Independent Spanning Trees on Recursive Circulant Graphs

• Main Authors: MengYu-Lin, 林孟玉
• Other Authors: YuLi-Wang
• Format: Others
• Language: zh-TW
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/94651256289912105016

碩士 === 國立臺灣科技大學 === 資訊管理系 === 91 === Two spanning trees of a given graph G = (V, E) are said to be independent if they are rooted at the same vertex, say r, and for each vertex v Î V\{r} the two paths from r to v, one path in each tree, are internally disjoint. A set of spanning trees of G is said to be independent if they are pairwise independent. Zehavi and Itai conjectured that any k-connected graph has k independent spanning trees rooted at an arbitrary vertex. This conjecture is still open for k > 3. Broadcasting in a distributed system is the message dissemination from a source node to every other node in the system. We can design a fault-tolerant broadcasting scheme based on independent spanning trees of a network. The fault-tolerance can be achieved by sending k copies of the message along k independent spanning trees rooted at the source node. The recursive circulant graph was proposed by Park and Chwa in 1994. Let G(cdm,d) denote a recursive circulant graph. Then G has N=cdm vertices, where 0<c<d and m>0, and every vertex i in G has 2m neighbors, i.e., i ± dk (mod N) (k = 0, 1, 2, ..., m-1). Since G(cdm,d) can be recursively partitioned into d induced subgraphs G(cdm-1,d), the circulant graph is named “recursive”. The connectivity of G(cdm,d) is 2m. Thus, if Zehavi's conjecture is true, then there are 2m independent spanning trees rooted at any vertex of the recursive circulant graph. In this thesis, we shall find out efficient algorithms to construct these independent spanning trees.