# A Distributed Approach to the Evasion Problem
## 3 Discussion  
In this work, we proposed an event-driven distributed algorithm that extends [PERSON] evasion path detection algorithm [2]. Sensors with limited information from their neighbors can collaboratively  
Figure 4: Backward propagation example progression of the evasion path algorithm. A single enclosed region gets split into two, each of which gets subsequently split into two regions each. Next, the resulting regions merge pairwise. A backward propagation evasion path enumeration will keep track of paths from the final _True_ regions, copying the paths whenever a merge event is encountered, and tracking the paths backward otherwise.  
Figure 3: Forward propagation example progression of the evasion path algorithm. A single enclosed region gets split into two, each of which gets subsequently split into two regions each. Next, two of the four resulting regions die. A forward propagation evasion path enumeration will keep track of all homotopy classes of paths, and then prune the graph of possible evasion paths.  
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 [PERSON] 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 [PERSON] 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.  
Conceptualization, M.V.-J.; methodology, M.V.-J.; software, D.K. and J.C.; investigation, D.K. and J.C.; writing-original draft preparation, all authors; writing-review and editing, all authors; visualization, D.K.; supervision, M.V.-J. and P.J.; project administration, M.V.-J.; funding acquisition, P.J. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.