Sparse Hypercube: A Minimal k-Line Broadcast Graph

This paper proposes a method for reducing the maximum degree of vertices in graphs that maintain optimal broadcast time when a vertex can call a vertex at distance at most k during any time unit. In the proposed method, we eliminate edges from binary ncubes. We show that, by this approach, the maximum degree of a vertex can be reduced from n to at most (2k 0 1)6 kp n 0k 7 , where 2 k < n, which asymptotically achieves the lower bound for any constant k.

• Type: Conference
• Year: 1999
• Where: IPPS
• Authors: Satoshi Fujita, Arthur M. Farley
• Keywords: Distributed And Parallel Computing, IPPS 1999, Maximum Degree, Optimal Broadcast Time, Time Unit