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

Dongxiao Yu

Department of Computer Science

The University of Hong Kong

Wireless Ad Hoc Networks

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Application Scenarios– Data gathering– Monitoring, Surveillance– Disaster relief– Medical Applications– Many others

Wireless Ad Hoc Network

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• 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

SINR-style Models

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Signal-to-Noise-plus-Interference Ratio model Message arrives if SINR is larger than β at the receiver

Problems Studied under SINR Model

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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

Motivation

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• 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

Motivation

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• 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

Communication Model

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• 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

Challenges

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• 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

Information Exchange

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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…

Main Result

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• 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

Node Coloring

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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

Main Result

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•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

Future Work

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• 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

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Thank You!