Constrained Delaunay triangulated irregular network is one kind of dynamic data structures used in geosciences. The research on point and edges insertion in CD-TIN is the basis of its application. Comparing with the a...Constrained Delaunay triangulated irregular network is one kind of dynamic data structures used in geosciences. The research on point and edges insertion in CD-TIN is the basis of its application. Comparing with the algorithms of points and constrained edge insertion, there are very a few researches on constrained edge deletion in CD-TIN. Based on the analysis of the polymorphism of constrained edge, virtual points are used to describe the intersection of constrained edges. A new algorithm is presented, called as influence domain retriangulating for virtual point （IDRVP）, to delete constrained edges with virtual points. The algorithm is complete in topology. Finally, the algorithm is tested by some applications cases.展开更多
Let P（t, n） and C（t, n） denote the minimum diameter of a connected graph obtained from a single path and a circle of order n plus t extra edges, respectively, and f（t, k） the maximum diameter of a connected grap...Let P（t, n） and C（t, n） denote the minimum diameter of a connected graph obtained from a single path and a circle of order n plus t extra edges, respectively, and f（t, k） the maximum diameter of a connected graph obtained by deleting t edges from a graph with diameter k. This paper shows that for any integers t ≥4 and n ≥ 5, P（4, n） ≤n-8/t＋1＋ 3, C（t,n）≤n-8/t＋1＋3 if t is odd and C（t,n） ≤n-7/t＋2 ＋3 if t is even; [n-1/5] ≤P（4,n） ≤ [n＋3/5] [n/4]-1≤C（3,n）≤[n/4]; and f（t, k）≥ （t ＋ 1）k - 2t ＋ 4 if k≥3 and is Odd, which improves some known results.展开更多
文摘Constrained Delaunay triangulated irregular network is one kind of dynamic data structures used in geosciences. The research on point and edges insertion in CD-TIN is the basis of its application. Comparing with the algorithms of points and constrained edge insertion, there are very a few researches on constrained edge deletion in CD-TIN. Based on the analysis of the polymorphism of constrained edge, virtual points are used to describe the intersection of constrained edges. A new algorithm is presented, called as influence domain retriangulating for virtual point （IDRVP）, to delete constrained edges with virtual points. The algorithm is complete in topology. Finally, the algorithm is tested by some applications cases.
基金the National Natural Science Foundation of China (10271114)
文摘Let P（t, n） and C（t, n） denote the minimum diameter of a connected graph obtained from a single path and a circle of order n plus t extra edges, respectively, and f（t, k） the maximum diameter of a connected graph obtained by deleting t edges from a graph with diameter k. This paper shows that for any integers t ≥4 and n ≥ 5, P（4, n） ≤n-8/t＋1＋ 3, C（t,n）≤n-8/t＋1＋3 if t is odd and C（t,n） ≤n-7/t＋2 ＋3 if t is even; [n-1/5] ≤P（4,n） ≤ [n＋3/5] [n/4]-1≤C（3,n）≤[n/4]; and f（t, k）≥ （t ＋ 1）k - 2t ＋ 4 if k≥3 and is Odd, which improves some known results.
