TY - GEN

T1 - Gossiping with bounded size messages in ad hoc radio networks

AU - Christersson, Malin

AU - Ga̧sieniec, Leszek

AU - Lingas, Andrzej

PY - 2002/12/1

Y1 - 2002/12/1

N2 - We study deterministic algorithms for the gossiping problem in ad hoc radio networks under the assumption that each combined message contains at most b(n) single messages or bits of auxiliary information, where b is an integer function and n is the number of nodes in the network.We term such a restricted gossiping problem b(n)-gossiping. We showthat √n-gossiping in an ad hoc radio network on n nodes can be done deterministically in time Õ(n 3/2) which asymptotically matches the best known upper bound on the time complexity of unrestricted deterministic gossiping†. Our upper bound on √n-gossiping is tight up to a poly-logarithmic factor and it implies similarly tight upper bounds on b(n)-gossiping where function b is computable and 1 ≤ b(n) ≤ √n holds. For symmetric ad hoc radio networks, we show that even 1-gossiping can be done deterministically in time Õ(n 3/2). We also demonstrate that O(nt)-gossiping in a symmetric ad hoc radio network on n nodes can be done in time O(n 2-t). Note that the latter upper bound is o(n3/2) when the size of a combined message is ω(n1/2). Furthermore, by adopting known results on repeated randomized broadcasting in symmetric ad hoc radio networks, we derive a randomized protocol for 1-gossiping in these networks running in time Õ(n) on the average. Finally, we observe that when a collision detection mechanism is available, even deterministic 1-gossiping in symmetric ad hoc radio networks can be performed in time Õ(n).

AB - We study deterministic algorithms for the gossiping problem in ad hoc radio networks under the assumption that each combined message contains at most b(n) single messages or bits of auxiliary information, where b is an integer function and n is the number of nodes in the network.We term such a restricted gossiping problem b(n)-gossiping. We showthat √n-gossiping in an ad hoc radio network on n nodes can be done deterministically in time Õ(n 3/2) which asymptotically matches the best known upper bound on the time complexity of unrestricted deterministic gossiping†. Our upper bound on √n-gossiping is tight up to a poly-logarithmic factor and it implies similarly tight upper bounds on b(n)-gossiping where function b is computable and 1 ≤ b(n) ≤ √n holds. For symmetric ad hoc radio networks, we show that even 1-gossiping can be done deterministically in time Õ(n 3/2). We also demonstrate that O(nt)-gossiping in a symmetric ad hoc radio network on n nodes can be done in time O(n 2-t). Note that the latter upper bound is o(n3/2) when the size of a combined message is ω(n1/2). Furthermore, by adopting known results on repeated randomized broadcasting in symmetric ad hoc radio networks, we derive a randomized protocol for 1-gossiping in these networks running in time Õ(n) on the average. Finally, we observe that when a collision detection mechanism is available, even deterministic 1-gossiping in symmetric ad hoc radio networks can be performed in time Õ(n).

UR - http://www.scopus.com/inward/record.url?scp=84869193784&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869193784&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84869193784

SN - 3540438645

SN - 9783540438649

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 377

EP - 389

BT - Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings

T2 - 29th International Colloquium on Automata, Languages, and Programming, ICALP 2002

Y2 - 8 July 2002 through 13 July 2002

ER -