Summary form only given. In a broadcasting problem, a message is sent from a source to all the other nodes in the network. Blind flooding is a classical mechanism for broadcasting, where each node retransmits received message to all its neighbors. We propose a new broadcasting and searching scheme over the Internet based on generalized relative neighborhood graphs (RNG). Messages are forwarded only on RNG links, and a link is in RNG if and only if it is not the longest edge in any triangle. We extend the existing definition of RNG, using geographic distance, to other metrics such as delay. RNG is a sparse connected structure based on local information at each node (distances to each neighbor and distances between neighbors). This new scheme is compared to the existing flooding, and rumor mongering (or gossip) schemes to evaluate its performance. Our parameterless RNG based scheme guarantees delivery to each node with considerably reduced number of messages with respect to flooding, and has comparable amount of message to rumor mongering/gossip scheme that does not guarantee delivery to each node and also uses parameters whose best value depend on underlying network density.