Tree spanner

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The tree k -spanner (or only k -spanner ) from the G chart is the T sub-level from G where the distance between each pair of nodes at most k times its distance at G.

Video Tree spanner

Known Results

There are several papers written about the key issue of the tree. One was titled Tree Spanners written by mathematicians Leizhen Cai and Derek Corneil, who explored the theoretical and algorithmic problems associated with tree rulers. Some of the conclusions from the paper are listed below:

(1) The 1-wrench tree, if any, is a minimum range tree and can be found in O (m log? (M, n)) time (in terms of complexity) for weighted graphs, where? (m, n) = min {i | log ^ {t} n \ leq m/n}.

(2) Sebuah pohon 2-kunci pas dapat dibangun dalam waktu linier, dan masalah t-kunci pohon adalah NP-lengkap untuk setiap bilangan bulat tetap ${\ displaystyle t & gt; 3}  ÂÂ$ .

(3) The complexity to find the minimal spanner tree in a digraph is O ((m n)? (M n, n)), where? (M n, n) is the functional inverse of the Ackermann function, m is the number of vertices of the graph, and n is the number of ends.

(4) Spanner minimum 1 dari grafik berbobot dapat ditemukan di ${\ displaystyle O (m \ kali n n ^ {2} \ kali masuk (n))}  ÂÂ$ waktu.

(5) For any fixed rational number ${\ displaystyle t & gt; 1}$ , it's NP-complete to determine whether a weighted graph contains t-key trees, even if all weights are positive integers.

(6) A tree spanner (or a minimum spanner tree) of a digraph can be found in linear time.

(7) A digraph contains at most one tree fitting.

(8) The quasi-tree wrench of the weighted digraph can be found in O (m \ times log? (M, n)) time.

(9) The 1-key tree of the G-weighted graph is the minimum range tree. Additionally, each weighted weighted 1-spanner graph contains a unique minimum spanning tree.

(10) Pohon 2-kunci (jika ada) grafik dapat ditemukan di ${\ displaystyle O (m n)}  ÂÂ$ waktu.

Maps Tree spanner

Lihat juga

• Grafik spanner
• Spanner geometrik

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Referensi

• Handke, Dagmar; Kortsarz, Guy (2000), "Penggaris pohon untuk subgraph dan masalah tutupan pohon terkait", Konsep Grafik-Teoretis dalam Ilmu Komputer: Lokakarya Internasional ke-26, WG 2000 Konstanz, Jerman, 15-17 Juni 2000, Prosiding , Catatan Kuliah dalam Ilmu Komputer, 1928 , pp. 206-217, doi: 10.1007/3-540-40064-8_20 .

Source of the article : Wikipedia