### Table 3: Constraints on the duration and the start time of the plan

2005

"... In PAGE 54: ... Again values in brackets represent the results obtained from a second CSP resolution. Table3 represents a restriction on the plan duration plus a restriction on the start time of the plan. First column de- note that the makespan must be below 250 seconds and the start time of the plan at any point later than time 10.... In PAGE 54: ...tart time of the plan at any point later than time 10.00. The missing data for the start/end time rows correpond to those cases where a plan is not found. We can also observe that CPU time is shorter in Table 1 than Table3 . In general, if only restrictions on the duration are considered then appropriate timing intervals combina- tions are found faster.... In PAGE 54: ...258 t.u.) is very close to the limit and the CPU time is very high (543 seconds) which indicates that almost all possible combinations of timing intervals have been searched until nding a solution. From comparing results in Table 2 and Table3 we can deduce that when there are restrictions on the start and end time of the plan the computation is faster ICAPS 2005 50... In PAGE 67: ... The set j100. Table3 and Table 4 show the results ob- tained in the case of the benchmark j100. In this case the difference of the two problem are smoother than in the pre- vious benchmark.... In PAGE 68: ...17 413.47 Table3 : ISESiC j100 j exj j dtj cpu npc mk GRASPiC+MINIDflex 0.207 0.... In PAGE 83: ...10 75.80 Table3 . Efficiency and stability on add STC restrictions.... ..."

### Table 2: A set of representative relaxations. Constraints

"... In PAGE 2: ... For example, we might require that every constraint that appears in a relaxation appears at least once in a relax- ation in our chosen subset. This is the scenario presented in Table2 . However, this approach has the potential to mislead the user.... ..."

### Table 4: The RCC-8 relations represented as interior algebra constraints RCC Rel. Equivalent Algebraic Constraint(s)

"... In PAGE 22: ... P and DC corre- spond directly to I formulae as given in Table 11. PO must rst be analysed as :DR ^ :P ^ :Pi as shown in Table4 . The (positive) model constraints correspond to the formula set fa ) b; b _ cg and the (negative) entailment constraints (including the non-null con- straints) to fa ) c; c ) a; (a ^ c); a; b; cg.... ..."

### Table 3: A set of representative exclusion sets. Constraints

### Table 4: The RCC-8 relations represented as interior algebra constraints

"... In PAGE 22: ... P and DC corre- spond directly to I formulae as given in Table 11. PO must rst be analysed as :DR ^ :P ^ :Pi as shown in Table4 . The (positive) model constraints correspond to the formula set fa ) b; b _ cg and the (negative) entailment constraints (including the non-null con- straints) to fa ) c; c ) a; (a ^ c); a; b; cg.... ..."

### Table 4. The RCC-8 relations represented as interior algebra constraints

1998

"... In PAGE 7: ... Hence each RCC-8 relation can be speci ed by a conjunction of interior algebraic equalities and disequalities. These are given in Table4 . Note that the theory of interior algebras and the constraints corresponding to the RCC-8 relations can be represented simply as a set of equational literals (those stemming from the theory contain variables which are implicitly universally quanti ed, whereas those associated with the RCC-8 relations are ground literals).... In PAGE 9: ... P and DC correspond directly to I formulae as given in Table 6. PO must rst be analysed as :DR ^ :P ^ :Pi as shown in Table4 . The (positive) model constraints correspond to the formula set fa ) b; b _ cg and the (negative) entailment constraints (including the non-null constraints) to fa ) c; c ) a; (a ^ c); a; b; cg.... In PAGE 11: ...11 Nebel apos;s analysis also provides the basis for a proof that the RCC-8 relation set (interpreted in accordance with Table4 ) is 3-compact w.... ..."

Cited by 7

### Table 2: Problem sizes of the #0Cnancial planning model

1999

"... In PAGE 16: ...1 Model Sizes Di#0Berent sizes of the ALM problem are created byvarying the number of branches p emanating from each node in the event tree for the 6-period model. Table2 reports the size of the deter- ministic equivalent linear program. This size refers to a standard linear program with equality constraints: slacks are added to the inequalities and free variables are split.... In PAGE 16: ... This size refers to a standard linear program with equality constraints: slacks are added to the inequalities and free variables are split. The large scale models reported in Table2 not only require considerable computational e#0Bort to be solved, they also need a huge amountofworkspace to be stored. The second column of Table 3 reports the 1 We thank the University of Cyprus for providing us access to their parallel machine, funded by the EU- project High Performance Computing for Financial Planning under Uncertainty.... In PAGE 17: ...way immediately afterwards. This is the approach used to solve the largest problems. 5.2 Model Generation and Solution Times We solved the 6-period ALM problems reported in Table2 with the L-shaped method on a Parsytec CC16 parallel machine with 16 processors. 2 In panel A of Table 4 we report the solution times of models that are split into a #0Crst stage master problem and a set of second stage subproblems starting at time 2.... ..."

### Table 2. Performance Characteristics for the MCASE Model coverageb

2006

"... In PAGE 4: ... MCASE Prediction Model. The performance characteristics for the MCASE prediction model are listed in Table2 . Both the training set and prediction set were predicted with compa- rable performances.... ..."

Cited by 2

### Table 1 Crop plans from the planning model

in Abstract

"... In PAGE 4: ..., 1981). Results are presented in Table1 . Max- imum (ZU) and minimum values (ZL) that can be obtained by each objective are denoted with sym- bol (+) and ( ), respectively.... ..."

### Table 1: Hard and soft constraints (the third column n represents the number of constraints)

1998

"... In PAGE 4: ... It is a design deci- sion why and when those constraints should be considered hard. Table1 lists all constraints used in our modeling sys- tem. Again, we use the notations ^ m and ^ n to represent the given line direction m and plane normal n, respectively.... ..."

Cited by 61