Cavalier, T., Grinde, R.: A New Algorithm for the Two-Polygon Containment Problem. Computers and Operations Research, 1996. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Solving Multiple Layer Containment Problems Using.. - Marques, Capela, Bernardo (2000) (Correct)
....to place, that can be viewed as physical elements. However, solving these large equations takes a large amount of time, what makes it useless in containment applications for the footwear industry; The Computational Geometry approach, which latest development in multi polygon rotational case [Cavalier96a] can place convex m gon P into convex n gon container Q by solving O(m 4 n 4 ) linear programs; The Operational Research approach, which can lead to practical results, but tend to become more complex when rotations are part of the equation; The Meta Heuristic approach, which can obtain ....
Cavalier, T., Grinde, R.: A New Algorithm for the Two-Polygon Containment Problem. Computers and Operations Research, 1996.
Rotational Polygon Overlap Minimization and Compaction - Milenkovic (1998) (1 citation) (Correct)
....exists. Chazelle [6] gave the first algorithm for the irregular (non convex) single polygon translational containment problem, and Avnaim and Boissonat [3] improve the running time. Agarwal et al. 2] give the best running times for single polygon rotational minimum enclosure. Grinde and Cavalier [10] give a rotational containment algorithm for two convex polygons. Finally, we give an algorithm for k polygon translational containment and minimum enclosure that is within a log factor of optimal [19] It is not clear how overlap minimization can improve the theoretical running times of these ....
R.B. Grinde, T.M. Cavalier, A new algorithm for the two-polygon containment problem, Comput. Oper. Res., to appear, 1996.
Rotational polygon containment and minimum enclosure using only .. - Milenkovic (1998) (5 citations) (Correct)
....which is equivalent to finding the minimum (scaled) enclosure. For convex Q the best running time is O(mn 2 log n) 1] and for non convex Q, O(m 2 n 2 ) 2] Grinde and Cavalier use an extensive case analysis and linear programming to place a single convex P [15] or convex P 1 and P 2 [16]. The running time of the first algorithm appears to be O(m 2 n 3 ) and it is not clear what the running time of the second is, but for one of its cases they are able to use parametric programming and find a solution by solving O(m 4 n 4 ) linear programs. For multi polygon translational ....
R.B. Grinde, T.M. Cavalier, A new algorithm for the two-polygon containment problem, Comput. Oper. Res., to appear, 1996.
Rotational Polygon Overlap Minimization - Milenkovic (1997) (Correct)
....which is equivalent to finding the minimum (scaled) enclosure. For convex Q the best running time is O(mn 2 log n) 1] and for non convex Q, O(m 2 n 2 ) 2] Grinde and Cavalier use an extensive case analysis and linear programming to place a single convex P [11] or convex P1 and P2 [12]. The running time of the first algorithm appears to be O(m 2 n 3 ) and it is not clear what the running time of the second is, but for one of its cases they are able to use parametric programming and find a solution by solving O(m 4 n 4 ) linear programs. This is the only previous result ....
R. B. Grinde and T. M. Cavalier. A new algorithm for the two-polygon containment problem. Computers and Operations Research, page to appear, 1996.
Rotational Polygon Containment and Minimum Enclosure - Milenkovic (1998) (5 citations) (Correct)
....which is equivalent to finding the minimum (scaled) enclosure. For convex Q the best running time is O(mn 2 log n) 1] and for non convex Q, O(m 2 n 2 ) 2] Grinde and Cavalier use an extensive case analysis and linear programming to place a single convex P [15] or convex P1 and P2 [16]. The running time of the first algorithm appears to be O(m 2 n 3 ) and it is not clear what the running time of the second is, but for one of its cases they are able to use parametric programming and find a solution by solving O(m 4 n 4 ) linear programs. For multi polygon translational ....
R. B. Grinde and T. M. Cavalier. A new algorithm for the two-polygon containment problem. Computers and Operations Research, page to appear, 1996.
Rotational Polygon Overlap Minimization and Compaction - Milenkovic (1998) (1 citation) (Correct)
....exists. Chazelle [5] gave the first algorithm for the irregular (non convex) singlepolygon translational containment problem, and Avnaim and Boissonat [2] improve the running time. Agarwal et al. 1] give the best running times for single polygon rotational minimum enclosure. Grinde and Cavalier [10] give a rotational containment algorithm for two convex polygons. Finally, we give an algorithm for k polygon translational containment and minimum enclosure that is within a log factor of optimal [19] It is not clear how overlap minimization can improve the theoretical running times of these ....
R. B. Grinde and T. M. Cavalier. A new algorithm for the two-polygon containment problem. Computers and Operations Research, page to appear, 1996.
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