How do the state-of-the-art pathfinding algorithms for changing graphs (D*, D*-Lite, LPA*, etc) differ?

A lot of pathfinding algorithms have been developed in recent years which can calculate the best path in response to graph changes much faster than A* - what are they, and how do they differ? Are they for different situations, or do some obsolete others? These are the ones I've been able to find so far: D* (1994) Focused D* (1995) DynamicSWSF-FP (1996) LPA (1997) LPA*/Incremental A* (2001) D* Lite (2002) SetA* (2002) HPA* (2004) Anytime D* (2005) PRA* (2005) Field D* (2007) Theta* (2007) HAA* (2008) GAA* (2008) LEARCH (2009) BDDD* (2009 - I cannot access this paper:|) Incremental Phi* (2009) GFRA* (2010) MTD*-Lite (2010) Tree-AA* (2011) I'm not sure which of these apply to my specific problem - I'll read them all if necessary, but it would save me a lot of time if someone could write up a summary. My specific problem: I have a grid with a start, a finish, and some walls. I'm currently using A* to find the best path from the start to the finish. The user will then move one wall, and I have to recalculate the entire path again. The "move-wall/recalculate-path" step happens many times in a row, so I'm looking for an algorithm that will be able to quickly recalculate the best path without having to run a full iteration of A*. Though, I am not necessarily looking for an alteration to A* - it could be a completely separate algorithm.