8,517 research outputs found
Hidden surface removal for rectangles
AbstractA simple but important special case of the hidden surface removal problem is one in which the scene consists of n rectangles with sides parallel to the x- and y-axes, with viewpoint at z=∞ (that is, an orthographic projection). This special case has application to overlapping windows in computer displays. An algorithm with running time O(n log n + k log n) is given for static scenes, where k is the number of line segments in the output. Algorithms are given for a dynamic setting (that is, rectangles may be inserted and deleted) that take time O(log2n log log n + k log2 n) per insert or delete, where k is now the number of visible line segments that change (appear or disappear). Algorithms for point location in the visible scene are also given
A Space-Optimal Hidden Surface Removal Algorithm for Iso-Oriented Rectangles
We investigate the problem of finding the visible pieces of a scene of
objects from a specified viewpoint. In particular, we are interested in the
design of an efficient hidden surface removal algorithm for a scene comprised
of iso-oriented rectangles. We propose an algorithm where given a set of
iso-oriented rectangles we report all visible surfaces in time
and linear space, where is the number of surfaces reported. The previous
best result by Bern, has the same time complexity but uses space
On Communication Protocols that Compute Almost Privately
A traditionally desired goal when designing auction mechanisms is incentive
compatibility, i.e., ensuring that bidders fare best by truthfully reporting
their preferences. A complementary goal, which has, thus far, received
significantly less attention, is to preserve privacy, i.e., to ensure that
bidders reveal no more information than necessary. We further investigate and
generalize the approximate privacy model for two-party communication recently
introduced by Feigenbaum et al.[8]. We explore the privacy properties of a
natural class of communication protocols that we refer to as "dissection
protocols". Dissection protocols include, among others, the bisection auction
in [9,10] and the bisection protocol for the millionaires problem in [8].
Informally, in a dissection protocol the communicating parties are restricted
to answering simple questions of the form "Is your input between the values
\alpha and \beta (under a predefined order over the possible inputs)?".
We prove that for a large class of functions, called tiling functions, which
include the 2nd-price Vickrey auction, 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.Comment: to appear in Theoretical Computer Science (series A
Binary Space Partitions for Fat Rectangles
This is the published version. Copyright © 2000 Society for Industrial and Applied Mathematic
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