Abstract
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” tree-growing 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 single-source optimal path tree. Our paradigm is based on the “marriage-before-conquer” strategy, the prune-and-search technique, and a 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 algorithmic solutions improve the space bounds (in certain cases, the time bounds as well) of the previously best known algorithms, and settle some open problems. Our techniques are likely to be applicable to other problems.
The work of the first, second, and fourth authors was supported in part by the National Science Foundation under Grant CCR-9623585. The work of the third author was supported in part by the National Science Foundation under Grant MIP-9701416 and by HP Labs, Bristol, England under an external research program grant.
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Chen, D.Z., Daescu, O., Hu, X.(., Xu, J. (1998). Finding an Optimal Path without Growing the Tree. In: Bilardi, G., Italiano, G.F., Pietracaprina, A., Pucci, G. (eds) Algorithms — ESA’ 98. ESA 1998. Lecture Notes in Computer Science, vol 1461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68530-8_30
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DOI: https://doi.org/10.1007/3-540-68530-8_30
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