A Graph-Search Based Navigation Algorithm for Traversing A Potentially Hazardous Area case, the region covered by D i should be forbid- den, that is, the marker Y i should be updated into 1. If the disambiguation discloses that X i = 0, then d i should be removed (and hence its marker Y i should be updated into 0), but the region cov- ered by D i may still be questionable since D i may intersect some other risk disks that have not been disambiguated yet. During the travel, the agent dynamically collects the new information through local disambiguations and updates its knowledge of the world. The cost for the agent to go from s to t has two-fold meanings. One is the actual distance the agent travels; the other is the cost paid for disambiguations. A realistic explanation of the disambiguation cost is that the agent spends time when it disambiguates. To unify the cost measures, we define the disambiguation cost as the additional "distance" that the agent travels. Hence the total cost for the agent to go from s to neighbors v i+1, j-1 , v i+1, j , v i+1, j+1 , v i, j-1 , v i, j+1 , v i-1, j-1 , v i-1, j , and v i-1, j+1 and > 0 represents the resolution. Compared with the TAG, which is a topo- logical superimposition of all the visibility graph generated by s, t, and D over all D {D 1 , D 2 , ..., D m }, the 8-adjacency grid is not a precise map representation. However, since according to Fishkind et al. (2007), the time complexity of setting up a TAG is O(m 3 logm), where O stands for the "big O" notation, as m is large, building a TAG representation will be inefficient. One ad- vantage of the grid representation is that the time complexity of constructing a directed grid graph with weighted arcs is not so sensitive to m. This can be reflected from the assembling of the weight function that we introduce the next. Let a = (u, v) denote the arc from node u to node v in our grid graph, say G. Let W(a) denote the weight of arc a. W(a) contains three types of information: the marker, the length, and the disambiguation cost.