### Table 3: Performance of the Method of Sentinels, GENPACK and the L-Approach in the par- ticular problem of packing identical rectangles within a rectangle.

2005

"... In PAGE 12: ... We apply the Method of Sentinels, the orthogonal packing procedure GENPACK described in (Birgin et al, 2005a) and the L-Approach introduced in (Lins et al, 2003, Birgin et al, 2005c). Table3 shows the obtained results and Figure 9 illustrates the solutions. Table 3 by here.... In PAGE 12: ... Table 3 shows the obtained results and Figure 9 illustrates the solutions. Table3 by here. Figure 9 by here.... ..."

### TABLE 10. Computational results for problem Set II Large random problems of Type I. For each instance, the table lists: m, the number of types of rectangles to be packed; Q, the upper bound on the number of rectangles of a given type that can be packed; and M, the maximum number of rectangles that can be packed, as well as average deviations (in percent) from the upper bounds for solutions found by PH (Beasley, 2004), GA (Hadjiconstantinou and Iori, 2006), GRASP (Alvarez-Valdes et al., 2005), and HH. Total average percentage deviations are shown in the last line of the table. Entries in boldface indicate best known value or better was obtained.

### TABLE 11. Computational results for problem Set II Large random problems of Type II. For each instance, the table lists: m, the number of types of rectangles to be packed; Q, the upper bound on the number of rectangles of a given type that can be packed; and M, the maximum number of rectangles that can be packed, as well as average deviations (in percent) from the upper bounds for solutions found by PH (Beasley, 2004), GA (Hadjiconstantinou and Iori, 2006), GRASP (Alvarez-Valdes et al., 2005), and HH. Total average percentage deviations are shown in the last line of the table. Entries in boldface indicate best known value or better was obtained.

### TABLE 12. Computational results for problem Set II Large random problems of Type III. For each instance, the table lists: m, the number of types of rectangles to be packed; Q, the upper bound on the number of rectangles of a given type that can be packed; and M, the maximum number of rectangles that can be packed, as well as average deviations (in percent) from the upper bounds for solutions found by PH (Beasley, 2004), GA (Hadjiconstantinou and Iori, 2006), GRASP (Alvarez-Valdes et al., 2005), and HH. Total average percentage deviations are shown in the last line of the table. Entries in boldface indicate best known value or better was obtained.

### TABLE 13. Average results for problem Set II Large random problems of Types I, II, and III. For each instance, the table lists: m, the number of types of rectangles that can be packed; Q, the upper bound on the number of rectangles of a particular type that can be packed; and M, the total number of rectangles that can be packed; as well as average deviations (in percent) from the upper bounds for solutions found by algorithms PH (Beasley, 2004), GA (Hadjiconstantinou and Iori, 2006), GRASP (Alvarez-Valdes et al., 2005), and HH. Averages are computed over all Type I, II, and III results. Entries in boldface indicate best known value or better was obtained.

### Table 1: Parameters for the rectangle generator

"... In PAGE 3: ...1 The Rectangle Generator At the Ecole Nationale Sup erieure des T el ecommunications (ENST) we have implemented a tool to generate sets of rectangles with edges parallel to the axes. Users can specify the parameters listed in Table1 . For the rst ve parameters, the user has to specify some statistical distribution with the usual parameters.... ..."

### Table 1: Parameters for the rectangle generator

"... In PAGE 3: ...1 The Rectangle Generator At the Ecole Nationale Sup erieure des T el ecommunications (ENST) we have implemented a tool to generate sets of rectangles with edges parallel to the axes. Users can specify the parameters listed in Table1 . For the rst ve parameters, the user has to specify some statistical distribution with the usual parameters.... ..."

### Table 2. Results of Branch-and-Bound for Various Partitioning Schemes Two Rectangles Four Rectangles Triangles and Rectangles

"... In PAGE 25: ... This triangular partitioning scheme was compared against a two-rectangle partitioning scheme, where the rectangle was divided into two subrectangles by bisecting the longest edge and a four-rectangle scheme obtained by bisecting the original rectangle along both edges. The results of the computational experiment are given in Table2 . Figure 9 shows a performance profile (see [10] for an explanation of performance profiles) of the number of nodes of the branch-and-bound tree, and Figure 10 shows a profile of the CPU time used by each of the three partitioning methods.... ..."

### Table 1. Test Suites for Rectangle Source and Varying Orientations

1993

"... In PAGE 9: ... Consequently only uniform linear results are reported. Table1 . Test Suites for Rectangle Source and Varying Orientations Test 1 Linear Test 1 Struct Test 2 Linear Test 2 Struct Test 3 Linear Test 3 Struct Test 4 Linear Test 4 Struct Test 5 Linear Test 5 Struct 9.... In PAGE 10: ... In Test 4 the receiver plane slowly rotates towards the source and finally in Test 5 a rotated plane moves under the source. In Table1 , we see the results for a total of 75 tests. The first and last few cases in each suite are typically situa- tions where the tail regions are dominant.... ..."

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