@inproceedings{4073, abstract = {A number of rendering algorithms in computer graphics sort three-dimensional objects by depth and assume that there is no cycle that makes the sorting impossible. One way to resolve the problem caused by cycles is to cut the objects into smaller pieces. The problem of estimating how many such cuts are always sufficient is addressed. A few related algorithmic and combinatorial geometry problems are considered.}, author = {Chazelle, Bernard and Edelsbrunner, Herbert and Guibas, Leonidas and Pollack, Richard and Seidel, Raimund and Sharir, Micha and Snoeyink, Jack}, booktitle = {31st Annual Symposium on Foundations of Computer Science}, isbn = {0-8186-2082-X}, location = {St. Louis, MO, United States of America}, pages = {242 -- 251}, publisher = {IEEE}, title = {{Counting and cutting cycles of lines and rods in space}}, doi = {10.1109/FSCS.1990.89543}, year = {1990}, } @article{4074, abstract = {We present upper and lower bounds for extremal problems defined for arrangements of lines, circles, spheres, and alike. For example, we prove that the maximum number of edges boundingm cells in an arrangement ofn lines is Θ(m 2/3 n 2/3 +n), and that it isO(m 2/3 n 2/3 β(n) +n) forn unit-circles, whereβ(n) (and laterβ(m, n)) is a function that depends on the inverse of Ackermann's function and grows extremely slowly. If we replace unit-circles by circles of arbitrary radii the upper bound goes up toO(m 3/5 n 4/5 β(n) +n). The same bounds (without theβ(n)-terms) hold for the maximum sum of degrees ofm vertices. In the case of vertex degrees in arrangements of lines and of unit-circles our bounds match previous results, but our proofs are considerably simpler than the previous ones. The maximum sum of degrees ofm vertices in an arrangement ofn spheres in three dimensions isO(m 4/7 n 9/7 β(m, n) +n 2), in general, andO(m 3/4 n 3/4 β(m, n) +n) if no three spheres intersect in a common circle. The latter bound implies that the maximum number of unit-distances amongm points in three dimensions isO(m 3/2 β(m)) which improves the best previous upper bound on this problem. Applications of our results to other distance problems are also given.}, author = {Clarkson, Kenneth and Edelsbrunner, Herbert and Guibas, Leonidas and Sharir, Micha and Welzl, Emo}, issn = {1432-0444}, journal = {Discrete & Computational Geometry}, number = {1}, pages = {99 -- 160}, publisher = {Springer}, title = {{Combinatorial complexity bounds for arrangements of curves and spheres}}, doi = {10.1007/BF02187783}, volume = {5}, year = {1990}, } @article{4075, abstract = {A key problem in computational geometry is the identification of subsets of a point set having particular properties. We study this problem for the properties of convexity and emptiness. We show that finding empty triangles is related to the problem of determining pairs of vertices that see each other in a star-shaped polygon. A linear-time algorithm for this problem which is of independent interest yields an optimal algorithm for finding all empty triangles. This result is then extended to an algorithm for finding empty convex r-gons (r> 3) and for determining a largest empty convex subset. Finally, extensions to higher dimensions are mentioned.}, author = {Dobkin, David and Edelsbrunner, Herbert and Overmars, Mark}, issn = {1432-0541}, journal = {Algorithmica}, number = {4}, pages = {561 -- 571}, publisher = {Springer}, title = {{Searching for empty convex polygons}}, doi = {10.1007/BF01840404}, volume = {5}, year = {1990}, } @inproceedings{4076, abstract = {We present an algorithm to compute a Euclidean minimum spanning tree of a given set S of n points in Ed in time O(Td(N, N) logd N), where Td(n, m) is the time required to compute a bichromatic closest pair among n red and m blue points in Ed. If Td(N, N) = Ω(N1+ε), for some fixed ε > 0, then the running time improves to O(Td(N, N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closets pair in expected time O((nm log n log m)2/3+m log2 n + n log2 m) in E3, which yields an O(N4/3log4/3 N) expected time algorithm for computing a Euclidean minimum spanning tree of N points in E3.}, author = {Agarwal, Pankaj and Edelsbrunner, Herbert and Schwarzkopf, Otfried and Welzl, Emo}, booktitle = {Proceedings of the 6th annual symposium on Computational geometry}, isbn = {978-0-89791-362-1}, location = {Berkeley, CA, United States}, pages = {203 -- 210}, publisher = {ACM}, title = {{ Euclidean minimum spanning trees and bichromatic closest pairs}}, doi = {10.1145/98524.98567}, year = {1990}, } @inproceedings{4077, abstract = {We prove that for any set S of n points in the plane and n3-α triangles spanned by the points of S there exists a point (not necessarily of S) contained in at least n3-3α/(512 log25 n) of the triangles. This implies that any set of n points in three - dimensional space defines at most 6.4n8/3 log5/3 n halving planes.}, author = {Aronov, Boris and Chazelle, Bernard and Edelsbrunner, Herbert and Guibas, Leonidas and Sharir, Micha and Wenger, Rephael}, booktitle = {Proceedings of the 6th annual symposium on Computational geometry}, isbn = {978-0-89791-362-1}, location = {Berkley, CA, United States}, pages = {112 -- 115}, publisher = {ACM}, title = {{Points and triangles in the plane and halving planes in space}}, doi = {10.1145/98524.98548}, year = {1990}, } @inproceedings{4078, abstract = {In this paper we derived combinatorial point selection results for geometric objects defined by pairs of points. In a nutshell, the results say that if many pairs of a set of n points in some fixed dimension each define a geometric object of some type, then there is a point covered by many of these objects. Based on such a result for three-dimensional spheres we show that the combinatorial size of the Delaunay triangulation of a point set in space can be reduced by adding new points. We believe that from a practical point of view this is the most important result of this paper.