 
Summary: JOURNAL OF COMPUTER AND SYSTEM SCIENCES 43, 290298 (1991)
A Lower Bound for Radio Broadcast
NOGA ALON*
TelAviv University, RamatAviv, TelAviv 69978, Israel;
and Bell Communications Research, Morristown, New Jersey 07060
AMOTZ BARN· Y +
Stanford University, Stanford, California 94305
NATHAN LINIAL
IBM Almaden Research Center, San Jose, California 95120;
and the Hebrew University, Jerusalem 91904, Israel
AND
DAVID PELEG *
Stanford University, Stanford, California 94305
Received March 2, 1988; revised October 30, 1988
A radio network is a synchronous network of processors that communicate by transmitting
messagesto their neighbors, where a processor receives a message in a given step if and only
if it is silent in this step and precisely one of its neighbors transmits. In this paper we prove
the existence of a family of radius2 networks on n vertices for which any broadcast schedule
requires at least sZ(log* n) rounds of transmissions. This matches an upper bound of O(log* n)
rounds for networks of radius 2 proved earlier by BarYehuda, Goldreich, and Itai, in
