On the Longest Vulnerable Path inside a Sensor Network from Boundary Regions Chowdhury Sayeed Hyder, Ashikur Rahman and Masud Hasan Department of Computer Science & Engineering Bangladesh University of Engineering & Technology Dhaka - 1000, Bangladesh sayeed@csebuet.org, ashikur@cse.buet.ac.bd, masudhasan@cse.buet.ac.bd Abstract One of the most fundamental problems in wireless sen- sor network is coverage problem. Higher coverage con- tributes to improving the quality of services provided by a sensor network. In this paper, we have investigated the cov- erage problem in heterogeneous sensor network from an in- truder’s point of view. We argue that a well covered area may still be vulnerable if there exist some paths that can be traversed without being discovered by any sensors. Af- ter defining vulnerable paths and weak points and demon- strating their properties we present an efficient algorithm with O(n log n) time complexity to find the longest vulner- able path from a given boundary point in non overlapping sensing regions. We claim that further sensor deployment based on the algorithm reduces vulnerability of the system and improves the quality of service significantly. We present simulation results to support our claim. 1 Introduction The primary objective of a sensor network is to moni- tor and report events or phenomena taking place within a particular area. Therefore, the key parameter which de- fines quality of a sensor network is “coverage” (or “expo- sure”). Quality of coverage depends upon several factors, e.g. the range, sensitivity, location and density of sensing nodes within a given region. However, in surveillance [7] and monitoring applications [8], fewer coverage holes do not always indicate higher degree of security. In spite of fewer coverage holes, if the target area contains some free paths, those will be equally responsible for weak security of the area. We refer such paths as vulnerable paths and the starting points on the boundary as weak points. Starting from the boundary, the longer the path, the more vulnerable it is. In most cases, such strategic vulnerable paths inside the network become serious security concern. Discovering these weak points and vulnerable paths, an intruder or at- tacker can silently enter to go through the system or roam inside the network and collect information covertly, caus- ing a major security problem. As a result, the primary goal of monitoring will suffer. Therefore, these paths need bet- ter treatment in applications like battlefield surveillance or enemy movement tracking where security is a high concern. In this paper, we address this coverage problem in heteroge- neous sensor network from that point of view. We present a novel algorithm to find the longest vulnerable path and sug- gest future sensor deployment plan. Our simulation result shows that significant improvement can be achieved follow- ing our deployment plan. 2 Related Works Sensor network has been widely used in diversified fields with different coverage constraints to address. As a result, research works on coverage are mostly application specific. For instance, research works on detecting and improving coverage can be classified based on the sensor mobility [3], degree of coverage [12, 11], network homogeneity [4] etc. Again, coverage support alone may not be enough to ad- dress the application requirement. Coverage with connectivity is often expected in the field of sensor network [2, 7, 14, 15]. However, coverage problem can also be explained in terms of exposure [6, 10, 13, 5]. The investigation at [9] includes best and worst case cov- erage for agents moving in a sensor field, characterized by maximal breach and maximal support path respectively. A maximum breach path from s to t is a path from s to t such that the minimum distance from a point p in the path to the sensor network is maximized: This distance is called the worst-case coverage distance of the network. Similarly, a maximum support path from s to t is a path such that the maximum distance of a point p in the path to the sensor