*** School of Information, Renmin University of China, China Bandwidth-aware Breach-free Barrier Construction with VANET nodes for Realtime Fugitive Search Donghyun Kim*, Junggab Son*, Wei Wang** , Deying Li***, Alade O. Tokuta*, Sunghyun Cho+ * Department of Mathematics and Physics, North Carolina Central University, Durham, NC, USA ** Schoo of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China *** School of Information, Renmin University of China, China + Department of Computer Science and Engineering, Hanyang University, South Korea

Agenda Introduction Problem Formulation Abstraction of Metropolitan Area Topology Breach of Sensor Barriers Formal Definition of Problem Main Contribution – Polynomial Time Exact Algorithm Checking Integrity of a VANET Barrier Barrier-breach between Two VANET Barriers Scheduling Subsets for Breach-free Barrier Concluding Remarks

Image source: http://adrianlatorre.com/projects/pfc/img/vanet_full.jpg Introduction Vehicular Ad hoc NETwork (VANET) An adhoc network of highly mobile nodes, in particular vehicles travelling on the road Image source: http://adrianlatorre.com/projects/pfc/img/vanet_full.jpg

Introduction VANET applications Remote vehicle personalization and diagnostics Internet access Digital map downloading On-demand-basis real-time visual data collection Pics-on-wheel (POW): mobile cloud-based real-time street visual data collection system [2] Vehicle Witnesses as a Service (VWaaS): privacy enhanced version of POW [3] and many more.

Image source: http://humandrama.tistory.com/975 Introduction Q: Collecting Real-time Visual Images of Suspects Who Are Trying to Leave Area of Interest using VANET nodes? VANET nodes are expected to have visual sensors and wireless transceivers Image source: http://humandrama.tistory.com/975

Image source: http://ipvm.com/ Introduction People care their privacy Normally, reluctant to reveal their current locations and/or their future travel schedule Under urgent/emergent situation, e.g. Boston Bombing Previous experiences show many people may voluntarily disclose their locations and give up their privacy Image source: http://ipvm.com/

Introduction Still, the future trajectories of VANET nodes may not be controllable, but may provide their current locations and short-term future trajectories Asking all nodes to transmit real-time video would generate too much network traffic ? https://cleanenergydurham.wordpress.com/category/neighborhoods/trinity-park/

Agenda Introduction Problem Formulation Abstraction of Metropolitan Area Topology Breach of Sensor Barriers Formal Definition of Problem Main Contribution – Polynomial Time Exact Algorithm Checking Integrity of a VANET Barrier Barrier-breach between Two VANET Barriers Scheduling Subsets for Breach-free Barrier Concluding Remarks

Problem Formulation Problem Statement How to operate a subset of VANET nodes to provide (inside-out) barrier-coverage over an area of interest to detect fugitives leaving an area of interest during a given mission period Assume the area of interest is a huge metropolitan area, the mission period consists of a series of time slots, the travel schedule of each VANET node is known for next T time slots, each participating VANET node is with visual sensors and wireless connectivity to the central authority, and are either moving on the road and parked on a parking lot,

r (a) (b) Problem Formulation Abstraction of Metropolitan Area Topology Assume the shape of the map M of a metropolitan area is a rectangle Partition M into regular squares whose length and width are r Construct a topology graph G=(V, E) (a) (b) r

Problem Formulation Barrier coverage of a sensor network and breach [27]

(a) (b) (c) Problem Formulation Adoption of the Concept of Breach to Our Context (a) (b) (c)

(a) (b) Problem Formulation Seamless VANET barrier coverage problem (SVBCP) Given the location of each VANET node at each time slot in [0, T], find a VANET node operation schedule (a collection of subsets of nodes) which does not have two subsets at t-time slot and (t+1)-time slot, between which there exists a breach, and (b) the size of each subset does not exceed a network limit, b. (a) (b)

Problem Formulation Seamless VANET barrier coverage problem (SVBCP) Q: There might be more than one choice from one slot to the next slot – which one does not lead to the dead end?

Agenda Introduction Problem Formulation Abstraction of Metropolitan Area Topology Breach of Sensor Barriers Formal Definition of Problem Main Contribution – Polynomial Time Exact Algorithm Checking Integrity of a VANET Barrier Barrier-breach between Two VANET Barriers Scheduling Subsets for Breach-free Barrier Concluding Remarks

Main Contributions Three Key Questions Given a city map abstraction 𝐺=(𝑉,𝐸), the initial location 𝑝, and a subset of nodes 𝐵 𝑖 , the locations of participating VANET nodes at the 𝑖-th time slot, how to determine if 𝐵 𝑖 provides a (inside-out) barrier coverage over 𝐺 against 𝑝? Given 𝐺 and two barriers 𝐵 𝑖 and 𝐵 𝑖+1 , how to determine if there is no breach when 𝐵 𝑖 is replaced by 𝐵 𝑖+1 . How to design a polynomial time exact algorithm for SVBCP?

Checking Integrity of a VANET Barrier Given a city map abstraction 𝐺=(𝑉,𝐸), the initial location 𝑝, and a subset of nodes 𝐵 𝑖 , the locations of participating VANET nodes at the 𝑖-th time slot, how to determine if 𝐵 𝑖 provides a (inside-out) barrier coverage over 𝐺 against 𝑝? Step 1: modify 𝐺 to a directional graph Step 2: compute a path from 𝑝 to 𝑞 the existence of such path implies the existence of a covert path for the fugitive such that any incoming directional edge to a VANET node in 𝐵 𝑖 is removed

Barrier-breach between Two VANET Barriers In our context, a breach between two barriers is a node in 𝐺 such that used to reachable to 𝑝, but not reachable to 𝑞, but now, not reachable to 𝑝, but reachable to 𝑞 (outside the current barrier, and thus get to 𝑞 almost immeidately)

Scheduling Subsets for Breach-free Barrier For each i-th time slot find all possible configurations (a subset with size b) edge from one configuration at i-th time slot to another configuration at i+1 time slot find s-t path … … … … … …

Analysis Theorem 1 The proposed strategy solves the SVBCP correctly. The running time of the proposed algorithm is polynomial

Agenda Introduction Problem Formulation Abstraction of Metropolitan Area Topology Breach of Sensor Barriers Formal Definition of Problem Main Contribution – Polynomial Time Exact Algorithm Checking Integrity of a VANET Barrier Barrier-breach between Two VANET Barriers Scheduling Subsets for Breach-free Barrier Concluding Remarks

Concluding Remarks Proposed a polynomial exact algorithm for SVBCP Will Consider Smaller running time Less assumptions more sophisticated assumption for network bandwidth more practical VANET node mobility unpredictability