}, author = {Chazelle, Bernard and Edelsbrunner, Herbert and Guibas, Leonidas and Hershberger, John and Seidel, Raimund and Sharir, Micha}, booktitle = {Proceedings of the 6th annual symposium on computational geometry}, isbn = {978-0-89791-362-1}, location = {Berkley, CA, United States}, pages = {116 -- 127}, publisher = {ACM}, title = {{Slimming down by adding; selecting heavily covered points}}, doi = {10.1145/98524.98551}, year = {1990}, } @article{4310, author = {Barton, Nicholas H and Jones, Steve}, issn = {1476-4687}, journal = {Nature}, pages = {415 -- 416}, publisher = {Nature Publishing Group}, title = {{The language of the genes}}, doi = {10.1038/346415a0}, volume = {346}, year = {1990}, } @inbook{4311, author = {Barton, Nicholas H and Clark, A.}, booktitle = {Population biology: Ecological and evolutionary viewpoints}, editor = {Wöhrmann, Klaus and Jain, Subodh}, isbn = { 978-3642744761}, pages = {115 -- 174}, publisher = {Springer}, title = {{Population structure and processes in evolution}}, doi = {10.1007/978-3-642-74474-7_5}, year = {1990}, } @inproceedings{4510, abstract = {The interleaving model is both adequate and sufficiently abstract to allow for the practical specification and verification of many properties of concurrent systems. We incorporate real time into this model by defining the abstract notion of a real-time transition system as a conservative extension of traditional transition systems: qualitative fairness requirements are replaced (and superseded) by quantitative lower-bound and upper-bound real-time requirements for transitions. We present proof rules to establish lower and upper real-time bounds for response properties of real-time transition systems. This proof system can be used to verify bounded-invariance and bounded-response properties, such as timely termination of shared-variables multi-process systems, whose semantics is defined in terms of real-time transition systems.}, author = {Henzinger, Thomas A and Manna, Zohar and Pnueli, Amir}, booktitle = { Proceedings of the 5th Jerusalem Conference on Information Technology}, isbn = {0-8186-2078-1}, location = {Jerusalem, Israel}, pages = {717 -- 730}, publisher = {IEEE}, title = {{An interleaving model for real time}}, doi = {10.1109/JCIT.1990.128356}, year = {1990}, } @inproceedings{4522, abstract = {We introduce a novel extension of propositional modal logic that is interpreted over Kripke structures in which a value is associated with every possible world. These values are. however, not treated as full first-order objects: they can be accessed only by a very restricted form of quantification: the "freeze" quantifier binds a variable to the value of the current world. We present a complete proof system for this ("half-order") modal logic. As a special case, we obtain the real-time temporal logic TPTL of [AH891: the models are restricted to infinite sequences of states, whose values are monotonically increasing natural numbers. The ordering relation between states is interpreted as temporal precedence. while the value associated with a state is interpreted as its "rear time. We extend our proof system to be complete for TPTL. and demonstrate how it can be used to derive real-time properties. }, author = {Henzinger, Thomas A}, booktitle = {Proceedings of the 9th annual ACM symposium on Principles of distributed computing}, isbn = {978-0-89791-404-8}, location = {Quebec City, Canada}, pages = {281 -- 296}, publisher = {ACM}, title = {{Half-order modal logic: How to prove real-time properties}}, doi = {10.1145/93385.93429}, year = {1990}, } @article{3649, abstract = {Selection on polygenic characters is generally analyzed by statistical methods that assume a Gaussian (normal) distribution of breeding values. We present an alternative analysis based on multilocus population genetics. We use a general representation of selection, recombination, and drift to analyze an idealized polygenic system in which all genetic effects are additive (i.e., both dominance and epistasis are absent), but no assumptions are made about the distribution of breeding values or the numbers of loci or alleles. Our analysis produces three results. First, our equations reproduce the standard recursions for the mean and additive variance if breeding values are Gaussian; but they also reveal how non-Gaussian distributions of breeding values will alter these dynamics. Second, an approximation valid for weak selection shows that even if genetic variance is attributable to an effectively infinite number of loci with only additive effects, selection will generally drive the distribution of breeding values away from a Gaussian distribution by creating multilocus linkage disequilibria. Long-term dynamics of means can depart substantially from the predictions of the standard selection recursions, but the discrepancy may often be negligible for short-term selection. Third, by including mutation, we show that, for realistic parameter values, linkage disequilibrium has little effect on the amount of additive variance maintained at an equilibrium between stabilizing selection and mutation. Each of these analytical results is supported by numerical calculations.}, author = {Turelli, Michael and Barton, Nicholas H}, issn = {0040-5809}, journal = {Theoretical Population Biology}, number = {1}, pages = {1 -- 57}, publisher = {Academic Press}, title = {{Dynamics of polygenic characters under selection}}, doi = {10.1016/0040-5809(90)90002-D}, volume = {38}, year = {1990}, }