Derandomizing algorithms for perfect target set selection

• Main Authors: Yan-Liang Chen, 陳彥良
• Other Authors: Ching-LuehChang
• Format: Others
• Language: zh-TW
• Online Access: http://ndltd.ncl.edu.tw/handle/44083440679520698047

碩士 === 元智大學 === 資訊工程學系 === 100 === In this paper, let G(V,E) be a simple undirected graph, with only two possible states for each vertex: Active or inactive. Only a set S of vertices are activated initially. Thereafter, an inactive vertex is activated when at least α fraction of its neighbors are active. The process will continue until no more vertices can be active. If all vertices are activated before the process ends, we call S an α perfect target set, abbreviated as α perfect target set. Chang [6] proposed a polynomial time randomized algorithm which, given any connected undirected graph, finds an α"-" PTS whose expected size does not exceed (2√2+3)⌈α|V|⌉. We use the method of conditional expectation to derandomize the algorithm of Chang. Therefore, our deterministic polynomial time algorithm can find an α"-" PTS of size no more than (2√2+3)⌈α|V|⌉ in any undirected connected graph.