Concurrent Broadcast-Based Permutation Routing Algorithms in Radio Networks

• Venue: ISCC '03 Proceedings of the Eighth IEEE International Symposium on Computers and Communications
• Year: 2003

In their recent work in1999, Nakano, Olariuand Schwing showed that the permutation routingof n items pretitled on a Radio Network Model of pprocessors and k channels (RN(p,k)) with k \le p \sqrt {\frac{p}{2}}and if each processor has anO\left( {\frac{n}{p}} \right)-memory locations, the permutations of thesen pretitled items can also be done in 2\frac{n}{k} + k - 1broadcast rounds.They left the permutation routingon an O\left( {\frac{n}{p}} \right)-RN(p, k) when k \sqrt {\frac{p}{2}}and on an O\left( {\frac{n}{p}} \right)-RN(p, k) with k \sqrt {\frac{p}{2}}c as open problems.This paper shows how to handle efficiently these openproblems.In order to get efficiency, we show that thisopen problems become those of concurrent broadcaston multiple channels.More precisely, in a concurrentbroadcast environment, we show that the permutationrouting problem on RN(p, k) with k \sqrt p can becarried out in 2\frac{n}{k} + z - 1broadcast rounds.We alsoprove that the permutation routing problem on anO\left( {\frac{n}{p}} \right) - RN\left( {p,k} \right)with k \sqrt {\frac{p}{2}} can be performed in2\frac{n}{k} + q - 1broadcast rounds.Where z and q are suchthat p = zk + r(z) and p = q(2k) + r(q) respectively,with r(z)