Many-to-Many Aggregation for Sensor Networks

Adam Silberstein and Jun Yang

Duke University

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Sensor Network Tasks

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Many-to-One TransmissionMany-to-Many Transmission

In-Network Control

• Multiple sources, multiple destinations– Each destination node computes aggregate

using readings from source nodes• Sources transmit directly to destinations

– Aggregate used as control signal to dictate behavior at destination

• i.e. adjust sampling rate

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Motivation

• Why spend transmission to control sensor sampling?– Radio typically dominant energy consumer– High-cost sensors: sap flux, swivel cameras

• Use low-cost sensors to tune sampling rates– Sap flux is negligible when soil moisture is low– Activate camera if motion sensors are triggered

• Why not out-of-network control?– Long round trips to root and back– Overtax nodes near root with forwarding

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Computing Aggregates In-Network

• Multicast– Sources required by multiple destinations– Build tree rooted at each source– Transmit value in “raw” form

• In-network Aggregation– Destination requires multiple sources– Build partial aggregates en-route

• TAG [Madden et al. 02]

– Aggregate destination- specific

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Multicast vs. Aggregation

• Intuitions– Favor multicast near source

• Many destinations per value

– Favor aggregation near destination• Destination has many values

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Edge Workloads

• How do we determine the workload for each edge?

• Multicast trees from each source dictate how data are routed– Minimality

• Trees have no extra edges

– Sharing • If two trees have paths between same pair of

nodes, paths are identical

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Single-Edge Problem

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Reduction

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Sources Destinations

weighted bipartitevertex cover

• Problem: Find minimal set of vertices such that all edges have one selected vertex

• Implications Select source = multicast: value transmitted raw over edge,

satisfying “column” Select destination = aggregate: values aggregated and

transmitted over edge, satisfying “row” Each selection contributes marginal cost of 1 to message

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Global Solution II

• Theorem: Optimal solutions for the individual MVC problems at each edge combine for consistent global plan

• Implications1. Solve global problem by solving edges in isolation

• Bipartite vertex cover solvable in polynomial time

2. When problem changes due to failures, route adjustments, workload adjustments, etc...• Only affected edges must be re-optimized!

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Plan Implementation

• For each s~d, store wd,s once in network– At edge where raw to aggregate transition

occurs

• 4 lightweight tables per node htuple_typei– Raw table: hs,gi– Pre-aggregation table: hs,d,wd,si– Partial aggregation table: hd,c,md,gi – Outgoing message table: hg,c,n’i

• Space consumed by tables no more than by pure multicast or aggregation plan

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Dynamic Features

• Suppression– Sources only transmit when readings change– Intuition: High suppression favors raw values– A node may override local solution

• Raws to be aggregated can be sent raw instead– Locally optimal decision, but must stay raw until

destinations, risking sub-optimal behavior downstream

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Dynamic Features

• Milestone– Rigid solution burdens routing layer– Don’t “solve” every routing hop

– Instead, set milestone nodes• Optimize over virtual edges, not physical edges

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Experimental Setup

• Simulation of Mica2 Motes– Accounting of bytes sent + received

• 68 nodes located as in 2003 Great Duck Island deployment (~20000 m2)

• Four Algorithms– Flood

• Each source transmits to ALL nodes

– Multicast– Aggregation– Optimal

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Varying # of Destinations

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• Fix number of sources per destination, vary number of destinations • Fewer destinations favors aggregation• Optimal makes best decision at all settings

Varying # Sources

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• Fix number of destinations, vary number of sources per• Fewer sources favors multicast• Optimal is again best at all settings

Suppression Override Policies

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• Policies dictate how much better locally optimal solution must be• Conservative (local must be dramatically better) gives benefit of of override at high suppression with little penalty at low