## Abstract

More and more wireless networks and devices now operate on multiple channels, which poses the question: How to use multiple channels to speed up communication? In this paper, we answer this question for the case of wireless ad-hoc networks where information dissemination is a primitive operation. Specifically, we propose a randomized distributed algorithm for information dissemination that is very near the optimal. The general information dissemination problem is to deliver \(k\) information packets, stored initially in \(k\) different nodes (the packet holders), to all the nodes in the network, and the objective is to minimize the time needed. With an eye toward the reality, we assume a model where the packet holders are determined by an adversary, and neither the number \(k\) nor the identities of packet holders are known to the nodes in advance. Not knowing the value of \(k\) sets this problem apart from broadcasting and all-to-all communication (gossiping). We study the information dissemination problem in single-hop networks with bounded-size messages. We present a randomized algorithm which can disseminate all packets in \(O(k(\frac{1}{\mathcal {F}}+\frac{1}{\mathcal {P}})+\log ^2n)\) rounds with high probability, where \(\mathcal {F}\) is the number of available channels and \(\mathcal {P}\) is the bound on the number of packets a message can carry. Compared with the lower bound \(\varOmega (k(\frac{1}{\mathcal {F}}+\frac{1}{\mathcal {P}}))\), the given algorithm is very close to the asymptotical optimal except for an additive factor. Our result provides the first solid evidence that multiple channels can indeed substantially speed up information dissemination, which also breaks the \(\varOmega (k)\) lower bound that holds for single-channel networks (even if \(\mathcal {P}\) is infinity).

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## References

Bar-yehuda R, Israeli A, Itai A (1993) Multiple communication in multi-hop radio networks. SIAM J Comput 22:875–887

Bermond J, Gargano L, Rescigno AA, Vaccaro U (1998) Fast gossiping by short messages. SIAM J Comput 27(4):917–941

Bluetooth Consortium (2007) Bluetooth Specification Version 2.1

Carzaniga A, Khazaei K, Kuhn F (2012) Oblivious low-congestion multicast routing in wireless networks. In: Proceedings of the thirteenth ACM international symposium on mobile ad hoc networking and computing (MobiHoc ’12). ACM, New York, NY, p 155–164

Chlebus BS, Kowalski DR, Rokicki MA (2006) Adversarial queuing on the multiple-access channel. In: Proceedings of the twenty-fifth annual ACM symposium on principles of distributed computing (PODC ’06). ACM, New York, NY, p 92–101

Christersson M, Gasieniec L, Lingas A (2002) Gossiping with bounded size messages in ad hoc radio networks. In: Widmayer P, Eidenbenz S, Triguero F, Morales R, Conejo R, Hennessy M (eds) Proceedings of the 29th colloquium on automata, languages and programming (ICALP’02). Springer-Verlag, Berlin, Heidelberg, p 377–389

Clementi AEF, Monti A, Silvestri Riccardo (2001) Selective families, superimposed codes, and broadcasting on unknown radio networks. In: Proceedings of the twelfth annual ACM-SIAM symposium on discrete algorithms (SODA ’01). Society for Industrial and Applied Mathematics, Philadelphia, PA, p 709–718

Daum S, Gilbert S, Kuhn F, Newport C (2012a) Leader election in shared spectrum radio networks. In: Proceedings of the 2012 ACM symposium on principles of distributed computing (PODC ’12). ACM, New York, NY, p 215–224

Daum S, Kuhn F, Newport C (2012b) Efficient symmetry breaking in multi-channel radio networks. In: Aguilera MK (ed) Proceedings of the 26th international conference on distributed computing (DISC’12). Springer-Verlag,Berlin, Heidelberg, p 238–252

Daum S, Ghaffari M, Gilbert S, Kuhn F, Newport C (2013) Maximal independent sets in multi-channel radio networks. In: Proceedings of the 2013 ACM symposium on principles of distributed computing (PODC ’13). ACM, New York, NY, p 335–344

Dolev S, Gilbert S, Khabbazian M, Newport C (2011) Leveraging channel diversity to gain efficiency and robustness for wireless broadcast. In: David Peleg (ed) Proceedings of the 25th international conference on distributed computing (DISC’11). Springer-Verlag, Berlin, Heidelberg, p 252–267

Fernandez-Anta A, Mosteiro MA, Ramon Munoz J (2013) Unbounded contention resolution in multiple-access channels. Algorithmica 67(3):295–314

Gobjuka H, Breitbart YJ (2010) Ethernet topology discovery for networks with incomplete information. IEEE/ACM Trans Netw 18(4):1220–1233

Goldberg LA, Jerrum M, Kannan S, Paterson M (2004) A bound on the capacity of backoff and acknowledgment-based protocols. SIAM J Comput 33(2):313–331

Hayes JF (1978) An adaptive technique for local distribution. IEEE Trans Commun COM 26:1178–1186

Holzer S, Pignolet Y-A, Smula J, Wattenhofer R (2011) Time-optimal information exchange on multiple channels. In: Proceedings of the 7th ACM SIGACT/SIGMOBILE international workshop on foundations of mobile computing (FOMC ’11). ACM, New York, NY, p 69–76

Holzer S, Locher T, Pignolet Y, Wattenhofer R (2012) Deterministic multi-channel information exchange. In: Proceedings of the twenty-fourth annual ACM symposium on parallelism in algorithms and architectures (SPAA ’12). ACM, New York, NY, p 109–120

IEEE 802.11 (1999) Wireless LAN MAC and physical layer specifications

Kowalski DR (2005) On selection problem in radio networks. In: Proceedings of the twenty-fourth annual ACM symposium on principles of distributed computing (PODC ’05). ACM, New York, NY, p 158–166

Martel CU (1994) Maximum finding on a multiple access broadcast network. Inf Process Lett 52(1):713

Mian AN, Baldoni R, Beraldi R (2009) A survey of service discovery protocols in multihop mobile ad hoc networks. Pervasive Comput 8(1):66–74

Shi W, Hua Q-S, Yu D, Wang Y, Lau FCM (2012) Efficient information dissemination in single-hop multi-channel radio networks. In: Wang X, Zheng R, Jing T, Xing K (eds) Proceedings of the 7th international conference on wireless algorithms, systems, and applications (WASA’12). Springer-Verlag, Berlin, Heidelberg, p 438–449

Yu D, Hua Q-S, Dai W, Wang Y, Lau FCM (2012) Dynamic contention resolution in multiple-access channels. In: Koucheryavy Y, Mamatas L, Matta I, Tsaoussidis V (eds) Proceedings of the 10th international conference on wired/wireless internet communication (WWIC’12). Springer-Verlag, Berlin, Heidelberg, p 232–243

## Acknowledgments

This work was supported in part by the National Natural Science Foundation of China Grants 61073174 and 61373027, Hong Kong RGC GRF Grant 714311, Shu Shengman Special Fund and Natural Science Foundation of Shandong Province Grant ZR2012FM023.

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Yan, Y., Yu, D., Wang, Y. *et al.* Bounded information dissemination in multi-channel wireless networks.
*J Comb Optim* **31, **996–1012 (2016). https://doi.org/10.1007/s10878-014-9804-3

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### Keywords

- Information dissemination
- Multi-channel wireless network
- Distributed algorithm
- Randomized algorithm