Computer Science Department
School of Computer Science, Carnegie Mellon University


Uniquely Represented Data Structures
for Computational Geometry

Guy E. Blelloch, Daniel Golovin, Virginia Vassilevska

April 2008


Keywords: Unique representation, canonical forms, history independence, oblivious data structures, ordered subsets, range trees, point location, convex hull

We present new techniques for the construction of uniquely represented data structures in a RAM, and use them to construct efficient uniquely represented data structures for orthogonal range queries, line intersection tests, point location, and 2-D dynamic convex hull. Uniquely represented data structures represent each logical state with a unique machine state. Such data structures are strongly history-independent. This eliminates the possibility of privacy violations caused by the leakage of information about the historical use of the data structure. Uniquely represented data structures may also simplify the debugging of complex parallel computations, by ensuring that two runs of a program that reach the same logical state reach the same physical state, even if various parallel processes executed in different orders during the two runs.

26 pages

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