## DFM algorithm

The DFM algorithm is inspired from the LPA* and D* Lite algorithms described in (Koenig et al., 2004). It is similar to the E* algorithm developed by Philippsen in (Philippsen & Siegwart, 2005) but we prefer to name this algorithm DFM instead of E* because the asterisk usually refers to heuristically guided search algorithms (such as A* and D* algorithms). Since no heuristic has been integrated yet in any dynamic version of the Fast Marching algorithm, we propose to use the abbreviation DFM for Dynamic Fast Marching. According to the principle of optimality it is not necessary to recompute an entire trajectory from A to B when a change appears in C somewhere between A and B. An efficient algorithm may only update the trajectory from C to B and leave the sub-trajectory from A to C unchanged.

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