Post on 01-Jan-2016
description
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
Environmental monitoring, intrusion detection, health care, etc.
Smart Earth (IBM), Sense China …
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
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)
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
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 Independent sub-segments: not found
Minimizing the Maximum Interference
Harder!! No-cross property: still holds Independent sub-segments: not found
In 2D networks: NP-hard (Buchin 2008) Bounded in
Minimizing the Maximum Interference
Harder!! No-cross property: still holds Independent sub-segments: not found
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
A skeleton : Record the nodes from s to t that can interfere with nodes
outside [s,t] with their transmission radii
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] with their transmission radii
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] with their transmission radii
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
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?
…