1

July 2015
Computational Geometry: Theory and Applications: Volume 48 Issue 5, July 2015

**Publisher:** Elsevier Science Publishers B. V.

We consider the problem of counting straight-edge triangulations of a given set P of n points in the plane. Until very recently it was not known whether the exact number of triangulations of P can be computed asymptotically faster than by enumerating all triangulations. We now know that the number ...

**Keywords**:
Counting algorithms, Algorithmic geometry, Approximation algorithms, Crossing-free structures, Triangulations

2

August 2013
Computational Geometry: Theory and Applications: Volume 46 Issue 6, August, 2013

**Publisher:** Elsevier Science Publishers B. V.

Given a set @S of spheres in E^d, with d>=3 and d odd, having a constant number of m distinct radii @r"1,@r"2,...,@r"m, we show that the worst-case combinatorial complexity of the convex hull of @S is @Q(@?"1"=<"i"<>"j"=<"mn"in"j^@?^d^2^@?), where n"i is the number of spheres in @S with radius @r"i. To ...

**Keywords**:
Disjoint convex polytopes, Discrete geometry, Combinatorial geometry, Convex hull, Spheres

3

June 2013
SoCG '13: Proceedings of the twenty-ninth annual symposium on Computational geometry

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 3

Downloads (6 Weeks): 4, Downloads (12 Months): 10, Downloads (Overall): 159

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We give an algorithm that determines the number (S) of straight line triangulations of a set S of n points in the plane in worst case time O(n 2 2 n ). This is the the first algorithm that is provably faster than enumeration, since (S) is known to be ...

**Keywords**:
counting, geometric graphs, triangulations

4

September 2011
ESA'11: Proceedings of the 19th European conference on Algorithms

**Publisher:** Springer-Verlag

Nearest Neighbor Searching, i.e. determining from a set S of n sites in the plane the one that is closest to a given query point q , is a classical problem in computational geometry. Fast theoretical solutions are known, e.g. point location in the Voronoi Diagram of S , or ...

5

August 2010
Computational Geometry: Theory and Applications: Volume 43 Issue 6-7, August, 2010

**Publisher:** Elsevier Science Publishers B. V.

This paper presents a very simple incremental randomized algorithm for computing the trapezoidal decomposition induced by a set S of n line segments in the plane. If S is given as a simple polygonal chain the expected running time of the algorithm is O(nlog^*n). This leads to a simple algorithm ...

6

February 2010
Computational Geometry: Theory and Applications: Volume 43 Issue 2, February, 2010

**Publisher:** Elsevier Science Publishers B. V.

We study the problem of approximating MST(P), the minimum weight spanning tree of a set P of n points in [0,1]^d, by a spanning tree of some subset

[email protected]?P. We show that if the weight of MST(P) is to be approximated, then in general Q must be large. If the ...

**Keywords**:
Approximation algorithms, Coresets, Minimum weight spanning tree, Hausdorff metric

7

January 2010
SODA '10: Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete algorithms

**Publisher:** Society for Industrial and Applied Mathematics

**Bibliometrics**:

Citation Count: 1

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We consider the complexity of sorting strings in the model that counts comparisons between symbols and not just comparisons between strings. We show that for any set of strings S the complexity of sorting S can naturally be expressed in terms of the trie induced by S . This holds ...

8

October 2009
Computational Geometry: Theory and Applications: Volume 42 Issue 8, October, 2009

**Publisher:** Elsevier Science Publishers B. V.

Computing shadow boundaries is a difficult problem in the case of non-point light sources. A point is in the umbra if it does not see any part of any light source; it is in full light if it sees entirely all the light sources; otherwise, it is in the penumbra. ...

**Keywords**:
Penumbra, Umbra, Complexity, Discontinuity mesh, Shadows

9

September 2009
Efficient Algorithms: Essays Dedicated to Kurt Mehlhorn on the Occasion of His 60th Birthday

**Publisher:** Springer-Verlag

We consider the problem of maintaing a random binary search tree under insertions and deletions under the conditions that (i) no extra permanent storage space be used besides the tree itself, and (ii) that at any point in time the tree be perfectly random, meaning that it is drawn from ...

**Keywords**:
Binary Search Trees, Randomized Data Structures

10

September 2008
SoftVis '08: Proceedings of the 4th ACM symposium on Software visualization

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 0

Downloads (6 Weeks): 0, Downloads (12 Months): 0, Downloads (Overall): 491

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Traditional algorithm animation attempts to provide visualizations of the execution of a program on concrete data. In recent years a different approach has been proposed which attempts to visualize an "abstract execution" on "abstract data." This is based on Cousots' notion of abstract interpretations, in particular in the case of ...

