Secure Scheduling for Barrier
Coverage
Ding-Zhu Du
University of Texas at Dallas
This talk is based on paper :
Zhao Zhang, Weili Wu, Jing Yuan, Ding - Zhu Du, Breach - free Sleep - Wakeup
Scheduling for Barrier Coverage with Heterogene ous Wireless Sensors , submitted.
Outline
 Background
 Our Research
 Future
2
Background
Sensor network
Internet /
Satellite
Sink
phenomenon
User1
User2
Sensing Area
Biological
Systems
intruder
Area of interest
Open belt
Closed belt
Barrier Cover
A barrier-cover is a set of sensors covering
a curve connecting two open boundaries.
Homogeneous Sensor Network
All sensors have the same size of sensing disks,
the same size of communication disks, and the
same lifetime, say unit time lifetime.
x
x

s
s
t



1

1
1
x
t
There may exist several barrier covers.
Sleep-wakeup scheduling may increase
the lifetime of barrier coverage.
B1
B2
But, there is a security problem!
There is a breach in scheduling (B2, B1)
B1
a
B2
There is a breach in scheduling (B2, B1)
intruder
a
B2
There is a breach in scheduling (B2, B1)
B1
a
intruder
There is no breach in scheduling (B1, B2)
B1
a
B2
Both (B2, B1) and (B1,B2) contain a breach.
B1
a
b
B2
Crossing is bad!
• Donghyun Kim, Hyunbum Kim, Deying Li,
Sung-Sik Kwon, Alade O. Tokuta, and Jorge A.
Cobb, "Maximum Lifetime Dependable
Barrier-coverage in Wireless Sensor
Networks," Ad Hoc Networks (ADHOC), vol.
36, issue P1, pp. 296-307, January 2016.
• This paper gave 3 approaches to removing
crossing by delete some barrier-covers.
Our Research
Observation
B1
B2
B3
Removal crossing is sufficient, but not necessary!
(B3,B2,B1) is a breach-free scheduling.
Starting with following Goals
• Goal 1: Find necessary and sufficient condition
for a sleep-wakeup scheduling to be breachfree.
• Goal 2: Given a set of barrier-covers, find a
maximum subset with breach-free scheduling.
(complexity & Algorithm)
We completely reached goals
1 Give necessary and sufficient condition for a
sleep-wakeup scheduling to be breach-free.
2 Given a set of barrier-covers, find a
maximum subset with breach-free scheduling.
(This problem is equivalent to the longest path
problem in directed graph. )
3 Heterogeneous sensor system
Necessary and Sufficient
1
A sleep - wakeup schedule ( B1 , B2 ,..., Bk ) is not beach - free
iff there is a point a and an index i such that a is above Bi 1
and below Bi .
Bi
a
Bi 1
2
Sleep-wakeup scheduling
Given a set of barrier - covers, find a maximum subset wit h
a beach - free scheduling .
How to find?
Step 1. Using the necessary and sufficient condition,
construct a breach-free digraph.
Step 2. Find the longest path in the beach-free
digraph.
B1
B2
B3
B1
B3
B2
Breach Digraph
B3
B1
B2
Breach-free Digraph
B1
B2
B3
(B3,B2,B1) is a breach-free scheduling.
Equivalence
For any digraph G without loop, there exists a set of barrier covers with breach digraph isomorphic to G.
i V (G)  Bi
(i1 , j1 )
(i2 , j2 )
(i3 , j3 )
B0
For every (i, j )  E (G ), construct
s
ij
j1
s
ij
j2
Bj
(i , j )
s
B0
siij2
ij
i1
Fig. 6
Bi
s
ij
j1
s
(i , j )
ij
j2
Bj
(i , j )
s
ij
i1
siij2
Bi
Corollary
For any digraph G without loop, there exists a set of barrier covers with breach - free digraph isomorphic to G.
The max lifetime sleep - wakeup scheduling problem is
equivalent to the longest path problem in digraph.
The longest path problem
Given a digraph G, find a longest path in G.
Longest Path
The longest path problem in digraphs is NP - hard.
It is impossible to approximat e the longest path
in digraphs within a factor of n1 unless NP  P
where   0.
There exist parameteri zed algorithms for
the longest path problem in digraphs.
3
Heterogeneous Sensors
x
x
1

1
1
x

s


t

t
s
lifetime of sensor x
x
x

s
s
t




x
t
Path Decomposition
The max flow can be decomposed into at most E (G )
path - flows.
Each path - flow represents a barrier - cover
with lifetime equal to the flow value of the path - flow.
sleep-wakeup scheduling
Given a set of barrier - covers with possibly different
lifetime, find a max total lifetime subset wit h a breach free scheduling .
Given a digraph G with node weights, find a max node
- weight path.
The longest path problem
Given a digraph G, find a longest path in G.
Node-weight  edge weight
w
w
Recall
• Find max flow.
• Decompose flow into path-flows. Each pathflow gives a barrier-cover with lifetime (=flow
value).
• Find a max-lifetime subset of barrier-covers
with a breach-free scheduling.
Questions
• Is decomposition unique? If not, how to give
the best decomposition?
• Does max flow give a solution with longest
lifetime breach-free scheduling?
Thanks, End