So, I skimmed through the papers, and this is what I gleamed. If there is anyone more knowledgable in the subject-matter, please correct me if I‘m wrong (or add your own answer, and I will accept it instead!).
Links to each paper can be found in the question-post, above.
- Simple recalculations
- D* (aka Dynamic A*) (1994): On the initial run, D* runs very similarly to A*, finding the best path from start to finish very quickly. However, as the unit moves from start to finish, if the graph changes, D* is able to very quickly recalculate the best path from that unit‘s position to the finish, much faster than simply running A* from that unit‘s position again. D*, however, has a reputation for being extremely complex, and has been completely obsoleted by the much simpler D*-Lite.
- Focused D* (1995): An improvement to D* to make it faster/"more realtime." I can‘t find any comparisons to D*-Lite, but given that this is older and D*-Lite is talked about a lot more, I assume that D*-Lite is somehow better.
- DynamicSWSF-FP (1996): Stores the distance from every node to the finish-node. Has a large initial setup to calculate all the distances. After changes to the graph, it‘s able to update only the nodes whose distances have changed. Unrelated to both A* and D*. Useful when you want to find the distance from multiple nodes to the finish after each change; otherwise, LPA* or D*-Lite are typically more useful.
- LPA*/Incremental A* (2001): LPA* (Lifelong Planning A*), also known as Incremental A* (and sometimes, confusingly, as "LPA," though it has no relation to the other algorithm named LPA) is a combination of DynamicSWSF-FP and A*. On the first run, it is exactly the same as A*. After minor changes to the graph, however, subsequent searches from the same start/finish pair are able to use the information from previous runs to drastically reduce the number of nodes which need to be examined, compared to A*. This is exactly my problem, so it sounds like LPA* will be my best fit. LPA* differs from D* in that it always finds the best path from the same start to the same finish; it is not used when the start point is moving (such as units moving along the initial best path). However...
- D*-Lite (2002): This algorithm uses LPA* to mimic D*; that is, it uses LPA* to find the new best path for a unit as it moves along the initial best path and the graph changes. D*-Lite is considered much simpler than D*, and since it always runs at least as fast as D*, it has completely obsoleted D*. Thus, there is never any reason to use D*; use D*-Lite instead.
- Any-angle movement
- Field D* (2007): A variant of D*-Lite which does not constrain movement to a grid; that is, the best path can have the unit moving along any angle, not just 45- (or 90-)degrees between grid-points. Was used by NASA to pathfind for the Mars rovers.
- Theta* (2007): A variant of A* that gives better (shorter) paths than Field D*. However, because it is based on A* rather than D*-Lite, it does not have the fast-replanning capabilities that Field D* does. See also.
- Incremental Phi* (2009): The best of both worlds. A version of Theta* that is incremental (aka allows fast-replanning)
- Moving Target Points
- GAA* (2008): GAA* (Generalized Adaptive A*) is a variant of A* that handles moving target points. It‘s a generalization of an even earlier algorithm called "Moving Target Adaptive A*"
- GRFA* (2010): GFRA* (Generalized Fringe-Retrieving A*) appears (?) to be a generalization of GAA* to arbitrary graphs (ie. not restricted to 2D) using techniques from another algorithm called FRA*.
- MTD*-Lite (2010): MTD*-Lite (Moving Target D*-Lite) is "an extension of D* Lite that uses the principle behind Generalized Fringe-Retrieving A*" to do fast-replanning moving-target searches.
- Tree-AA* (2011): (???) Appears to be an algorithm for searching unknown terrain, but is based on Adaptive A*, like all other algorithms in this section, so I put it here. Not sure how it compares to the others in this section.
- Fast/Sub-optimal
- Anytime D* (2005): This is an "Anytime" variant of D*-Lite, done by combining D*-Lite with an algorithm called Anytime Repairing A*. An "Anytime" algorithm is one which can run under any time constraints - it will find a very suboptimal path very quickly to begin with, then improve upon that path the more time it is given.
- HPA* (2004): HPA* (Hierarchical Path-Finding A*) is for path-finding a large number of units on a large graph, such as in RTS (real-time strategy) video games. They will all have different starting locations, and potentially different ending locations. HPA* breaks the graph into a hierarchy in order to quickly find "near-optimal" paths for all these units much more quickly than running A* on each of them individually. See also
- PRA* (2005): From what I understand, PRA* (Partial Refinement A*) solves the same problem as HPA*, but in a different way. They both have "similar performance characteristics."
- HAA* (2008): HAA* (Hierarchical Annotated A*) is a generalization of HPA* that allows for restricted traversal of some units over some terrains (ex. a small pathway that some units can walk through but larger ones can‘t; or a hole that only flying units can cross; etc.)
- Other/Unknown
- LPA (1997): LPA (Loop-free path-finding algorithm) appears to be a routing-algorithm only marginally related to the problems the other algorithms here solve. I only mention it because this paper is confusingly (and incorrectly) referenced on several places on the Internet as the paper introducing LPA*, which it is not.
- LEARCH (2009): LEARCH is a combination of machine-learning algorithms, used to teach robots how to find near-optimal paths on their own. The authors suggest combining LEARCH with Field D* for better results.
- BDDD* (2009): ??? I cannot access the paper.
- SetA* (2002): ??? This is, apparently, a variant of A* that searches over the "binary decision diagram" (BDD) model of the graph? They claim that it runs "several orders of magnitude faster than A*" in some cases. However, if I‘m understanding correctly, those cases are when each node on the graph has many edges?
Given all this, it appears that LPA* is the best fit for my problem.
