that the coe cients of tw are larger than the corresponding coe cients of ts for each scheme. The tw terms will dominate the ts terms if JI2 I pP gt; ts tw and J I2 Pc gt;

1994

Cited by 16