Choosing heuristic for A* algorithm where cost is less than absolute distance Looking for information on choosing a heuristic for instances where the cost of traversing an edge can be less than one. 

For example, say movement is allowed in the cardinal directions. Should all edge costs be at least one, then I would consider diagonal distance. However, if costs can be less than one, this could lead to an instance where diagonal distance will be an overestimate and thus is not an admissible heuristic.

My thought on the matter is perhaps to find the smallest possible cost and figure out a constant to divide diagonal distance by to guarantee it will never overestimate?

Would appreciate some guidance or some resources to look further into this.
The simple options are to either multiply all path costs such that minimum cost is 1. Or multiply the heuristic such that the min cost is more or equal than the heuristic tells you for the same path.

The more complicated option is to look at the graph and estimate the chance that you will end up going through the low cost area. This requires some precalculation of the low cost areas and their influence on paths. 

For example a low cost highway, any heuristic that is close to it will need to get a bonus to account for taking the highway. But heuristics that are not going to take the highway can use the larger estimation.