ROLE
BOOKMARK & SHARE


Result page:
1
2
3
4
5
6
7
8
9
1
September 2017
Discrete & Computational Geometry: Volume 58 Issue 2, September 2017
Publisher: SpringerVerlag New York, Inc.
Consider a weighted graph G whose vertices are points in the plane and edges are line segments between pairs of points. The weight of each edge is the Euclidean distance between its two endpoints. A routing algorithm on G has a competitive ratio of c if the length of the ...
Keywords:
Competitive ratio, 68U05, Online routing, Routing ratio, 65D18, Delaunay triangulation
2
July 2017
Graphs and Combinatorics: Volume 33 Issue 4, July 2017
Publisher: SpringerVerlag
We prove that the facial nonrepetitive chromatic number of any outerplanar graph is at most 11 and of any planar graph is at most 22.
3
January 2017
Computational Geometry: Theory and Applications: Volume 60 Issue C, January 2017
Publisher: Elsevier Science Publishers B. V.
Given a set of n points in the plane, we show that O ( n 2 ) exchanging flips suffice to transform any edgelabelled pointed pseudotriangulation into any other with the same set of labels. By using insertion, deletion and exchanging flips, we can transform any edgelabelled pseudotriangulation into any ...
Keywords:
Edge label, Diagonal flip, Edge flip, Pseudotriangulation
4
December 2016
Discrete & Computational Geometry: Volume 56 Issue 4, December 2016
Publisher: SpringerVerlag New York, Inc.
Let P be a closed simple polygon with n vertices. For any two points in P, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in P. The geodesic center of P is the unique point in P that minimizes ...
Keywords:
Geodesic distance, Facility location, Simple polygons, 65D18
5
December 2016
Algorithmica: Volume 76 Issue 4, December 2016
Publisher: SpringerVerlag New York, Inc.
We consider the problem of performing predecessor searches in a bounded universe while achieving query times that depend on the distribution of queries. We obtain several data structures with various properties: in particular, we give data structures that achieve expected query times logarithmic in the entropy of the distribution of ...
Keywords:
Biased search trees, Data structures, Predecessor search, Entropy
6
December 2016
Algorithmica: Volume 76 Issue 4, December 2016
Publisher: SpringerVerlag New York, Inc.
A static binary search tree where every search starts from where the previous one ends (lazy finger) is considered. Such a search method is more powerful than that of the classic optimal static trees, where every search starts from the root (root finger), and less powerful than when rotations are ...
7
August 2016
Computational Geometry: Theory and Applications: Volume 57 Issue C, August 2016
Publisher: Elsevier Science Publishers B. V.
Let S be a finite set of points in the interior of a simple polygon P. A geodesic graph, G P ( S , E ) , is a graph with vertex set S and edge set E such that each edge ( a , b ) ź E is ...
Keywords:
Hamiltonian cycles, Perfect matchings, Spanning trees, Noncrossing graphs, Geodesic graphs
8
February 2016
Theoretical Computer Science: Volume 616 Issue C, February 2016
Publisher: Elsevier Science Publishers Ltd.
We present improved upper and lower bounds on the spanning ratio of �graphs with at least six cones. Given a set of points in the plane, a �graph partitions the plane around each vertex u into m disjoint cones, each having aperture � = 2 π / m , and ...
Keywords:
Spanners, Tight bounds, Computational geometry, Thetagraphs, Spanning ratio
9
July 2015
Computational Geometry: Theory and Applications: Volume 48 Issue 5, July 2015
Publisher: Elsevier Science Publishers B. V.
In this paper, we show that the �graph with three cones is connected. We also provide an alternative proof of the connectivity of the Yao graph with three cones.
Keywords:
Connected networks, Spanning graphs, Yao graphs, Theta graphs
10
March 2015
Theoretical Computer Science: Volume 569 Issue C, March 2015
Publisher: Elsevier Science Publishers Ltd.
We revisit the problem of searching for a target at an unknown location on a line when given upper and lower bounds on the distance D that separates the initial position of the searcher from the target. Prior to this work, only asymptotic bounds were known for the optimal competitive ...
Keywords:
Computational geometry, Fibonacci polynomials, Optimization, Online algorithms
11
October 2014
Computational Geometry: Theory and Applications: Volume 48 Issue 2, February, 2015
Publisher: Elsevier Science Publishers B. V.
Given a set of points in the plane, we show that the �graph with 5 cones is a geometric spanner with spanning ratio at most 50 + 22 5 � 9.960 . This is the first constant upper bound on the spanning ratio of this graph. The upper bound uses ...
