Abstract
We consider the problem of computing the length of a curve from digitized versions of the curve using parallel computation. Our aim is to study the inherent parallel computational complexity of this problem as a function of the digitization level. Precise formulations for the digitization, the parallel computation, and notions of local and nonlocal computations are given. We show that length cannot be computed locally from digitizations on rectangular tessellations. However, for a random tessellation and appropriate deterministic ones, we show that the length of straight line segments can be computed locally.
This work was supported in part by the U.S. Army Research Office under Contract DAAL03-86-K-0171, by the Dept. of the Navy under Air Force Contract F19628-90C-0002, and by the National Science Foundation under contract ECS-8552419.
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© 1993 Springer-Verlag Berlin Heidelberg
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Kulkarni, S.R., Mitter, S.K., Richardson, T.J., Tsitsiklis, J.N. (1993). Local versus non-local computation of length of digitized curves. In: Shyamasundar, R.K. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1993. Lecture Notes in Computer Science, vol 761. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57529-4_45
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DOI: https://doi.org/10.1007/3-540-57529-4_45
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