Distributed Algorithms in Multi-channel Wireless Ad Hoc Networks under the SINR Model

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 • Composedbyautonomous devices (nodes) • No built-in infrastructure • Communicateonshared 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+log2n) 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+log2n) 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! *