### Table 21: Non-approximability of various levels of the Function Bounded NP Query Hierarchy. y Applies only to complete problems.

"... In PAGE 82: ...P query hierarchy. Though the correspondence is not exact ([Kre88, p. 492]; [CP91, p. 243]), there is a pattern of approximability and non-approximability (see Table21 ). This pattern may assume greater signi cance in the light of future discoveries of lower limits on approximability.... ..."

### Table 21: Non-approximability of various levels of the Function Bounded NP Query Hierarchy. y Applies only to complete problems.

"... In PAGE 89: ...P query hierarchy. Though the correspondence is not exact ([Kre88, p. 492]; [CP91, p. 243]), there is a pattern of approximability and non-approximability (see Table21 ). This pattern may assume greater signi cance in the light of future discoveries of lower limits on approximability.... ..."

### Table 2. SQP optimization of exact and approximated design for the AUV problem

"... In PAGE 13: ... In either case the total simulation time to either hit or miss and also the closest encounter distance are calculated. The flnal results for the optimization run on the actual model and approximated kriging model are presented in Table2 . The global minimum of this problem is not currently known.... In PAGE 13: ... In further work a Pareto curve could be generated for difierent weightings of the multiobjective merit function. Furthermore, in Table2 it is shown that for the kriging surrogate model of the design space, an optimum design is found with an objective value of -32.... ..."

### Table 3: Results for the Combined Problem: exact and approximate solutions

2001

"... In PAGE 12: ... The two values of WBE that are obtained are almost identical, with the di erence so small as to be plausibly due to numerical errors. The results are in Table3 . Note the heavy usage of the residual network, which together with the uniformity of the earnings parameter constitute conditions in which we expect the approximate solution to be close to the optimum.... ..."

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### Table 1. Root Mean Square Error of the approximate solu- tions with respect to the exact euclidean distances at different grid resolutions.

### Table 1. Example of the assignment matrix for the assignment problem

2006

"... In PAGE 5: ... 4.1 Linear Optimization The assignment problem can be best represented by an assignment matrix shown in Table1 . Each entry in the table is the cost or gain of pairing the corresponding track and observation.... In PAGE 5: ... The objective is to minimize the cost or maximize the gain subject to a set of constraints. Given the assignment matrix shown in Table1 , the objective is to find a set X = {xij}, which are binary indicators, that maximizes or minimizes the objective function C = summationtextn i=1 summationtextm j=1 aijxij subject to some linear constrains. Linear programming was initially used to solve this problem.... ..."

Cited by 3

### Table 1. Example of the assignment matrix for the assignment problem.

2006

"... In PAGE 5: ... 4.1 Linear Optimization The assignment problem can be best represented by an assignment matrix shown in Table1 . Each entry in the table is the cost or gain of pairing the corresponding track and observation.... In PAGE 5: ... The objective is to minimize the cost or maximize the gain subject to a set of constraints. Given the assignment matrix shown in Table1 , the objective is to flnd a set X = fxijg, which are binary indicators, that maximizes or minimizes the objective function C = Pn i=1 Pm j=1 aijxij subject to some linear constrains. Linear programming was initially used to solve this problem.... ..."

Cited by 3

### Table 1: Exact vs. approximate LP solutions

"... In PAGE 13: ... However many of these were weakly violated and were discarded. On the problems corresponding to Table1 (27 nodes) the enumeration procedure was somewhat more successful, at least in terms of the nal output of APPROX. Typically the cutting step nished with some 100-200 cuts in the formulation.... ..."

### Table 2: Comparison of Exact, Approximate and Pre-procesed Identifications

"... In PAGE 7: ...vector compaction methods. In Table2 we show that high fault coverage of the MCNC benchmarks is obtained by using the smal eror spectrum asumption in UTS test patern generation. The table also reports the time and space needed to construct BDs (needed in one of our redundancy identifications).... ..."

### Table 2. Effect of number of service classes on QoS. There are a number of performance results including adaptability to nonstationary changes, pricing and cost e ciency, user population diversity, multi-dimensional QoS vectors (e.g., delay and jitter), problem instance generation and robustness which have been omitted due to space constraints. We refer the reader to [1] for a more detailed exposition.

1998

"... In PAGE 10: ...pigeon hole principle). Table2 shows the QoS re- quirement make-up of a subset of connections| ows 1, 8, and 10|whose stringency and diversity has been increased from what they were before. We observe that in the 2 service classe case, our architecture is unable to nd a service class assignment across the switches that satis es the QoS requirements of all three ows.... In PAGE 10: ... Indeed, it is not di cult to show that unless the service weights are allowed to be changed, satisfying all three QoS requirements is impossible. Table2 also shows that increasing the number of service classes from 2 to 3/4 helps resolve this problem. Having 4 service classes does not further improve system performance but nei-... ..."

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