Sensors Everywhere

1. Sensors Everywhere Panos Pardalos Distinguished Professor Center for Applied Optimization Dept. of Industrial and Systems Engineering, University of Florida DIMACS/DyDAn Workshop: Approximation Algorithms in Wireless Ad Hoc and Sensor Networks April 22 - 24, 2009

2. Sensors Everywhere • Introduction • Data Fusion • Sensor Network Design • Sensor Network Localization • Sensor Scheduling • Network Interdiction

3. Sensors Everywhere • Introduction • Data Fusion • Sensor Network Design • Sensor Network Localization • Sensor Scheduling • Network Interdiction

4. What are sensors? • A sensor is a device that responds to a physical stimulus (e.g. heat, light, sound, pressure, magnetism, or motion). It collects and measures data regarding some property of a phenomenon, object, or material. Typical sensors are cameras, radiometers and scanners, lasers, radio frequency receivers, radar systems, sonar, thermal devices, seismographs, magnetometers, gravimeters, and scintillometers. • The term "Remote Sensing" indicates that the measuring device is not physically in close proximity with the phenomenon being observed.

5. Each year hundreds millions of sensors are manufactured. They are in domestic appliances, medical equipment, industrial control systems, air-conditioning systems, aircraft, satellites and toys. • Sensors are becoming smarter, more accurate and cheaper. They will play an ever increasing role in just about every field imaginable.

6. How can nanotechnology improve the performance of sensors? • The application of nanotechnology to sensors should allow improvements in functionality. In particular, new biosensor technology combined with micro and nanofabrication technology can deliver a huge range of applications. They should also lead to much decreased size, enabling the integration of nanosensors into many other devices.

7. Sensor Networks • A sensor network is a collection of some (sometimes even hundreds & thousands) smart sensor nodes which collaborate among themselves to form a sensingnetwork.

8. Sensor Applications • Homeland security • Radiation detection and standards • X-ray detectors and imaging • Integrated System Health Management (ISHM) • Multisensor Data Fusion • Nondestructive Evaluation and Remote Sensing • Commercial Development • Environmental sensing • Medical/healthcare sensing • Robotic and remote sensing Tomography • Domestic electronics and smart homes • Crime prevention • Automotive and aerospace • Leisure industry and toys • Food and agriculture • Marine • Energy and Power

9. Sensors Everywhere • Introduction • Data Fusion • Sensor Network Design • Sensor Network Localization • Sensor Scheduling • Network Interdiction

10. Data Fusion • Combine information from many sensors to have a better picture than the sensors were used individually • More accurate, more complete, more reliable • Sensors fusion algorithms use machine learning techniques: • Statistical inference and forecasting • Kalman Filter • Bayesian Networks • Neural Networks • Fuzzy Logic • Dempster-Shaffer

11. Sensor Network Design • Finding optimal network topology accounts the following characteristics: • Fault tolerance • The ability to sustain sensor network functionalities without any interruption due to sensor node failures • Scalability • A well designed architecture must be able to work with large number of nodes • Costs constraints • Deployment, Maintenance, etc • Hardware constraints • Size, Weight, Transmitting, etc

12. Sensors Everywhere • Introduction • Data Fusion • Sensor Network Design • Sensor Network Localization • Sensor Scheduling • Network Interdiction

13. Sensor Network Localization • Network topology identification: • Ad hoc and dynamics networks; • Sensor’s parameters can depend on it’s location: • Transmission characteristics; • Energy consumption; • Reliability. • Installing GPS receivers in every sensor – too expensive; • Mathematical programming techniques often allow to find efficient solutions.

14. Ad hoc positioning system using angle of arrival • Typically, a few nodes of the network know their location - landmarks (equipped with GPS); • The rest of the nodes can communicate to other nodes; • Every node has a capability to determine the angle of the arriving signal; • Every node in the network has fixed main axis to measure all angles against it. • Every node can only communicate with its neighbors within the radio range (they may not know their location).

15. Ad hoc positioning system using angle of arrival Nodes with angle of arrival (AOA) capability

16. Ad hoc positioning system using angle of arrival • Nodes immediately adjacent to a landmark get their angle directly from the landmark. • If a node has some neighbors with orientation for a landmark, it will be able to compute its own orientation with respect to that landmark, and forward it further into the network. • Knowledge of orientation to two other nodes (which are not on one line) allows to calculate location of the node by triangulation.

17. Ad hoc positioning system using angle of arrival Node A computes its orientation to remote node L using information from B and C

18. Ad hoc positioning system using angle of arrival Probability for a node to satisfy conditions necessary for orientation forwarding

19. Ad hoc positioning system using angle of arrival • The proposed method calculates position of nodes in Ad hoc network where nodes can measure angle of arriving signal; • All nodes have AOA capability and only a fraction have self position capability • Simulations showed that resulted positions have an accuracy comparable to the radio range between nodes, and resulted orientations are usable for navigational or tracking purposes.

