Toward Optimal Sniffer-Channel
Assignment for Reliable Monitoring in
Multi-Channel Wireless Networks
Donghoon Shin, Saurabh Bagchi and Chih-Chun Wang
Dependable Computing Systems Lab (DCSL)
School of Electrical and Computer Engineering
Purdue University
Slide 1
Outline

Introduction: Passive Monitoring in Wireless Networks

Existing Works and Motivation

Problem Statement: Optimal Sniffer-Channel Assignment
for Reliable Monitoring

Proposed Algorithms

Simulation Results

Conclusion
Slide 2
Introduction

Passive monitoring in wireless networks
 A set of sniffers are used to capture and analyze network traffic to
estimate network conditions and performance
− Sniffers are software or hardware devices that intercept and log packets
 Such estimates are utilized for efficient network operation such as:
−
−
−
−

Resource management
Network configuration
Fault detection/diagnosis
Network intrusion detection
A major issue with passive monitoring in multi-channel wireless
networks: “sniffer-channel assignment problem”
How to assign a set of channels to the sniffers’ radios so as
to capture as large an amount of traffic as possible?
Slide 3
Existing Studies on Monitoring in
Multi-Channel Wireless Networks




[Shin et al, MobiHoc’09]
Optimal placement and channel assignment of sniffers in wireless
mesh networks
[Chhetri et al, MobiHoc’10]
Two models of sniffers that assume different capabilities of
sniffers’ capturing traffic
[Arora et al., INFOCOM’11]
Trade-off between assigning sniffers’ radios to the channels known
to be busiest based on the current knowledge, versus exploring
channels that are under-observed
[Arora et al., GLOBECOM’11], [Shin et al, INFOCOM’12]
Distributed algorithms for optimal sniffer-channel assignment
Slide 4
Motivation and Solution Approach

All previous works assumed that sniffers are perfect

In practice, sniffers may probabilistically stop functioning and/or
generate erroneous reports on monitoring due to:




Poor reception (due to packet collisions or poor channel conditions)
Compromise by an adversary
Operational failure
Sleep mode for saving energy

In this paper, we allow for imperfect sniffers

For accurate and reliable monitoring, we provide sniffer redundancy
to each node
 That is, each node has to meet a coverage requirement, i.e., the
minimum number of sniffers required to reliably monitor the node
Slide 5
Notation & Terminology


S: Set of sniffers
N: Set of nodes
 Each node’s radio is tuned to a specific wireless channel


C: Set of available wireless channels
wn: Weight assigned to node n
 Captures various application-specific objectives of monitoring

rn: Coverage requirement assigned to node n
 Minimum number of sniffers required to reliably monitor node n

Ks,c: Coverage-set of sniffer s on channel c
 Contains the nodes that can be overheard by sniffer s operating on
channel c

Sniffer-channel assignment: A collection of coverage-sets that
include only one coverage-set for each sniffer
Slide 6
Channel Assignment for Reliable Monitoring

Full-Coverage Reliable Monitoring (FCRM): Find a sniffer-channel
assignment that covers all nodes in the network
 A node is covered if it is overhead by at least rn sniffers

Theorem 1:
FCRM is NP-hard, even for |C| = 2 and rn = 2 for some node n
 Complexity grows exponentially with the number of sniffers

Maximum-Coverage Reliable Monitoring (MCRM): Find a snifferchannel assignment that maximizes the total weight of nodes being
covered

Corollary 1:
MCRM is NP-hard, even for |C| = 2 and rn = 2 for some node n
Slide 7
Channel Assignment for Reliable Monitoring

Corollary 2:
For any ε > 0, it is NP-hard to solve MCRM within a factor of 7/8
+ ε of the maximum coverage, even for |C| = 2 and rn = 2 for all n

Theorem 2:
For MCRM with rn = 1 for all n, the weight function w is
submodular. However, MCRM with rn ≥ 2 for some n, the weight
function w is not submodular.
 Intuitively, submodularity is a diminishing-return property
 Submodularity allows to efficiently find provably (near-)optimal
solutions
− Similar to convexity in continuous optimization
 Known that non-submodular functions are difficult to deal with
Slide 8
Greedy Approach

Naïve greedy algorithms: at each iteration, pick one coverage-set that
maximizes:
 Coverage improvement
 Sum of the weights of the hitherto uncovered nodes

Look-ahead greedy algorithms: consider combinations of multiple
coverage-sets at each step
 Look-t-steps-ahead greedy algorithm
− At each step, picks one coverage-set through the following procedure:
1. Find a collection of t + 1 coverage-sets that achieve the maximum
coverage improvement for the current step and the next t steps
2. Among the coverage-sets in the selected collection, picks one
coverage-set that maximizes coverage improvement at the current step
 t-sniffers-at-one-step greedy algorithm
− At each step, picks a collection of at most t coverage-sets that maximize
the per-sniffer coverage improvement
Slide 9
Relaxation-and-Rounding Approach

