Improved gossipings by short messages in 2-dimensional meshes

This paper discusses gossiping problems in two-dimensional meshes under two different models: one-port telephone model and full-port model. It is assumed in both models that only one packet can be transmitted through each link at one time step. Our algorithms are based on very similar ideas and improve on the previous results in (SIAM J. Comput. 27 (1998) 917; IEEE Trans. Parallel Distrib. Systems 10(12) (1999) 1252), respectively.