A note on the height of binary search trees
Journal of the ACM (JACM)
Upper bounds for time-space trade-offs in sorting and selection
Journal of Computer and System Sciences
Selection from read-only memory and sorting with minimum data movement
Theoretical Computer Science
Space-efficient online computation of quantile summaries
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Improved Upper Bounds for Time-Space Tradeoffs for Selection with Limited Storage
SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
Visibility Algorithms in the Plane
Visibility Algorithms in the Plane
Multi-Pass Geometric Algorithms
Discrete & Computational Geometry
Comparison-based time-space lower bounds for selection
ACM Transactions on Algorithms (TALG)
Constant-Work-Space algorithm for a shortest path in a simple polygon
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Reprint of: Memory-constrained algorithms for simple polygons
Computational Geometry: Theory and Applications
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We present several algorithms for computing the visibility polygon of a simple polygon $\ensuremath{\mathcal{P}}$ from a viewpoint inside the polygon, when the polygon resides in read-only memory and only few working variables can be used. The first algorithm uses a constant number of variables, and outputs the vertices of the visibility polygon in $O(n\ensuremath{\bar{r}})$ time, where $\ensuremath{\bar{r}}$ denotes the number of reflex vertices of $\ensuremath{\mathcal{P}}$ that are part of the output. The next two algorithms use O(logr) variables, and output the visibility polygon in O(nlogr) randomized expected time or O(nlog2r) deterministic time, where r is the number of reflex vertices of $\ensuremath{\mathcal{P}}$.