1. Slide 1 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

2. Slide 2 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

3. Slide 3 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?

4. Slide 4 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

5. Slide 5 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

6. Slide 6 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 w n : Weight assigned to node n  Captures various application-specific objectives of monitoring r n : Coverage requirement assigned to node n  Minimum number of sniffers required to reliably monitor node n K s,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

7. Slide 7 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 r n sniffers Theorem 1:  Complexity grows exponentially with the number of sniffers Maximum-Coverage Reliable Monitoring (MCRM): Find a sniffer- channel assignment that maximizes the total weight of nodes being covered Corollary 1: FCRM is NP-hard, even for |C| = 2 and r n = 2 for some node n MCRM is NP-hard, even for |C| = 2 and r n = 2 for some node n

8. Slide 8 Channel Assignment for Reliable Monitoring Corollary 2: Theorem 2:  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 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 r n = 2 for all n For MCRM with r n = 1 for all n, the weight function w is submodular. However, MCRM with r n ≥ 2 for some n, the weight function w is not submodular.

9. Slide 9 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

10. Slide 10 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.Linear Program (LP) relaxation ii.SemiDefinite Program (SDP) relaxation  tighter relaxation

11. Slide 11 Relaxation-and-Rounding Approach Two rounding algorithms designed  Randomized Rounding Algorithm (RRA) −Probabilistically round the optimal LP/SDP solution {y s,c * } such that: where Y s,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: 2.Find the sniffer-channel pair (s #, c # ) whose associated adjusted values achieve the maximum coverage improvement 3.Update the fractional values of sniffer s # to the adjusted values P(Y s,c = 1) = y s,c * y s,c * = 1 indicates that sniffer s tunes its radio to channel c

12. Slide 12 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., w n = 1) and the same coverage requirement of two (i.e., r n = 2)

13. Slide 13 Coverage in Random Network Look-ahead greedy algorithms show reasonably good performance (at least 92% of maximum coverage) SDP + GRA and LP + GRA show coverage comparable to the maximum achievable coverage (i.e., at least 95% and 94% of maximum coverage) Look-ahead greedy algorithms ILP optimum (maximum coverage) Rounding by GRA Rounding by RRA After rounding, GRA maintains the solution quality closer to the maximum coverage, while RRA results in the degradation of the solution quality Naïve greedy algorithm-2 (which picks the 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 greedy algorithm-2 shows reasonable coverage, while naïve greedy algorithm-1 shows poor coverage

14. Slide 14 Coverage in Scale-free Network SDP-based algorithms achieve a higher coverage improvement (by 2~5%) compared to LP-based algorithms, than in random network SDP-relaxation based algorithms LP-relaxation based algorithms Gap from the upper bound by SDP relaxation Gap from the upper bound by LP relaxation SDP relaxation shows a noticeable improvement on the upper bound of the maximum achievable coverage (by 4~7%)

15. Slide 15 Running Time in Random Network SDP-relaxation and rounding algorithms show reasonably fast running time LP-relaxation and rounding algorithms show the fastest running time CPU: 2.4 GHz Memory: 4 GB Bus: 1.07 GHz y-axis for look- ahead greedy algorithms (5x left y-axis) y-axis for the other algorithms LP-relaxation based algorithms 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 Look-ahead greedy algorithms SDP-relaxation based algorithms

16. Slide 16 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)

17. Slide 17 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

18. Slide 18 Thank You Contact Info: Donghoon Shin (donghoon.shin.2@asu.edu) Questions?