@inproceedings{4059,
abstract = {Let P be a simple polygon with n vertices. We present a simple decomposition scheme that partitions the interior of P into O(n) so-called geodesic triangles, so that any line segment interior to P crosses at most 2 log n of these triangles. This decomposition can be used to preprocess P in time O(n log n) and storage O(n), so that any ray-shooting query can be answered in time O(log n).The algorithms are fairly simple and easy to implement. We also extend this technique to the case of ray-shooting amidst k polygonal obstacles with a total of n edges, so that a query can be answered in O(radicklog n) time.},
author = {Chazelle, Bernard and Herbert Edelsbrunner and Grigni, Michelangelo and Guibas, Leonidas and Hershberger, John and Sharir, Micha and Snoeyink, Jack},
pages = {661 -- 673},
publisher = {Springer},
title = {{Ray shooting in polygons using geodesic triangulations}},
doi = {10.1007/3-540-54233-7_172},
volume = {510},
year = {1991},
}
@article{4061,
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(Fd (N,N) logd N), where Fd (n,m) is the time required to compute a bichromatic closest pair among n red and m green points in Ed . If Fd (N,N)=Ω(N1+ε), for some fixed e{open}>0, then the running time improves to O(Fd (N,N)). Furthermore, we describe a randomized algorithm to compute a bichromatic closest pair in expected time O((nm log n log m)2/3+m log2 n+n log2 m) in E3, which yields an O(N4/3 log4/3 N) expected time, algorithm for computing a Euclidean minimum spanning tree of N points in E3. In d≥4 dimensions we obtain expected time O((nm)1-1/([d/2]+1)+ε+m log n+n log m) for the bichromatic closest pair problem and O(N2-2/([d/2]+1)ε) for the Euclidean minimum spanning tree problem, for any positive e{open}.},
author = {Agarwal, Pankaj K and Herbert Edelsbrunner and Schwarzkopf, Otfried and Welzl, Emo},
journal = {Discrete & Computational Geometry},
number = {1},
pages = {407 -- 422},
publisher = {Springer},
title = {{Euclidean minimum spanning trees and bichromatic closest pairs}},
doi = {10.1007/BF02574698},
volume = {6},
year = {1991},
}
@article{4062,
abstract = {We prove that for any set S of n points in the plane and n3-α triangles spanned by the points in S there exists a point (not necessarily in S) contained in at least n3-3α/(c log5 n) of the triangles. This implies that any set of n points in three-dimensional space defines at most {Mathematical expression} halving planes.},
author = {Aronov, Boris and Chazelle, Bernard and Herbert Edelsbrunner and Guibas, Leonidas J and Sharir, Micha and Wenger, Rephael},
journal = {Discrete & Computational Geometry},
number = {1},
pages = {435 -- 442},
publisher = {Springer},
title = {{Points and triangles in the plane and halving planes in space}},
doi = {10.1007/BF02574700},
volume = {6},
year = {1991},
}
@inproceedings{4508,
abstract = {We extend the specification language of temporal logic, the corresponding verification framework, and the underlying computational model to deal with real-time properties of concurrent and reactive systems. A global, discrete, and asynchronous clock is incorporated into the 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 upperbound real-time requirements for transitions. We show how to model real-time systems that communicate either through shared variables or by message passing, and how to represent the important real-time constructs of priorities (interrupts), scheduling, and timeouts in this framework. Two styles for the specification of real-time properties are presented. The first style uses bounded versions of the temporal operators; the real-time requirements expressed in this style are classified ...},
author = {Thomas Henzinger and Manna, Zohar and Pnueli,Amir},
pages = {353 -- 366},
publisher = {ACM},
title = {{Temporal proof methodologies for real-time systems}},
doi = {10.1145/99583.99629},
year = {1991},
}
@phdthesis{4516,
author = {Thomas Henzinger},
publisher = {Stanford University},
title = {{The Temporal Specification and Verification of Real-time Systems }},
year = {1991},
}