Three-Dimensional Broadcasting with
Optimized Transmission Efficiency in
Dense Wireless Networks
Presented by Prof. Jehn-Ruey Jiang
National Central University, Taiwan
Outline
 Introduction
 Related Work
 Our Solution:
• Hexagonal Prism Ring Pattern
• 3D Optimized Broadcasting Protocol (3DOBP)
 Performance Comparisons
 Conclusion
2
Outline
 Introduction
 Related Work
 Our Solution:
• Hexagonal Prism Ring Pattern
• 3D Optimized Broadcasting Protocol (3DOBP)
 Performance Comparisons
 Conclusion
3
Broadcasting in 3D Wireless Networks
 3D wireless networks are deployed in
• Multi-storey building (or warehouse)
• Outer space (gravity-free factory)
• Ocean (underwater sensor network)
(acoustic but not wireless)
 We assume the network is dense;
i.e., there are many nodes within a
node’s wireless transmission area.
 3D broadcasting
• A source node disseminates a broadcast message
(e.g., control command or reprogramming code)
to every node in the network.
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 We’d like to apply a certain
structure as the underlay.
Let’s first examine
some special structures!
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Honeycomb – hexagonal lattice (grid)
Assume we’d like to use equal-radius
circles to cover a plane. If the centers of
circles are located at the centers of cells of
a hexagonal grid, then we’ve got the
minimum number of circles.
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As we are talking about 3D
broadcasting, we focus on the 3D
honeycomb (i.e., hexagonal grid with
thickness),
which
consists
of
hexagonal prisms.
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Cube (6 faces)
Rhombic Dodecahedron (12 faces)
Hexagonal Prism (8 faces)
Truncated Octahedron (14 faces)
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Flooding
 A simple protocol for broadcasting
• The source node sends out the broadcast message
• Every other node rebroadcasts the message once
• It is likely that every node gets the message
 Drawbacks:
• Broadcast storm problem (too many collisions)
• Low transmission efficiency
due to a lot of redundant
rebroadcast space
Redundant rebroadcast space
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Transmission Efficiency
BENEFIT
Effective_ Volumn
TE 
Number _ Nodes  Sphere _ Volumn
COST
The theoretical upper bound
of transmission efficiency is
0.61 for the 2D plane, and
0.84 for the 3D space.
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Optimized Transmission Efficiency
 Goal: Selecting as few as possible rebroadcast
nodes to forward the message sent by the source
node
• to fully span all nodes in the network (coverage)
• to keep all rebroadcast nodes connected (connectivity)
• to achieve the optimized transmission efficiency
to save energy
to reduce collision
to prolong the network lifetime
Selecting 4 (out of 8) nodes to
rebroadcast can span all network nodes.
Is this good enough?
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3D Connected Sphere Coverage Problem
 Transmission range of a node is assumed
as a sphere.
 The problem can be modeled as the
3D Connected Sphere Coverage Problem in Geometry.
 “How to place a minimum number of center-connected
spheres to fully cover a 3D space”
Hexagonal Prism
Cube
Rhombic Dodecahedron
Truncated Octahedron
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Outline
 Introduction
 Related Work
 Our Solution:
• Hexagonal Prism Ring Pattern
• 3D Optimized Broadcasting Protocol (3DOBP)
 Performance Comparisons
 Conclusion
13
Existing Work in 3D broadcasting
 Most are Polyhedron Space-Filling Approaches:
• Transmission range of a node is reduced to a polyhedron
• Trying to cover (or fill) the given space with a regular arrangement
of space-filling polyhedrons (and a node at the center of a
polyhedron is a rebroadcast node).
is reduced to
Transmission
Range
Sphere
to fill space
Cube
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Space-Filling Polyhedron (1/5)
 Polyhedron
• is a 3D shape consisting of a finite number
of polygonal faces
• E.g., cube
, hexagonal prism
,…
 Space-Filling Polyhedron
• is a polyhedron that can be used to fill a
space without any overlap or gap
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Space-Filling Polyhedron (2/5)
 Finding a space-filling polyhedron
is difficult
• In 350 BC, Aristotle claimed that the
tetrahedron is space-filling
• The claim was incorrect. The mistake
remained unnoticed until the 16th
century!
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Space-Filling Polyhedron (3/5)
 In 1887, Lord Kelvin asked:
• “What is the optimal way to fill a 3D space
with cells of equal volume, so that the
surface area between cells is minimized?”
Lord Kelvin
• Kelvin’s conjecture: 14-faced truncated octahedron is
the best way
Truncated Octahedron
