E. P. M#cke, I. Saias, and B. Zhu. Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 274283, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....(insertion step) by linking M to the elements of the set F (M) of edges of the boundary of the simply connected region R(M) the union of the triangles in conAEict with M (see Fig.1) Based on this approach, there exists several incremental algorithms. They dioeer mainly in the way they nd R(M) [2, 11, 6, 7, 8, 10]. M M R(M) F (M) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 M 1 1 1 1 1 1 1 Figure 1: Inserting a site in the Delaunay triangulation. 3.2 Insertion step analysis We study here the cost of retriangulating R(M) which is independent of the location technique, and common to all incremental algorithms. The ....

....2 log k k is asymptotically optimal. 3. 3 Location step analysis The shuing buoeer strategy has also an inAEuence on the main part of the cost that comes from the point location strategy, we present below some results (without the detailed analysis by lack of space) The jump and walk strategy [10] locates a new point by searching its nearest neighbor in a sample of m points and walking from there to nd R(M) Choosing m = p n and k = p n log n gives the same complexity O(n p n) in the randomized and shuing buoeer analysis, this is the best randomized complexity without hypotheses on ....

E. P. M#cke, I. Saias, and B. Zhu. Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 274283, 1996.

....case is processed in an easier way. All the vertices belonging to the convex hull are incident to this point, and an innite triangle is associated to all the edges of the convex hull. Based on this approach, there exists several incremental algorithms. They dioeer mainly in the way they nd R(M) [2, 12, 7, 8, 9, 11]. The complexity of the location step, which strongly depends on the location strategy will be evoked in the next section. We rst focus our interest on the triangulation of R(M) M M R(M) F (M) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 M 1 1 1 1 1 1 1 Figure 2: Inserting a site in the Delaunay ....

....results. The straightforward strategy which examines all the triangles is quadratic in any cases and is not aoeected by the order. Location using walk is quadratic without hypothesis on the input distribution, and this bound is not improved by a random order hypothesis. The jump and walk strategy [11] locates a new point by searching its nearest neighbor in a sample of m points and walking from there to nd R(M) Choosing m = p n and k = p n log n gives the same complexity O(n p n) in the randomized and shuing buoeer analysis, this is the best randomized complexity without hypotheses ....

E. P. M#cke, I. Saias, and B. Zhu. Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 274283, 1996.

....algorithms have the two following properties: they are incremental and they do not used complicated data structures in addition to the triangulation itself. Among these algorithms, let us mention the historical algorithm of Green and Sibson [GS78] or some other variants [MSZ96, BD95, Dev98, DLM98, Lem97]. All perform a walk in the triangulation to accelerate point location. The advantage of that category of incremental Delaunay algorithms is that they may easily be turned into fully dynamic Delaunay algorithms. Since there is no complicated data structure for point location, the deletion of a ....

Ernst P. Mcke, Isaac Saias, and Binhai Zhu. Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 274--283, 1996.

....of the order of insertion, of ensuring an O(log 2 n) location time for any point, and of allowing deletions in an easier way than the Delaunay tree [DMT92] However, the additional memory is still important and the location structure is not especially simple. In 1996, Mcke, Saias and Zhu [MSZ96] proposed a very simple structure to handle triangulation of random points. The structure reduces to a random subset of 3 p n points, and pointers from these points to an incident triangle in the Delaunay triangulation. A new point is located by finding the nearest neighbor in the sample by ....

....3 = 32 6:2 p ff: Since the number of level is log ff n = log 2 n log 2 ff we get a cost of c 0 (n) 32 6:2 p ff) l log 2 n log 2 ff m which is close to its minimum ( 2 [13:3 log 2 n; 14 log 2 n] for ff 2 [18; 90] with the minimum occuring for ff 40. 4. 5 Comparison with [MSZ96] Similar counting of f.p.o. in Mcke et al. algorithm, using a random sample of fi 3 p n points, produces a cost of c MSZ (n) 5 4(3 n fin 1 3 p ) 7 n fin 1 3 p 5fi 3 p n = 17 3 p n 6:2 p fi 5fi which is close to its minimal value for 0:5 fi 1. As ....

[Article contains additional citation context not shown here]

Ernst P. Mcke, Isaac Saias, and Binhai Zhu. Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 274--283, 1996.

....of the order of insertion, of ensuring an O(log 2 n) location time for any point, and of allowing deletions in an easier way than the Delaunay tree [DMT92] However, the additional memory is still important and the location structure is not especially simple. In 1996, M#cke, Saias and Zhu [MSZ96] proposed a very simple structure to handle triangulation of random points. The structure reduces to a random subset of 3 p n points, and pointers from these points to an incident triangle in the Delaunay triangulation. A new RR n# 3298 4 O. Devillers point is located by nding the nearest ....

.... Delta 3 = 32 6:2 p ff: Since the number of level is log ff n = log 2 n log 2 ff we get a cost of c 0 (n) 29 6:2 p ff) l log 2 n log 2 ff m which is close to its minimum ( 2 [13:3 log 2 n; 14 log 2 n] for ff 2 [18; 90] with the minimum occuring for ff 40. 4. 5 Comparison with [MSZ96] Similar counting of f.p.o. in M#cke et al. algorithm, using a random sample of fi 3 p n points, produces a cost of c MSZ (n) 5 4(3 n fin 1 3 p ) 7 n fin 1 3 p 5fi 3 p n = 17 3 p n 6:2 p fi 5fi which is close to its minimal value for 0:5 fi 1. As ....

[Article contains additional citation context not shown here]

Ernst P. M#cke, Isaac Saias, and Binhai Zhu. Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 274283, 1996.

No context found.

E. P. M#cke, I. Saias, and B. Zhu. Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 274283, 1996.

No context found.

E. P. M#cke, I. Saias, and B. Zhu. Fast randomized point location without preprocessing in two- and three-dimensional Delaunay triangulations. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 274283, 1996.

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