Finding an optimal path without growing the tree

For problems on computing an optimal path as well as its length in a certain setting, the “standard” approach for finding an actual optimal path is by building (or “growing”) a single-source optimal path tree. In this paper, we study a class of optimal path problems with the following phenomenon: The space complexity of the algorithms for reporting the lengths of single-source optimal paths for these problems is asymptotically smaller than the space complexity of the “standard ” treegrowing algorithms for finding actual optimal paths. We present a general and efficient algorithmic paradigm for finding an actual optimal path for such problems without having to grow a singlesource optimal path tree. Our paradigm is based on the “marriage-before-conquer ” strategy, the prune-and-search technique, and a new data structure called clipped trees. The paradigm enables us to compute an actual path for a number of optimal path problems and dynamic programming problems in computational geometry, graph theory, and combinatorial optimization. Our algorithmi