Journal of the Korean Society for Precision Engineering (한국정밀공학회지)

Korean Society for Precision Engineering (한국정밀공학회)
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Solving a Path Assignment Problem using s-t Cuts

그래프의 s-t 절단을 이용한 경로 배정 문제 풀이

  • Published : 2009.02.25
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Abstract

We introduce a noble method to find a variation of the optimal path problem. The problem is to find the optimal decomposition of an original planar region such that the number of paths in the region is minimized. The paths are required to uniformly cover each subregion and the directions of the paths in each sub-region are required to be either entirely vertical or entirely horizontal. We show how we can transform the path problem into a graph s-t cut problem. We solve the transformed s-t cut problem using the Ford-Fulkerson method and show its performance. The approach can be used in zig-zag milling and layerd manufacturing.

Keywords

References

  1. Held, M., "Voronoi diagrams and offset curves of curvilinear polygons," Computer-Aided Design, Vol. 30, No. 4, pp. 287-300, 1998 https://doi.org/10.1016/S0010-4485(97)00071-7
  2. Kim, H. C. and Yang, M. Y., "An Optimum 2.5D Contour Parallel Tool Path," J. of KSPE, Vol. 23, No. 2, pp. 35-42, 2006
  3. Kim, B. H. and Choi, B. K., "Machining Efficiency Comparison of Direction-parallel Tool Path with Contour-parallel Tool Path," Computer-Aided Design,Vol. 34, No. 2, pp. 88-95, 2002 https://doi.org/10.1016/S0010-4485(00)00139-1
  4. Dragomatz, D. and Mann, S., "A classified bibliography of literature on NC milling path generation," Computer-Aided Design, Vol. 29, No. 3, pp. 239-247, 1997 https://doi.org/10.1016/S0010-4485(96)00060-7
  5. Marshall, S. and Griffiths, J. G., "A survey of cutter path construction techniques for milling process," International Journal of Production Research, Vol. 32, Issue 12, pp. 2861-2877, 1994 https://doi.org/10.1080/00207549408957105
  6. Sarma, S. E., "The crossing function and its application to zig-zag tool paths," Computer-Aided Design, Vol. 31, No. 14, pp. 881-890, 1999 https://doi.org/10.1016/S0010-4485(99)00075-5
  7. Bang, T., "A Solution to the Plank Problem," Proceedings of American Mathematical Society, Vol. 2, pp. 990-993, 1951 https://doi.org/10.2307/2031721
  8. Kreyzig, E., "Advanced Engineering Mathematics," Jon Wiley & Sons, pp. 1156-1165, 1988
  9. Papadimitriou, C. H. and Steiglitz, K., "Combinatorial Optimization," Dover Publications, Inc., pp. 114-123, 1998
  10. Ford, L. R. and Fulkerson, D. R., "Maximal flow through a network," Canadian Journal of Mathematics, Vol. 8, pp. 399-404, 1956 https://doi.org/10.4153/CJM-1956-045-5