(8 hexagons + 6 squares)
 Kelvin’s conjecture has not been proven yet. (Weaire–
Phelan structure has a surface area 0.3% less than that
of the truncated octahedron. However, the structure
contains two kinds of cells, irregular 12-faced
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dodecahedron and 14-faced tetrakaidecahedron.)
Space-Filling Polyhedron (4/5)
 What polyhedrons can be used to fill space ?
• Cubes, Hexagonal prisms, Rhombic dodecahedrons,
and Truncated octahedrons
Cube
6-faced
Hexagonal prism
8-faced
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Space-Filling Polyhedron (5/5)
 What polyhedrons can be used to fill space ?
• Cubes, Hexagonal prisms, Rhombic dodecahedrons, and
Truncated octahedrons
Rhombic dodecahedrons
Truncated octahedrons
12-faced
14-faced
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Observation
 In polyhedron space-filling approaches, the
transmission radius should be large enough to
reach neighboring nodes, which leads to high
redundancy and thus low transmission efficiency
transmission radius
A
A
B
B
redundant overlap region
Can we have better arrangement ?
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Outline
 Introduction
 Related Work
 Our Solution:
• Hexagonal Prism Ring Pattern
• 3D Optimized Broadcasting Protocol (3DOBP)
 Performance Comparisons
 Conclusion
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OUR SOLUTION:
3DOBP USING
HEXAGONAL PRISM RING PATTERN
Center node
Source node
Vertex node
S
Top View
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Hexagonal Prism Ring Pattern (1/4)
 The network space is divided into N layers, each of which is composed of
hexagonal prisms
 Layer 1 is covered by a set of rebroadcasting (forwarding) nodes
…
Layer N is covered by a set of rebroadcasting (forwarding) nodes
Layer 2
Layer 1
Problem: How to activate (or
choose) rebroadcasting
(forwarding) nodes based on the
hexagonal prism ring pattern to
fully cover the space in a layer?
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Hexagonal Prism Ring Pattern (2/4)
R: Transmission Radius
 Reducing spheres to hexagonal prisms
• The size of hexagonal prisms is
determined by R: L = R ; H = 2
3/2
H
●
R
3
L
 Basic procedures to cover a layer of prisms:
(1) Source node initially sends out the broadcast message
(2) Nodes are activated to rebroadcast to form hexagonal prism rings
to cover the entire space in a layer
Initial source
(center) node
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Hexagonal Prism Ring Pattern (3/4)
• To activate nodes to rebroadcast ring by ring (in 2D top view)
 To activate all center nodes of hexagons
 via some vertex nodes of hexagons
S
S
S
Source Node
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.
Activation Target Mapping
• q stands for the index of the 6 sectors,
each of which spans 60 degrees.
• Ck,i stands for the ith center node in the
ring of level k. For example, C0,0 is the
source node.
Sector 1
C3,5
C3,6
C3,4
Sector 2
Sector 0
C2,2
C3,7
C2,4
C1,2
C2,5
C2,6
S
C1,3
C2,1
C1,0
C1,5
C1,4
C3,10
C1,1
C2,0
C3,11 C2,8
C3,12
C3,0
A0
C2,11
C3,17
C2,7
A4
C3,1
C0,0
C3,9
3
C3,2
C2,3
C3,8
• The mapping is from one center node to an empty A
set or a set of two next-level nearest center nodes
to be activated.
• The source node activates 6 center nodes. Other Sector 3
center nodes activate 0 or 2 center nodes. But, a center
node cannot reach a next-level center node. A vertex
node located at the centroid of the three center nodes
(1 Tx and 2 Rx) should help forward the message.
C3,3
C2,9
C3,13
C2,10
C3,14
Sector 4
C3,16
C3,15
A5
Sector 5
.
Geometric Mapping
• The mapping is from one center node
to a location relative to the source
node s. (The source node is regarded
as the origin.)
starting axis of sector 3
• Zk,q stands for the location relative to
the source node of the hexagon center
of the level-k hexagon ring on the
starting axis of sector q.
starting axis of sector 0
3DOBP : Contention Control
 (1) Contention Control
• Location-based contention control
2
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Packet P < destination >
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Sender:
1. Sends a packet with the destination
of the rebroadcasting node
Receiver:
1. Calculates distance from itself to destination
2. Set backoff-timer: Shorter distance  Shorter backoff
3. Wait for backoff-timer to expire to rebroadcast
***The nodes with the shortest distance will rebroadcast
• If all nodes exchange their location information periodically, then a node
will certainly know that itself is the node closest to the destination and
can thus rebroadcast the packet at once.
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3DOBP : Intralayer Activation
 Intralayer activation at layer t
Packet P <Vt,1,0,
Vt,1,1, Vt,1,2>

