Abstract
We examine the problem of searching for a given item in several sets. Let U be a linearly ordered universe and C be a finite collection of subsets of U; given an arbitrary query (x, H) with x ε U and H \(\subseteq\) C, search for x in each set of H. This operation, termed iterative search, is the bottleneck of a large number of retrieval problems. To perform it efficiently, we introduce a new technique, called fractional cascading. We demonstrate its versatility by applying it to a number of different geometric problems. Among the major applications of fractional cascading, we find improved methods for answering range queries, searching in the past, computing functions on d-ranges, intersection searching, solving general extensions of classical retrieval problems, answering visibility questions in the context of ray-tracing, etc.
Extended Abstract
The first author was supported in part by NSF grant MCS 83-03925.
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Chazelle, B., Guibas, L.J. (1985). Fractional cascading: A data structuring technique with geometric applications. In: Brauer, W. (eds) Automata, Languages and Programming. ICALP 1985. Lecture Notes in Computer Science, vol 194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015734
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DOI: https://doi.org/10.1007/BFb0015734
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