1. An O(n 1.5 ) Deterministic Gossiping Algorithm for Radio Networks Ying Xu 田文錦

2. Radio Network 1 2 3 6 4 5 1.All processor work synchronously and have unique identifiers 2.Message collision 3.Assume strongly connected

3. Two Problems Broadcasting problem One distinguished source node has a message that needs to be sent to all other nodes. Gossiping problem Each node is initially given a different message that needs to be distributed to all other nodes. 每個 processor 在發送 message 的 時候是把自己和之前收到的一起 發送給所有相鄰的 processor

4. Round Robin Algorithm 1 2 3 6 4 5 Time Complexity O(Dn) = O(n 2 )

5. An O(n 1.5 logn) Time Gossiping Algorithm

6. 1 2 3 6 4 5 1 3 6 5 1 2 3 5 4 2 times round robin

7. Analysis r n 忽略 B(n) = O(nlogn) O(n)O(n)

8. 1 2 3 6 4 5 1 2 1 3 1 3 4 1 5 1 3 6 1 2 3 5 4 6

9. O(n 1.5 ) Time Algorithm B(n) = O(nlogn) r n 忽略 O(n)O(n) O(n)O(n) O(n)O(n)

10. Reference L. Gasieniec and A. Linags, On adaptive deterministic gossiping in ad hoc radio networks, Inform. Process. Lett., 2(2002),89-93 M. Chrobak, L. Gassieniec, and W. Rytter, Fast broadcasting and gossiping in radio networks, in Proc. 41st IEEE Symposium on Foundations of Computer Science, 200, pp575-581