Many-to-Many Aggregation for Sensor Networks
Adam Silberstein and Jun Yang
Duke University
04/18/23 1
Sensor Network Tasks
04/18/23 3
ag
hc
e
i
m
jl
d
fk
b
k
l
m
fk(vb,vc,vd)
fl(va,vb,ve)
fm(vb,vc)
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
04/18/23 4
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
04/18/23 5
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
04/18/23 6
i j l
k
m
vi
a
b
c
i jwava+wbvb+wcvc
Multicast vs. Aggregation
• Intuitions– Favor multicast near source
• Many destinations per value
– Favor aggregation near destination• Destination has many values
04/18/23 7
a
b
ci j
wk,ava+wk,bvb+wk,cvc+wk,dvd
d
l
m
k
wl,ava+wl,bvb+wl,cvc
wm,ava
raw: va
agg: wk,bvb+wk,cvc+wk,dvd
agg: wl,bvb+wl,cvc
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
04/18/23 9
Single-Edge Problem
04/18/23 10
a b c d
k 1 1 1 1
l 1 1 1
m 1
SourcesDest.
S i→j
D i→j
a
b
ci j
d
l
m
k wk,ava+wk,bvb+wk,cvc+wk,dvd
wl,ava+wl,bvb+wl,cvc
wm,ava
~ i!j denotes producer-consumer relationship between i and j
Reduction
04/18/23 11
a b c d
k 1 1 1 1
l 1 1 1
m 1
SourcesDest.
S i→j
D i→j
c
a
b
dm
l
k
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
1
1c
1 1 1 l
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!
04/18/23 13
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
04/18/23 15
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
04/18/23 16
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
04/18/23 17
a b c d eoptimize optimize optimize optimize
a b c d e
optimizeoptimize
??
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
04/18/23 18
Varying # of Destinations
04/18/23 19
• Fix number of sources per destination, vary number of destinations • Fewer destinations favors aggregation• Optimal makes best decision at all settings
Varying # Sources
04/18/23 20
• Fix number of destinations, vary number of sources per• Fewer sources favors multicast• Optimal is again best at all settings
Suppression Override Policies
04/18/23 21
• 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