S


Packet P <Ct,1,2,
Ct,1,3>
Packet P <Ct,1,0,
Vt,1,1
Ct,1,1>
Vt,1,0
S
S
Vt,1,2
Packet P <Ct,1,4,
Ct,1,5>
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3DOBP: Interlayer Activation
Layer 1
Layer 0
Source node
(or start node S0 at layer 0)
Layer -1
◎

◎

◎
Start node S1 at layer 1
Interlayer node I1
Interlayer node I-1
Start node S-1 at layer -1
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Short Summary
 3DOBP uses 3 major mechanisms to broadcast a
message (packet) throughout the network
2
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(1) Contention Control
(2) Intralayer Activation
(3) Interlayer Activation
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Outline
 Introduction
 Related Work
 Our Solution:
• Hexagonal Prism Ring Pattern
• 3D Optimized Broadcasting Protocol (3DOBP)
 Performance Comparisons
 Conclusion
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Transmission Efficiency
 Cube
circumsphere
Rc: radius of circumsphere
L: cube length
R: transmission radius
Transmission Efficiency
 Rhombic dodecahedron
circumsphere
Rc: radius of circumsphere
A rhombic dodecahedron can be constructed by two cubes of the
length L.
The radius Rc of the circumsphere is L.
The volume RDV of a rhombic dodecahedron is 2L3.
Transmision radius R=
Transmission Efficiency
 Truncated octahedron
circumsphere
Rc: radius of circumsphere
L: length
R: transmission radius
Transmission Efficiency
 Hexagonal prism
circumsphere
R
Rc: radius of circumsphere
L: length; H: height
R: transmission radius
Transmission Efficiency
 3DOBP
circumsphere
R: transmission radius
Rc: radius of circumsphere
We assume a hexagonal prism is with side length L and height H, and that the center of
each hexagonal prism is located by a node with transmission radius R.
L: length; H: height
Nc: the number of center nodes
Nv: the number of vertex nodes
Transmission Efficiency
 3DOPB
We consider a hexagonal prism ring patter of an infinite number
of levels of rings (J), and we apply the L’Hospital Rule to
derive the transmission efficiency TE.
Comparisons of Transmission Efficiency
 Transmission Efficiency
Approach
Transmission Efficiency
Truncated Octahedron-based
3/8π ≈ 0.119366
Hexagonal Prism-based
3/( 4 2 ) ≈ 0.168809
Rhombic Dodecahedron-based 3/( 4 2 ) ≈ 0.168809
Cube-based
3/4π ≈ 0.238732
Hexagonal Prism Ring-based
1/π ≈ 0.31831
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Conclusion
 We introduce the 3D Optimized Broadcast Protocol
(3DOBP) using the Hexagonal Prism Ring Pattern
(HPRP) to optimize the transmission efficiency
of 3D broadcasting in dense wireless networks
 The protocol is the best solution so far:
2D: 0.55/0.61
3D: 0.31/0.84
 Future work:
• Derive better upper bounds
• Design better protocols
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Related Publication





Jehn-Ruey Jiang and Tzu-Ming Sung, “Energy-Efficient Coverage and
Connectivity Maintenance for Wireless Sensor Networks,” Journal of Networks,
Vol. 4, No. 6, pp. 403-410, 2009.
Yung-Liang Lai and Jehn-Ruey Jiang, “Broadcasting with Optimized
Transmission Efficiency in Wireless Networks,” in Proc. of Fifth International
Conference on Wireless and Mobile Communications, 2009.
Yung-Liang Lai and Jehn-Ruey Jiang, “Broadcasting with Optimized
Transmission Efficiency in 3-Dimensional Wireless Networks,” in Proc. of
International Conference on Parallel and Distributed Systems (ICPADS 2009),
2009.
Jehn-Ruey Jiang and Yung-Liang Lai, “Wireless Broadcasting with Optimized
Transmission Efficiency,” Journal of Information Science and Engineering
(JISE), Vol28, No.3, pp. 479-502, 2012.
Yung-Liang Lai and Jehn-Ruey Jiang, “A 3-dimensional broadcast protocol with
optimised transmission efficiency in wireless networks,” International Journal of
Ad Hoc and Ubiquitous Computing (IJAHUC), Vol. 12, Issue 4, pp. 205-215, 2013.
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Thank You!
Jiang, Jehn-Ruey
Professor, NCU, Taiwan
ncujjr@gmail.com
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