**Keywords**:
algorithm animation, algorithm visualisation, invariants, shape analysis, shape graphs

11

August 2007
WADS'07: Proceedings of the 10th international conference on Algorithms and Data Structures

**Publisher:** Springer-Verlag

We consider the problem of computing the centroid of all the vertices in a non-degenerate arrangement of n lines. The trivial approach requires the enumeration of all ( n 2) vertices. We present an O ( n log 2 n ) algorithm for computing this centroid. For arrangements of n ...

12

July 2007
COCOON'07: Proceedings of the 13th annual international conference on Computing and Combinatorics

**Publisher:** Springer-Verlag

We investigate the maximum number of simple cycles and the maximum number of Hamiltonian cycles in a planar graph G with n vertices. Using the transfer matrix method we construct a family of graphs which have at least 2.4262n simple cycles and at least 2.0845n Hamilton cycles. Based on counting ...

13

June 2007
SCG '07: Proceedings of the twenty-third annual symposium on Computational geometry

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 0

Downloads (6 Weeks): 0, Downloads (12 Months): 2, Downloads (Overall): 205

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Computing shadow boundaries is a difficult problem in the case of non-pointlight sources. A point is in the umbra if it does not see any part of anylight source; it is in full light if it sees entirely all the light sources;otherwise, it is in the penumbra. While the common ...

**Keywords**:
complexity, discontinuity mesh, penumbra, shadows, umbra

14

October 2006
Information Processing Letters: Volume 100 Issue 2, 31 October 2006

**Publisher:** Elsevier North-Holland, Inc.

In this note we give upper bounds for the number of vertices of the polyhedron P(A,b) = { x ∈ R d : Ax < b } when the m × d constraint matrix A is subjected to certain restriction. For instance, if A is a 0/1-matrix, then there can ...

**Keywords**:
polyhedron, computational geometry, linear programming, upper bounds

15

July 2006
SWAT'06: Proceedings of the 10th Scandinavian conference on Algorithm Theory

**Publisher:** Springer-Verlag

Path compression is used in a number of algorithms, most notably in various very natural solutions to the so-called Union-Find problem. This problem is basic and important enough to be covered in most introductory courses and textbooks on algorithms and data structures. However the performance analysis of the solutions is ...

16

December 2005
FSTTCS '05: Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science

**Publisher:** Springer-Verlag

We survey and highlight some of the developments in data structure research during the time of the first 25 years of the FSTTCS conference series.

17

June 2005
SCG '05: Proceedings of the twenty-first annual symposium on Computational geometry

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 38

Downloads (6 Weeks): 1, Downloads (12 Months): 3, Downloads (Overall): 313

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We consider the problem of computing a representation of the plane graph induced by one (or more) algebraic curves in the real plane. We make no assumptions about the curves, in particular we allow arbitrary singularities and arbitrary intersection. This problem has been well studied for the case of a ...

**Keywords**:
algebraic curves, exact geometric computation, computational geometry, robustness

18

May 2005
SoftVis '05: Proceedings of the 2005 ACM symposium on Software visualization

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 4

Downloads (6 Weeks): 0, Downloads (12 Months): 3, Downloads (Overall): 580

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This paper describes progress in a non-traditional approach to algorithm animation. We visualise the abstract execution of an algorithm instead of animating the algorithm for executions on concrete input data. Algorithms under consideration are imperative pointer-based algorithms. For our purpose, we need to compute invariants which describe the state of ...

**Keywords**:
algorithm animation, tree, invariant, shape analysis, abstract execution, visualisation

19

March 2005
SIAM Journal on Computing: Volume 34 Issue 3, 2005

**Publisher:** Society for Industrial and Applied Mathematics

We present a new analysis of the worst-case cost of path compression, which is an operation that is used in various well-known "union-find" algorithms. In contrast to previous analyses which are essentially based on bottom-up approaches, our method proceeds top-down, yielding recurrence relations from which the various bounds arise naturally. ...

**Keywords**:
path compression, union-find problem, inverse Ackermann function, disjoint sets data structure

20

April 2003
Journal of Combinatorial Theory Series A: Volume 102 Issue 1, April 2003

**Publisher:** Academic Press, Inc.

We show that a point set of cardinality n in the plane cannot be the vertex set of more than O(59 n n -6 ) straight-edge triangulations of its convex hull. This improves the previous upper bound of 276.75 n + O (log( n )) .