Emo Welzl
ETH Zurich
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Featured researches published by Emo Welzl.
Discrete and Computational Geometry | 1987
David Haussler; Emo Welzl
AbstractWe demonstrate the existence of data structures for half-space and simplex range queries on finite point sets ind-dimensional space,d≥2, with linear storage andO(nα) query time, % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVC0xe9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Gqpi0x% c9q8qqaqFj0df9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey% ypa0ZaaSaaaeaacaWGKbGaaiikaiaadsgacqGHsislcaaIXaGaaiyk% aaqaaiaadsgacaGGOaGaamizaiabgkHiTiaaigdacaGGPaGaey4kaS% IaaGymaaaacqGHRaWkcqaHZoWzieaacaWFGaGaa8hiaiaa-bcacaWF% GaGaa8hiaiaa-bcacaWFGaGaa8Nzaiaa-9gacaWFYbGaa8hiaiaa-f% gacaWFSbGaa8hBaiaa-bcacaWFGaGaa8hiaiabeo7aNjaa-5dacaWF% Waaaaa!574F!
Discrete and Computational Geometry | 1990
Kenneth L. Clarkson; Herbert Edelsbrunner; Leonidas J. Guibas; Micha Sharir; Emo Welzl
Information Processing Letters | 1985
Emo Welzl
\alpha = \frac{{d(d - 1)}}{{d(d - 1) + 1}} + \gamma for all \gamma > 0
international conference on computer communications | 2009
Olga Goussevskaia; Roger Wattenhofer; Magnús M. Halldórsson; Emo Welzl
symposium on computational geometry | 1987
Helmut Alt; Kurt Mehlhorn; Hubert Wagener; Emo Welzl
.These bounds are better than those previously published for alld≥2. Based on ideas due to Vapnik and Chervonenkis, we introduce the concept of an ɛ-net of a set of points for an abstract set of ranges and give sufficient conditions that a random sample is an ɛ-net with any desired probability. Using these results, we demonstrate how random samples can be used to build a partition-tree structure that achieves the above query time.
Theoretical Computer Science | 1997
Tetsuo Asano; Desh Ranjan; Thomas Roos; Emo Welzl; Peter Widmayer
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(m2/3n2/3 +n), and that it isO(m2/3n2/3β(n) +n) forn unit-circles, whereβ(n) (and laterβ(m, n)) is a function that depends on the inverse of Ackermanns function and grows extremely slowly. If we replace unit-circles by circles of arbitrary radii the upper bound goes up toO(m3/5n4/5β(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(m4/7n9/7β(m, n) +n2), in general, andO(m3/4n3/4β(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(m3/2β(m)) which improves the best previous upper bound on this problem. Applications of our results to other distance problems are also given.
symposium on theoretical aspects of computer science | 1992
Micha Sharir; Emo Welzl
Abstract Given a set S of line segments in the plane, its visibility graph G S is the undirected graph which has the endpoints of the line segments in S as nodes and in which two nodes (points) are adjacent whenever they ‘see’ each other (the line segments in S are regarded as nontransparent obstacles). It is shown that G S can be constructed in O(n 2 ) time and space for a set S of n nonintersecting line segments. As an immediate implication, the shortest path between two points in the plane avoiding a set of n nonintersecting line segments can be computed in O(n 2 ) time and space
SIAM Journal on Computing | 1994
Jirí Matousek; János Pach; Micha Sharir; Shmuel Sifrony; Emo Welzl
In this work we study the problem of determining the throughput capacity of a wireless network. We propose a scheduling algorithm to achieve this capacity within an approximation factor. Our analysis is performed in the physical interference model, where nodes are arbitrarily distributed in Euclidean space. We consider the problem separately from the routing problem and the power control problem, i.e., all requests are single-hop, and all nodes transmit at a fixed power level. The existing solutions to this problem have either concentrated on special-case topologies, or presented optimality guarantees which become arbitrarily bad (linear in the number of nodes) depending on the networks topology. We propose the first scheduling algorithm with approximation guarantee independent of the topology of the network. The algorithm has a constant approximation guarantee for the problem of maximizing the number of links scheduled in one time-slot. Furthermore, we obtain a O(log n) approximation for the problem of minimizing the number of time slots needed to schedule a given set of requests. Simulation results indicate that our algorithm does not only have an exponentially better approximation ratio in theory, but also achieves superior performance in various practical network scenarios. Furthermore, we prove that the analysis of the algorithm is extendable to higher-dimensional Euclidean spaces, and to more realistic bounded-distortion spaces, induced by non-isotropic signal distortions. Finally, we show that it is NP-hard to approximate the scheduling problem to within n 1-epsiv factor, for any constant epsiv > 0, in the non-geometric SINR model, in which path-loss is independent of the Euclidean coordinates of the nodes.
symposium on computational geometry | 1992
Jiří Matoušek; Micha Sharir; Emo Welzl
We consider the problem of computing geometric transformations (rotation, translation, reflexion) that map a point setA exactly or approximately into a point setB. We derive efficient algorithms for various cases (Euclidean or maximum metric, translation or rotation, or general congruence).
symposium on computational geometry | 1989
Bernard Chazelle; Emo Welzl
We are given a two-dimensional square grid of size N×N, where N∶=2n and n≥0. A space filling curve (SFC) is a numbering of the cells of this grid with numbers from c+1 to c+N2, for some c≥0. We call a SFC recursive (RSFC) if it can be recursively divided into four square RSFCs of equal size. Examples of well-known RSFCs include the Hilbert curve, the z-curve, and the Gray code.