# Minimizing interference for the

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21 Νοε 2013 (πριν από 4 χρόνια και 7 μήνες)

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Minimizing interference for the
-
hoc
and Sensor Networks

Haisheng Tan
, Tiancheng, Lou, Francis C.M. Lau,
YuexuanWang, Shiteng Chen

CS, The University of Hong Kong, Hong Kong, China

ITCS, Tsinghua University, Beijing, China

Jan. 25
th
, SOFSEM, 2011

Outline

Introduction

Problem Definitions

Minimizing the Average Interference

Minimizing the Maximum Interference

Discussions and Future work

Q & A

Introduction

Wireless Ad hoc and Sensor Networks

Introduction

Wireless Ad hoc and Sensor Networks

Environmental monitoring, intrusion detection, health
care, etc.

Smart Earth (IBM), Sense China …

Introduction

Energy !

Introduction

Energy !

Interference

Introduction

Energy !

Interference

-
centric interference

Problem Definitions

the
average interference
of a graph G

the
maximum interference
of a graph G

Problem Definitions

the
average interference
of a graph G

the
maximum interference
of a graph G

Problems:

Given nodes arbitrarily deployed along a 1D line (
the highway model
)

Connected

Min
-
Avg or Min
-
max interference

The optimal solution is actually
a spanning tree
.

Observations

Observations

small node degrees

Observations

small node degrees

sparse topology

Observations

small node degrees

sparse topology

Nearest Neighbor Forest
(each node is connected to its
nearest neighbor)

Observations

small node degrees

sparse topology

Nearest Neighbor Forest
(each node is connected to its
nearest neighbor)

a)

b)

c)

Minimizing the Average Interference

In 2D networks:

an asymptotically optimal algorithm with an approximation ratio of
O(log n)
(Moscibroda et al. 2005)

Minimizing the Average Interference

In 2D networks:

an asymptotically optimal algorithm with an approximation ratio of
O(log n)
(Moscibroda et al. 2005)

In the highway model (Our work):

a polynomial
-
time exact algorithm

Minimizing the Average Interference

In 2D networks:

an asymptotically optimal algorithm with an approximation ratio of
O(log n)
(Moscibroda et al. 2005)

In the highway model (Our work):

1. No
-
cross property

Minimizing the Average Interference

In 2D networks:

an asymptotically optimal algorithm with an approximation ratio of
O(log n)
(Moscibroda et al. 2005)

In the highway model (Our work):

1. No
-
cross property

when |ac| <=|bc|+|cd|

† † †

Minimizing the Average Interference

In the highway model:

2. Calculate the total interference via the interference
created
by each
node

Minimizing the Average Interference

In the highway model:

2. Calculate the total interference via the interference
created
by each
node

Minimizing the Average Interference

In the highway model:

2. Calculate the total interference via the interference
created
by each
node

Independent sub
-
problems

Minimizing the Average Interference

Two questions:

How to divide the whole line into sub
-
segments

How to connect the nodes inside each segment

Minimizing the Average Interference

Two questions:

How to divide the whole line into sub
-
segments

How to connect the nodes inside each segment

Functions for DP

F(s,t), s<t, which is short for

Compute the minimum total interference created by the nodes from s+1
to t
-
1 , such that

Minimizing the Average Interference

Two questions:

How to divide the whole line into sub
-
segments

How to connect the nodes inside each segment

Functions for DP

F(s,t), s<t, which is short for

OR

Minimizing the Average Interference

Two questions:

How to divide the whole line into sub
-
segments

How to connect the nodes inside each segment

Functions for DP

F(s,t), s<t, which is short for

OR

Minimizing the Average Interference

Functions for DP

G(s,t), s<t

Compute the minimum total interference created by nodes from s +1 to
t
-
1, such that

Minimizing the Average Interference

Functions for DP

G(s,t), s<t

Minimizing the Average Interference

Functions for DP

G(s,t), s<t

Minimizing the Average Interference

Functions for DP

G(s,t), s<t

The minimum average interference

Minimizing the Average Interference

Correctness

Verified by the brute
-
force search running in time

the maximum node degree

Minimizing the Average Interference

Correctness

Verified by the brute
-
force search running in time

Time complexity:

the maximum node degree

Minimizing the Average Interference

Correctness

Verified by the brute
-
force search running in time

Time complexity:

(the numbers are the interference created by the nodes)

the maximum node degree

Minimizing the Average Interference

Correctness

Verified by the brute
-
force search running in time

Time complexity:

(the numbers are the interference created by the nodes)

Can we do better ??
Y!

the maximum node degree

Minimizing the Maximum Interference

Harder!!

No
-
cross property: still holds

Minimizing the Maximum Interference

Harder!!

No
-
cross property: still holds

Independent sub
-

Minimizing the Maximum Interference

Harder!!

No
-
cross property: still holds

Independent sub
-

In 2D networks: NP
-
hard (Buchin 2008)

Bounded in

Minimizing the Maximum Interference

Harder!!

No
-
cross property: still holds

Independent sub
-

In 2D networks: NP
-
hard (Buchin 2008)

Bounded in

In 1D networks:

An appr. with ratio (von Richenbach, et al. 2005)

A sub
-
exponential
-
time exact algorithm (Our work
)

Minimizing the Maximum Interference

Check whether the min
-
max can be k, where 1<k<n

Minimizing the Maximum Interference

Check whether the min
-
max can be k, where 1<k<n

A
skeleton :

Record the nodes from s to t that can interfere with nodes outside [s,t]

Minimizing the Maximum Interference

Check whether the min
-
max can be k, where 1<k<n

A
skeleton :

Record the nodes from s to t that can interfere with nodes outside [s,t]

Minimizing the Maximum Interference

Check whether the min
-
max can be k, where 1<k<n

A
skeleton :

Record the nodes from s to t that can interfere with nodes outside [s,t]

Minimizing the Maximum Interference

Functions:

boolean

F*(s,t), which is short for

Minimizing the Maximum Interference

Functions:

boolean

F*(s,t), which is short for

OR

Minimizing the Maximum Interference

Functions:

boolean

F*(s,t), which is short for

OR

Minimizing the Maximum Interference

Functions:

boolean

G*(s,t)

Minimizing the Maximum Interference

Functions:

boolean

G*(s,t)

Minimizing the Maximum Interference

Functions:

boolean

G*(s,t)

Minimizing the Maximum Interference

Functions:

boolean

G*(s,t)

Check the whole line

Minimizing the Maximum Interference

Time complexity

# of the different valid skeletons for a segment from s to t, where s>0
and t<n
-
1:

Minimizing the Maximum Interference

Time complexity

# of the different valid skeletons for a segment from s to t, where s>0
and t<n
-
1:

Time complexity:

Minimizing the Maximum Interference

Time complexity

# of the different valid skeletons for a segment from s to t, where s>0
and t<n
-
1:

Time complexity:

Can we do better?
No idea yet

Discussion and Future work

Planarity

Multiple optimal spanning trees

the min
-
max for the 6
-
node exponential chain

Discussion and Future work

Planarity

Multiple optimal spanning trees

Is min
-
max in 1D NP
-
hard?

How to design efficient approximations to minimize the
maximum in 2D networks?

How to tackle interference minimization with other
network properties, such as small node degree and
spanner?

Q & A

Thanks!