Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Efficient binary space partitions for hidden-surface removal and solid modeling
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
A zero-one law for Boolean privacy
SIAM Journal on Discrete Mathematics
Privacy and communication complexity
SIAM Journal on Discrete Mathematics
Optimal binary space partitions for orthogonal objects
Journal of Algorithms
On the optimal binary plane partition for sets of isothetic rectangles
Information Processing Letters
Communication complexity
Exact Size of Binary Space Partitionings and Improved Rectangle Tiling Algorithms
SIAM Journal on Discrete Mathematics
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Approximate privacy: foundations and quantification (extended abstract)
Proceedings of the 11th ACM conference on Electronic commerce
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Privacy, additional information and communication
IEEE Transactions on Information Theory
The communication complexity of private value single-item auctions
Operations Research Letters
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We further investigate and generalize the approximate privacy model recently introduced by Feigenbaum et al. (2010) [7]. We explore the privacy properties of a natural class of communication protocols that we refer to as ''dissection protocols''. Informally, in a dissection protocol the communicating parties are restricted to answering questions of the form ''Is your input between the values @a and @b (under a pre-defined order over the possible inputs)?''. We prove that for a large class of functions, called tiling functions, there always exists a dissection protocol that provides a constant average-case privacy approximation ratio for uniform or ''almost uniform'' probability distributions over inputs. To establish this result we present an interesting connection between the approximate privacy framework and basic concepts in computational geometry. We show that such a good privacy approximation ratio for tiling functions does not, in general, exist in the worst case. We also discuss extensions of the basic setup to more than two parties and to non-tiling functions, and provide calculations of privacy approximation ratios for two functions of interest.