20. Localization via Semidefinite Programming • Tomorrow (April, 23) • Semidefinite Programming, Graph Realization, and Sensor Network Localization. Yinyu Ye, Stanford University • Reduction to Semidefinite Programming • Solution existence • Statistical interpretation of the formulation (distance values are random with normally distributed measurement errors)

21. Reference • Sorokin, A.; Boyko N.; Boginski V.; Uryasev S.; Pardalos P. Mathematical Programming Techniques for Sensor Networks. Algoritms, 2009, p. 565-581

22. Sensors Everywhere • Introduction • Data Fusion • Sensor Network Design • Sensor Network Localization • Sensor Scheduling • Network Interdiction

23. Sensor Scheduling • Scheduling problem – m sensors, n sites to observe, n>m. The problem is to find the schedule that reduces potential loss of limited observations. • Single sensor scheduling • Multiple sensor schedule using percentile type constrains

24. Sensor Scheduling • Scheduling problem – m sensors, n sites to observe, n>m. The problem is to find the schedule that reduces potential loss of limited observations. • Single sensor scheduling • Multiple sensor schedule using percentile type constrains

25. Single Sensor Scheduling • The simplest case is to model one sensor that observes a group of sites at discreet time point • Time for changing a site being observed is negligibly small • Assume we need to observe n sites during T time periods • During every period a sensor is allowed to watch only at one of n sites

26. Single Sensor Scheduling Decision variable: Penalty for not observing site i at time t: - fixed penalty; - variable penalty; - time of last observing site i before time moment t; is set to t if and only if the sensor is observing site i at time t otherwise it remains constant - only one site may be observed at a time

27. Single Sensor Scheduling Problem Formulation:

28. Reference • This problem was first formulated for one sensor in • M. Yavuz and D.E. Jeffcoat. Single sensor scheduling for multi-site surveillance. Technical report, Air Force Research Laboratory, 2007.

29. Sensor Scheduling • Single sensor scheduling • Multiple sensor schedule using percentile type constrains

30. Multiple Sensor Scheduling • Next talk: Vladimir Boginski will present sensors scheduling problem • Multiple sensors • Stochastic Setup • Robust formulation using Conditional Value at Risk (CVaR) • Joint work with N. Boyko, T. Turko, D.E. Jeffcoat, S. Uryasev, P.M. Pardalos

31. Sensors Everywhere • Introduction • Data Fusion • Sensor Network Design • Sensor Network Localization • Sensor Scheduling • Network Interdiction

32. Network Interdiction • An important issue in military applications is to neutralize the communication in the sensors network of the enemy • Given a graph whose arcs represent the communication links in the graph. • (Offense) Select at most k nodes to target whose removal creates the maximum network disruption. • (Defense) Determine which of your nodes to protect from enemy disruptions.

35. ProblemDefinition • Decision Version: K-CNP • Input: Undirected graph G = (V,E) and integer k • Question: Is there a set M, where M is the set of all maximal connected components of G obtained by deleting k nodes or less, such that where σi is the cardinality of component i, for all i in M?

36. Theoretical Results • Lemma 1: Let M be a partition of G = (V,E) in to L components obtained by deleting a set D, where |D| = k Then the objective function • with equality holding if and only σi=σj, for all i,j in M, where σi is the size of ith component of M. • Objective function is best when components are of average size.

37. Theoretical Results • Lemma 2: Let M1andM2be a two sets of partitions of G = (V,E) obtained by deleting a set D1 and D2 sets of nodes respectively, where |D1| = |D2| = k. Let L1 and L2 be the number of components in M1andM2 respectively, and L1 ≥ L2. If σi=σj, for all i,j in M1, then we obtain a better objective function value by deleting D1.

38. Proofof NP-Completeness • NP-complete: Reduction from Independent Set Problem by a simple transformation and the result follow from the above Lemmas.

39. Formulation • Let ui,j = 1, if i and j are in the same component of G(V \ A), and 0 otherwise. • Let vi = 1, if node i is deleted in the optimal solution, and 0 otherwise. • We can formulate the CNP as the following integer linear program

40. Formulation

41. Formulation Ifi and j in different components and there is an edge between them, at least one must be deleted

42. Formulation Number of nodes deleted is at most k.

43. Formulation For all triplets (i,j,k), if (i,j) in same comp and (j,k) in same comp, then (i,k) in same comp.

44. Heuristics • We implement a heuristic based on Maximal Independent Sets • Why? Because induced subgraph is empty • Maximum Independent Set provides upper bound on # of components in optimal solution. • Greedy type procedure • Enhanced with local search procedure • Results are excellent • Heuristic obtains optimal solutions in fraction of time required by CPLEX • Runs in O(k2 + |V|k) time.

47. Results • This is the case you just saw!! • Optimal solutions computed for all values of k for this graph • The solutions are computed very quickly

48. Conclusions and Future Work • Identified nodes of sparse • Breakdown communication • Integer Programming and Heuristics • Approximation algorithms • Weighted version of the problems

49. Reference • A. Arulselvan, C.W. Commander, P.M. Pardalos, and O. Shylo. Managing network risk via critical node identification. Risk Management in Telecommunication Networks, N. Gulpinar and B. Rustem (editors), Springer, 2009

50. Conclusions • Applications • Health care • Military • Security and law enforcement • Satellite surveillance • … essentially Everywhere! • Research Directions • Computational complexity • Stochasticity • Robustness • …