Keywords:
Stretch factor, Theta graph, Spanning ratio, Spanner
12
October 2014
Computational Geometry: Theory and Applications: Volume 47 Issue 9, October, 2014
Publisher: Elsevier Science Publishers B. V.
In this paper, we show that the @qgraph with three cones is connected. We also provide an alternative proof of the connectivity of the Yao graph with three cones.
Keywords:
Connected networks, Spanning graphs, Yao graphs, Theta graphs
13
June 2014
SOCG'14: Proceedings of the thirtieth annual symposium on Computational geometry
Publisher: ACM
Bibliometrics:
Citation Count: 4
Downloads (6 Weeks): 2, Downloads (12 Months): 19, Downloads (Overall): 109
Full text available:
PDF
For a set of points in the plane and a fixed integer k > 0, the Yao graph Yk partitions the space around each point into k equiangular cones of angle &thetas; = 2π/k, and connects each point to a nearest neighbor in each cone. It is known for all ...
14
February 2014
Computational Geometry: Theory and Applications: Volume 47 Issue 2, February, 2014
Publisher: Elsevier Science Publishers B. V.
We propose a new model of realistic input: kguardable objects. An object is kguardable if its boundary can be seen by k guards. We show that kguardable polygons generalize two previously identified classes of realistic input. Following this, we give two simple algorithms for triangulating kguardable polygons. One algorithm requires ...
Keywords:
Polygon, Art gallery, Guarding, Triangulation
15
February 2014
Computational Geometry: Theory and Applications: Volume 47 Issue 2, February, 2014
Publisher: Elsevier Science Publishers B. V.
We show that any combinatorial triangulation on n vertices can be transformed into a 4connected one using at most @?(3n9)/ [email protected]? edge flips. We also give an example of an infinite family of triangulations that requires this many flips to be made 4connected, showing that our bound is tight. In addition, ...
Keywords:
Diagonal flip, Triangulation, Flip graph, Hamiltonian triangulation, 4Connected triangulation
16
January 2014
Computational Geometry: Theory and Applications: Volume 47 Issue 1, January, 2014
Publisher: Elsevier Science Publishers B. V.
Given a set S of n points in the plane and a fixed angle 0<@w<@p, we show how to find in O(nlogn) time all triangles of minimum area with one angle @w that enclose S. We prove that in general, the solution cannot be written without cubic roots. We also ...
Keywords:
Geometric optimization, Computational geometry, Enclosing problems
17
August 2013
WADS'13: Proceedings of the 13th international conference on Algorithms and Data Structures
Publisher: SpringerVerlag
We present improved upper bounds on the spanning ratio of a large family of θ graphs. A θ graph partitions the plane around each vertex into m disjoint cones, each having aperture θ =2 π / m . We show that for any integer k ≥1, θ graphs with 4 ...
Keywords:
computational geometry, spanners, θgraphs, spanning ratio
18
August 2013
WADS'13: Proceedings of the 13th international conference on Algorithms and Data Structures
Publisher: SpringerVerlag
In this paper we show that the θ graph with 4 cones has constant stretch factor, i.e., there is a path between any pair of vertices in this graph whose length is at most a constant times the Euclidean distance between that pair of vertices. This is the last θ ...
Keywords:
geometric spanners, θgraphs, computational geometry
19
June 2013
SoCG '13: Proceedings of the twentyninth annual symposium on Computational geometry
Publisher: ACM
Bibliometrics:
Citation Count: 1
Downloads (6 Weeks): 0, Downloads (12 Months): 4, Downloads (Overall): 79
Full text available:
PDF
Highly connected and yet sparse graphs (such as expanders or graphs of high treewidth) are fundamental, widely a pplicable and extensively studied combinatorial objects. We initiate the study of such highly connected graphs that are, in addition, geometric spanners. We define a property of spanners called robustness. Informally, when one ...
Keywords:
faultytolerance, geometric spanners, high treewidth
20
February 2013
Computational Geometry: Theory and Applications: Volume 46 Issue 2, February, 2013
Publisher: Elsevier Science Publishers B. V.
We consider two classes of higher order proximity graphs defined on a set of points in the plane, namely, the kDelaunay graph and the kGabriel graph. We give bounds on the following combinatorial and geometric properties of these graphs: spanning ratio, diameter, connectivity, chromatic number, and minimum number of layers ...
Keywords:
Proximity graphs, Geometric graphs

