As we enter the era of Internet of Things (IoT), sensors are becoming ubiquitous for many real world applications. Keeping the points of interest (PoI) or regions covered as much as possible by sensors is essential for sensor networks to accomplish information gathering, exploration, or monitoring. This often translates into two closely related problems that have been extensively studied in many different perspectives—the coverage and the evasion problems in static and mobile sensor networks, which have also attracted significant attention within the Topological Data Analysis community.
problem aims to achieve the maximum coverage and robustness with optimal deployment in sensor networks, with respect to different metrics or tradeoff. The Evasion
] is the question of whether—given a collection of sensors and a particular movement pattern over time—it is possible to stay undetected within the domain over the same stretch of time.
Each sensor has a limited sensing range and can only collect information within it. In certain settings, a PoI or a region needs to be covered at all times to ensure completeness of the data collection. Given the limited battery life of a sensor, one PoI may need to be covered by multiple sensors to ensure robustness of detection. On the other hand, solving the evasion problem is particularly useful for applications such as mineral exploration and disaster recovery, in which maximum coverage is not required at all times, especially when moving sensors deployment is possible.
The Coverage problem in sensor networks has been studied extensively [4
]. Depending on the circumstances, the goal of covering a region can be modeled in various ways. Generally speaking, a coverage problem aims to achieve either area coverage or target coverage. In the area coverage problem, a continuous region of interest needs to be monitored for collecting information; while the target coverage problem usually deals with a set of points of interest(PoI) being monitored by the sensors.
In general, the level of coverage can be different depending on the underlying applications. For example, for tracking a target, simple coverage [6
] requires that every point in the region is covered by at least one sensor. K-coverage [7
] improves the reliability from simple coverage by considering the fact that sensors may run out of battery or be out of service for various reasons, thus each target point needs to be covered by at least k
sensors. Q-coverage [9
] evolves from k-coverage, in which a coverage vector Q
is introduced to define desired level of coverage for each target point. When full coverage is not required, there are many partial coverage models that emphasize for different scenarios, in which the coverage could be only up to a certain level p
. There are also models focusing on specific points of interest or certain path in the target region. For example, barrier-coverage [10
] is one particular model that covers the boundary of a region and can be useful for intrusion detection, and monitoring animals etc. The target coverage problem may also be considered to be partial coverage problem of an entire region. Sweep coverage [11
] is another partial coverage model where PoI is periodically monitored.
The study of Topological Data Analysis on sensor coverage and evasion problems was initiated in [1
], in which the authors identified a sufficient and necessary criterion for coverage based on relative homology. Their work inspired several follow-up attempts. In [14
], the authors construct a distributed algorithm for homology computation and demonstrate it on a solution for distributed computation of the homology-based coverage criterion. Simultaneously, [15
] uses zig-zag persistent homology to localize coverage holes in both static and dynamic sensor networks.
The first sufficient and necessary criterion for the evasion problem was introduced in [2
]. Our paper is built on this work [2
] but with significant extensions. In [2
], the authors prove that the sensor model used in previous work is insufficient for a full solution to the evasion problem, and further provide an algorithm that—using slightly increased sensor capabilities—provides a sufficient and necessary criterion for evasion. Another and more complex sufficient and necessary criterion using sheaf theory was proposed in [3
Most of the models mentioned above are focused on deployment of sensors to achieve the goal of covering a certain region with static sensors. However, another interesting perspective of the problem is dynamic coverage, where mobile sensors are deployed or dispatched. In particular, in the scenario of tracking down a target when assuming the target is static, using mobile sensors may help increasing the covered region over time such that tracking scheme may require fewer sensors to be deployed. There has been research [16
] in the direction of sensor deployment, where mobile sensor were used to increase the coverage in addition to static sensors. In our work, we are more interested in determining if a target can be detected, rather than focusing on whether or not a certain region is covered completely by a sensor network.
Therefore, in this work, we primarily focus on the Evasion problem as described above. After the evasion problem was introduced in [1
], it took until [2
] before a sufficient and necessary criterion was constructed for the existence of an evasion path. In this paper, building on the previous work, we make two important contributions to the field:
The rest of this paper is structured as follows: Section 2
presents Adams’ algorithm from [2
], extends it to a distributed sensor network setting and proposes evasion path tracking with both forwards and backwards schemes. Section 3
summarizes this work and discusses potential directions for future work.
In this work, we proposed an event-driven distributed algorithm that extends Adams’ evasion path detection algorithm [2
]. Sensors with limited information from their neighbors can collaboratively track the existence or non-existence of an evasion path through a motion pattern. Evasion path algorithms are most closely related to classical coverage problems in sensor networks research but differ fundamentally in that the sensors are kept mobile, and the coverage criteria are adapted to this dynamic situation. With our adaptation, it is possible to implement the algorithm as a distributed sensor network system.
We also developed two algorithms to enumerate all possible evasion paths (up to homotopy)—one with a forward pass and one with a backward pass. The backward pass reviews the history of the motion pattern and is economical with its computation, since only paths that actually lead to the end are considered. The forward pass algorithm could be executed simultaneously with Adams’ or our algorithm to produce evasion path enumeration in an online fashion.
In the future work, we plan to accomplish both implementations and applications of our algorithm. As a first future step, we will implement the algorithm in a simulated environment and evaluate the performance with respect to multiple metrics—we have yet to determine what specific metrics to use. We also plan to apply the evasion path detection system for evaluating the search strategies. As additional information for a search strategy, the region tracking scheme in both Adams’ and our algorithms should mark redundancies and critical memberships in a search team. Using this information, a search strategy could reallocate resources to cover more ground in shorter time, with less movement and a lower probability of evasion without losing track of the regions already cleared by the search team. In addition, by measuring the area of the False regions, we will get a new metric for evaluating specific search strategies.