### Table 3: Transition table for equilibria of the rectangles R

2000

"... In PAGE 25: ... This table has mE rows and m columns. Table3 shows the transitions for parts R 10 and R 20 . Each entry in T can be determined either by dynamic analysis, or by simulation.... In PAGE 25: ... Each entry in T can be determined either by dynamic analysis, or by simulation. The values in Table3 were generated by our planner using simulation. Figure 19 shows a trace of such a simulation: The initial pose of part R 20 is equilibrium e 3 =#283; 2; 2:86#29.... ..."

Cited by 23

### TABLE 15. Computational results for Set III Jigsaw-type test problems of Leung et al. (2003). For each problem instance, the table lists: the reference of the problem source; the instance number; the dimension (W H) of the stock rectangle; m, the number of types of rectangles to be packed; M, the total number of rectangles to be packed; the value of the optimal solution (all but Instance 1 of Lai and Chan (1997b) are zero-waste solutions); the solutions found by GRASP and HH; as well as the HH CPU time. Summary statistics are presented at the bottom of the table. Entries in boldface indicate best known value or better was obtained.

### Table 3. Transition table for equilibria of the rectangles R10 and R20, with finite field operators AB, BA, CD, and DC. For both rectangles, there exist a total of E D 8 equilibria and m D 4 finite field operators.

"... In PAGE 25: ... This table has mE rows and m columns. Table3 shows the transitions for parts R10 and R20. Each entry in T can be determined either by dynamic analysis, or by simulation.... In PAGE 25: ... Each entry in T can be determined either by dynamic analysis, or by simulation. The values in Table3 were generated by our planner using simulation. Figure 19 shows a trace of such a simulation: The initial pose of part R20 is equilibrium e3 D .... ..."

### Table 3: Transition table for equilibria of the rectangles R10 and R20, with nite eld operators AB, BA, CD, and DC. For both rectangles, there exist a total of E = 8 equilibria, and m = 4 nite eld operators.

"... In PAGE 24: ... This table has mE rows and m columns. Table3 shows the transitions for parts R10 and R20. Each entry in T can be determined either by dynamic analysis, or by simulation.... In PAGE 24: ... Each entry in T can be determined either by dynamic analysis, or by simulation. The values in Table3 were generated by our planner using simulation. Figure 19 shows a trace of such a simulation: The initial pose of part R20 is equilibrium e3 = (3; 2; 2:86).... ..."

### Table 3: Transition table for equilibria of the rectangles R10 and R20, with nite eld operators AB, BA, CD, and DC. For both rectangles, there exist a total of E = 8 equilibria, and m = 4 nite eld operators.

"... In PAGE 25: ... This table has mE rows and m columns. Table3 shows the transitions for parts R10 and R20. Each entry in T can be determined either by dynamic analysis, or by simulation.... In PAGE 25: ...nd m columns. Table 3 shows the transitions for parts R10 and R20. Each entry in T can be determined either by dynamic analysis, or by simulation. The values in Table3 were generated by our planner using simulation. Figure 19 shows a trace of such a simulation: The initial pose of part R20 is equilibrium e3 = (3; 2; 2:86).... ..."

### Table 3: Transition table for equilibria of the rectangles R10 and R20, with nite eld operators AB, BA, CD, and DC. For both rectangles, there exist a total of E = 8 equilibria, and m = 4 nite eld operators.

"... In PAGE 23: ... This table has mE rows and m columns. Table3 shows the transitions for parts R10 and R20. Each entry in T can be determined either by dynamic analysis, or by simulation.... In PAGE 23: ...nd m columns. Table 3 shows the transitions for parts R10 and R20. Each entry in T can be determined either by dynamic analysis, or by simulation. The values in Table3 were generated by our planner using simulation. Figure 19 shows a trace of such a simulation: The initial pose of part R20 is equilibrium e3 = (3; 2; 2:86).... ..."

### Table 3. Classi cation of Areas in Lemma 3 3. EXTENSION In the previous analyses, we require the shape exibility r to be at least two. This is justi ed by our assumption that each rectangle has a considerable amount of exibility in its shape. In this section, we modify the packing technique slightly to accommodate the case when r = 2 ? where is a small positive number. We are able to obtain a similar result as before. Due to the limitation in space, we will not show the proof here. Theorem 2 Given a set of soft rectangles of total area Atotal, maximum area Amax and shape exibility r = 2 ? where is a small positive number, there exists a slicing oorplan F such that

1997

"... In PAGE 5: ... The areas are again classi ed into groups. The areas, the widths and the heights of di erent groups are shown in Table3 . We use a similar packing technique as before.... ..."

Cited by 11

### TABLE 3. The symmetry operations R of a rectangle, and S of a square.

### Table 14. The Offline-Rect-Dp algorithm for o -line, rectangle-based dynamic programming for counter-planning domains.

1995

"... In PAGE 37: ... To store and retrieve these regions, a multi-dimensional rectangle tree is employed (Edelsbrunner, 1983) that provides a retrieval complexity of O(log2d(2d) + N), where d is the number of pieces in the region and N is the number of regions retrieved. The modi ed Offline-Rect-Dp algorithm is given in Table14 and begins by inserting the goal regions onto the minimizer apos;s and maximizer apos;s region queues, Qmin and Qmax: Then it enters a maximizing phase. This process is illustrated in Figure 13 for the king versus king-and-rook endgame.... ..."

Cited by 39