All-to-all Broadcast Problems on Cartesian Product Graphs

• Main Authors: Jen-Chun Lin, 林仁俊
• Other Authors: Ta-Wei Kuo
• Format: Others
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/36723390071716391784

碩士 === 國立東華大學 === 應用數學系 === 101 === All-to-all communication occurs in many important applications in parallel processing. In this thesis, we study the all-to-all broadcast number(the shortest time needed to complete the all-to-all broadcast) of Cartesian product of graphs under the assumption that: each vertex can use all of its links at the same time, and each communication link is half duplex and can carry only one message at a unit of time. We give upper and lower bounds for the all-to-all broadcast number of Cartesian product of graphs and give formulas for the all-to-all broadcast numbers of some classes of graphs, such as the Cartesian product of two cycles, the Cartesian product of a cycle with a complete graph of odd order, the Cartesian product of two complete graphs of odd order, and the hypercube Q2n under this model.