Steps for relaxation-and-rounding algorithms to solve MCRM
1) Formulate MCRM into an integer program (IP)
2) Transform the IP into a relaxed program by removing the integer
constraints
−
Find as tight a relaxed program as possible, while keeping the relaxed
program solvable in polynomial time
3) Solve the relaxed program to find the optimal fractional solution
4) Round the non-integer values from Step 3 to obtain an integer
solution feasible for the original IP
−

In rounding, the goal is to minimize the degradation of the quality of
the resulting integer solution
Two relaxations devised
i.
ii.
Linear Program (LP) relaxation
SemiDefinite Program (SDP) relaxation  tighter relaxation
Slide 10
Relaxation-and-Rounding Approach

Two rounding algorithms designed

ys,c* = 1 indicates that sniffer
Randomized Rounding Algorithm (RRA) s
tunes its{y
radio*}tosuch
channel
− Probabilistically round the optimal LP/SDP solution
that:c
s,c
P(Ys,c = 1) = ys,c*
where Ys,c is the integer value resulted from rounding

Greedy Rounding Algorithm (GRA)
− At each iteration, rounds (at least) one fractional value as the followings:
1. For each sniffer-channel pair (s, c) whose value is not rounded to an
integer, adjust the fractional values of the sniffer s according to:
y *s, c  0,
y *s, c  y *s, c  /  y *s, c  c c
c C
2.
3.
(s#,
c#)
Find the sniffer-channel pair
whose associated adjusted values
achieve the maximum coverage improvement
Update the fractional values of sniffer s# to the adjusted values

Slide 11
Simulation Settings

Two metrics
 Coverage
 Running time

Two kinds of networks
 Random network: Nodes are randomly deployed in the network with a
uniform distribution
 Scale-free network: Nodes are deployed such that the distribution of
the nodes with degree d follows a power law in a form of d-r

Parameter settings
 Number of nodes: 40
 Number of channels: 3
 All nodes have the same weight of one (i.e., wn = 1) and the same
coverage requirement of two (i.e., rn = 2)
Slide 12
Coverage in Random Network
ILP optimum
(maximum coverage)
Rounding by GRA
Look-ahead
greedyalgorithm-2
algorithms
Naïve greedy
Rounding
bythe
RRA
(which picks
coverage-set that achieves the
maximum total weight of the uncovered nodes)
Naïve greedy algorithm-1
(which picks the coverage-set of the
maximum coverage improvement)
 Naïve
SDP
+rounding,
GRA greedy
and
LPalgorithms
+maintains
GRA shows
show
comparable
to to
the
maximum
Look-ahead
show
reasonably
good
performance
(at
After
GRA
thecoverage
solution
quality
closer
the
maximum
greedy
algorithm-2
reasonable
coverage,
while
naïve
achievable
coverage
at least
and 94% of
of the
maximum
least 92%
of
maximum
coverage)
coverage,
while
RRA(i.e.,
results
in the95%
degradation
solutioncoverage)
quality
greedy
algorithm-1
shows
poor
coverage
Slide 13
Coverage in Scale-free Network
Gap from the upper
bound by LP relaxation
Gap from the upper
bound by SDP relaxation
SDP-relaxation
based algorithms

LP-relaxation
based algorithms
SDP relaxation
SDP-based
algorithms
shows aachieve
noticeable
a higher
improvement
coverage on
improvement
the upper (by
2~5%) of
bound
compared
the maximum
to LP-based
achievable
algorithms,
coverage
than
(byin4~7%)
random network
Slide 14
Running Time in Random Network
y-axis for the
other algorithms
LP-relaxation
based algorithms
SDP-relaxation
based algorithms
Look-ahead
greedy algorithms

y-axis for lookahead greedy
algorithms
(5x left y-axis)
CPU: 2.4 GHz
Memory: 4 GB
Bus: 1.07 GHz

LP-relaxation and rounding algorithms show the fastest running time
SDP-relaxation and rounding algorithms show reasonably fast running time

Look-ahead greedy algorithms show the slowest running time
 Grow rapidly as the number of sniffers increases
 Running time of the t-sniffers-at-one-step greedy algorithm is almost half of the
running time of the look-t-steps-ahead greedy algorithm
Slide 15
Summary of Simulation Results

SDP + GRA achieves the highest coverage close to the maximum
coverage, but shows a (relatively) slow running time
 Favored, especially, for monitoring applications where a higher
coverage is more emphasized (e.g., critical security monitoring)

LP + GRA attains the coverage comparable to the coverage of the
SDP + GRA, and also shows a fast running time
 A good compromise between coverage and running-time
 Favored for monitoring applications requiring fast running-time (e.g.,
monitoring dynamic network environments)
Slide 16
Conclusion

Studied the optimal sniffer-channel assignment problem for reliable
monitoring in multi-channel wireless networks

Showed that the problem is fundamentally differs from the
previously studied problems that assume perfect sniffers and thus
do not need to consider sniffer redundancy

Proposed various approximation algorithms based on two basic
approaches:
 Greedy
 Relaxation and rounding

Present a comparative analysis of the proposed algorithms through
simulations
Slide 17
Thank You
Questions?
Contact Info:
Donghoon Shin
([email protected])
Slide 18