1. * Distributed Algorithms in Multi-channel Wireless Ad Hoc Networks under the SINR Model Dongxiao Yu Department of Computer Science The University of Hong Kong

2. Wireless Ad Hoc Networks *  Application Scenarios –Data gathering –Monitoring, Surveillance –Disaster relief –Medical Applications –Many others

3. Wireless Ad Hoc Network * Composed by autonomous devices (nodes)  No built-in infrastructure  Communicate on shared channels -- collisions, interference, …  Limited hardware capability  Little knowledge on network  Asynchronous deployment  Mobility

4. SINR-style Models *  Signal-to-Noise-plus-Interference Ratio model  Message arrives if SINR is larger than β at the receiver

5. Problems Studied under SINR Model *  Problems Studied -- Dominating set -- Local broadcast -- Broadcast and Multiple-message broadcast -- Data aggregation and collection -- Capacity and link scheduling -- Connectivity -- Coloring -- Many others Most Work are done in single-channel networks

6. Motivation * Wireless devices can now operate on multiple channels -- Devices using the 802.11 standard have access to around a dozen channels -- Devices using the Bluetooth standard have access to around 75

7. Motivation * Under the graph-based model -- Symmetry breaking problems, such as  leader election  wake-up  maximal independent set  connected dominating set -- Communication problems, such as  broadcast and multiple-message broadcast Largely unexplored how to leverage the utilization of multiple channels to speed up communications, especially under the SINR model

8. Communication Model * n nodes are arbitrarily placed on the plane Multi-hop Synchronous communications No collision detection and physical carrier sensing Interference Model: SINR F channels --In each round, a node selects one channel to operate on: transmit or listen --Learns nothing about events on other channels

9. Challenges * Intuitively, it might think that F channels can always speed up communication for F times This is not easy -- In each round, each node can only operate on one channel For some problems, e.g., multi-hop wake up, multiple channels can not help giving faster algorithms even in the UDG model

10. Information Exchange * Given a network with n nodes, Each node initially holds a distinct information packet Each node then tries to send its packet to all nodes within a given range R Objective: minimize the time of accomplishing the information exchange task, over all network topologies A building block for many upper-layer applications -- Information broadcast -- Routing -- Network topology learning -- Many others…

11. Main Result * A randomized algorithm accomplishing information exchange in O((Δ/F+Δlogn/P)logn+log 2 n) rounds with high probability -- P is the bound on the number of packets in a message

12. Node Coloring * Given a network with n nodes and a distance parameter R, The node coloring problem is color all nodes such that any pair of nodes within distance R are assigned different colors Objective: minimize the number of colors and the time of the coloring process In theory, one of the most basic symmetry breaking problem in distributed computing In practice, abstract MAC protocol design, such as TDMA and FDMA

13. Main Result * A randomized algorithm properly coloring all nodes using O(Δ) colors in O(Δlogn/F+polylog n) rounds with high probability Comparing to the best O(Δlog n+log 2 n) result in single-channel networks

14. Future Work * Consider more fundamental problems in multi-channel networks, e.g., broadcast and multiple-message broadcast Consider lower bound Consider deterministic algorithms Consider multi-channel models with harsher restrictions, such as unreliable channels, asynchronous communications

15. * Thank You!