"... In PAGE 23: ... A problem generator was written on the CM to generate random dense bipartite graphs in a controlled fashion. Table3 gives the performance measures of a problem with size 1024 1024, and 1 million arcs. Herewith the data are the average taken over ve test runs to hide the randomness.... ..."

"... In PAGE 8: ..., 1995) was used to learn descriptions of shape from positive and negative training examples. Since AQ15c operates on discrete attributes, the real-valued attributes, such as Length and Major ( Table1 ), required discretization. To further optimize the representation space, integer-valued attributes, like Area, can be projected into a smaller range.... ..."

"... In PAGE 18: ... For the sake of simplicity, we assume that the BOW-specification is 1-near-consistent. Given a maximization problem in Table1 11, our approxi- mation algorithm takes time O(N T (Nl+1)) to achieve a performance guarantee of ( l l+1) F BEST . Here, l is a constant that depends only on the performance guarantee parameter , T (Nl+1) denotes the running time of a heuristic which can process flat specifications of size O(Nl+1) and which has a performance guarantee F BEST .... ..."

"... In PAGE 14: ... This comes from the observation that a grid of a0 a7a57 a0 a30 a1 a39 elements obtained using only local a15 -refinement yields a solution energy of a8 a1 a49 a18 a30 a57 a0 a30 a8 and, when this is optimized, the solution energy only reduces to a8 a30 a49 a1 a1 a57 a22 a16 a39 . A summary of all of these computational results is provided in Table2 and an illustration of the meshes obtained using multilevel optimization with local a15 -refinement is given in Figure 7. 5.... In PAGE 18: ... It should be noted that, although quite complex to implement in a57 -d, the edge/face swap- ping component of the hybrid algorithm is crucial. This may be demonstrated, for example, by contrasting the results of Table2 with those obtained for the same test problem but without the connectivity optimization step included in Figure 1 (see [8] for further details). Such modified results are presented in Table 4 and clearly demonstrate the limitations of the adaptive algo- rithm when edge/face swapping is neglected.... ..."

"... In PAGE 10: ... This comes from the observation that a grid of a0 a22 a0 a30 a1 a3 elements obtained using only local a0 -refinement yields a solution energy of a8 a1 a13 a0 a30 a22 a0 a30 a8 and, when this is optimized, the solution en- ergy only reduces to a8 a30 a13 a1 a1 a22 a4 a1 a3 . A summary of all of these computational results is provided in Table2 and an illustration of the meshes obtained using multilevel opti- mization with local a0 -refinement is given in Figure 7. 5.... In PAGE 13: ... It should be noted that, although quite complex to implement in a22 -d, the edge/face swapping component of the hybrid algorithm is crucial. This may be demonstrated, for example, by contrasting the results of Table2 with those obtained for the same test problem but without the connectivity optimization step included in Figure 1. Such modified results are presented in Table 4 and clearly demonstrate the limitations of the adaptive algorithm when edge/face swapping is neglected.... ..."

"... In PAGE 8: ..., 1995) was used to learn descriptions of shape from positive and negative training examples. Since AQ15c operates on discrete attributes, the real-valued attributes, such as Length and Major ( Table1 ), required discretization. To further optimize the representation space, integer-valued attributes, like Area, can be projected into a smaller range.... ..."