Minimizing interference for the highway model in Wireless Ad-hoc and Sensor Networks Haisheng Tan, Tiancheng, Lou, Francis C.M. Lau, YuexuanWang, Shiteng.

Minimizing interference for the highway model in Wireless Ad-hoc and Sensor Networks

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

CS, The University of Hong Kong, Hong Kong, ChinaITCS, Tsinghua University, Beijing, China

Jan. 25th, SOFSEM, 2011

Outline

IntroductionProblem DefinitionsMinimizing the Average InterferenceMinimizing the Maximum InterferenceDiscussions and Future workQ & 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

Receiver-centric interference transmission radius of u

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 degreessparse topology

Observations

small node degreessparse topologyNearest 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)



In the highway model (Our work):

a polynomial-time exact algorithm




1. No-cross property




1. No-cross property when |ac| <=|

bc|+|cd|


In the highway model: 2. Calculate the total interference via the interference created

by each node



by each node



by each node

Independent sub-problems


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



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

OR



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

OR


Functions for DP G(s,t), s<t Compute the minimum total interference created by nodes

from s +1 to t-1, such that


Functions for DP G(s,t), s<t





The minimum average interference


Correctness Verified by the brute-force search running in time

the maximum node degree



Time complexity:




Time complexity:

(the numbers are the interference created by the nodes)




Time complexity:

(the numbers are the interference created by the nodes)

Can we do better ?? Y!


Minimizing the Maximum Interference

Harder!! No-cross property: still holds


Harder!! No-cross property: still holds Independent sub-segments: not found



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



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)


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] with their transmission radii










Functions: boolean F*(s,t), which is short for



OR



OR


Functions: boolean G*(s,t)







Check the whole line


Time complexity # of the different valid skeletons for a segment from s to t,

where s>0 and t<n-1:




Time complexity:




Time complexity:

Can we do better? No idea yet

Discussion and Future work

PlanarityMultiple optimal spanning trees

the min-max for the 6-node exponential chain

Discussion and Future work

PlanarityMultiple optimal spanning trees

Is min-max in 1D NP-hard? How about 3D networks?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!

Minimizing interference for the highway model in Wireless Ad-hoc and Sensor Networks Haisheng Tan, Tiancheng, Lou, Francis C.M. Lau, YuexuanWang, Shiteng.

Documents

interference slide

average interference

graph g slide

nearest neighbor slide

max interference

cross property slide

b c slide

d networks