Results 1  10
of
75
On Straightening LowDiameter Unit Trees
 In Proc. 13th International Symposium on Graph Drawing
, 2005
"... A polygonal chain is a sequence of consecutively joined edges embedded in space. A kchain is a chain of k edges. A polygonal tree is a set of edges joined into a tree structure embedded in space. A unit tree is a tree with only edges of unit length. A chain or a tree is simple if nonadjacent edges ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
A polygonal chain is a sequence of consecutively joined edges embedded in space. A kchain is a chain of k edges. A polygonal tree is a set of edges joined into a tree structure embedded in space. A unit tree is a tree with only edges of unit length. A chain or a tree is simple if nonadjacent edges do not intersect. We consider the problem about the reconfiguration of a simple chain or tree through a series of continuous motions such that the lengths of all tree edges are preserved and no edge crossings are allowed. A chain or tree can be straightened if all its edges can be aligned along a common straight line such that each edge points “away ” from a designed leaf node. Otherwise it is called locked. Graph reconfiguration problems have wide applications in contexts including robotics, molecular conformation, rigidity and knot theory. The motivation for us to study unit trees is that for instance, the bondinglengths in molecules are often similar, as are the segments of robot arms. A chain in 2D can always be straightened [4, 5]. In 4D or higher, a tree can always be straightened [3]. There exist trees [2] in 2D and 5chains in 3D that
Optimizing active ranges for consistent dynamic map labeling
 IN PROCEEDINGS OF THE 24TH ANNUAL SYMPOSIUM ON COMPUTATIONAL GEOMETRY
, 2008
"... Map labeling encounters unique issues in the context of dynamic maps with continuous zooming and panning—an application with increasing practical importance. In consistent dynamic map labeling, distracting behavior such as popping and jumping is avoided. In our model a dynamic label placement is a c ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
Map labeling encounters unique issues in the context of dynamic maps with continuous zooming and panning—an application with increasing practical importance. In consistent dynamic map labeling, distracting behavior such as popping and jumping is avoided. In our model a dynamic label placement is a continuous function that assigns a 2dlabel to each scale. This defines a 3dsolid, with scale as the third dimension. To avoid popping, we truncate each solid to a single scale range, called its active range. This range corresponds to the interval of scales at which the label is visible. The active range optimization (ARO) problem is to select active ranges so that no two truncated solids overlap and the sum of the active ranges is maximized. We show that the ARO problem is NPcomplete, even for quite simple solid shapes, and we present constantfactor approximations for different variants of the problem.
Experience
"... • Conduct research in algorithms for combinatorial problems in computational geometry and topology as a ..."
Abstract
 Add to MetaCart
• Conduct research in algorithms for combinatorial problems in computational geometry and topology as a
Fáry’s Theorem for 1Planar Graphs
"... Abstract. Fáry’s theorem states that every plane graph can be drawn as a straightline drawing. A plane graph is a graph embedded in a plane without edge crossings. In this paper, we extend Fáry’s theorem to nonplanar graphs. More specifically, we study the problem of drawing 1plane graphs with str ..."
Abstract

Cited by 14 (4 self)
 Add to MetaCart
Abstract. Fáry’s theorem states that every plane graph can be drawn as a straightline drawing. A plane graph is a graph embedded in a plane without edge crossings. In this paper, we extend Fáry’s theorem to nonplanar graphs. More specifically, we study the problem of drawing 1plane graphs with straightline edges. A 1plane graph is a graph embedded in a plane with at most one crossing per edge. We give a characterisation of those 1plane graphs that admit a straightline drawing. The proof of the characterisation consists of a linear time testing algorithm and a drawing algorithm. We also show that there are 1plane graphs for which every straightline drawing has exponential area. To our best knowledge, this is the first result to extend Fáry’s theorem to nonplanar graphs. 1
On Unfolding Trees and Polygons on Various Lattices
"... We consider the problem of unfolding lattice trees and polygons in hexagonal or triangular lattice in two dimensions. We show that a hexagonal/triangular lattice chain (resp. tree) can be straightened in O(n) (resp. O(n 2)) moves and time, and a hexagonal/triangular lattice polygon can be convexifie ..."
Abstract
 Add to MetaCart
We consider the problem of unfolding lattice trees and polygons in hexagonal or triangular lattice in two dimensions. We show that a hexagonal/triangular lattice chain (resp. tree) can be straightened in O(n) (resp. O(n 2)) moves and time, and a hexagonal/triangular lattice polygon can be convexified in O(n 2) moves and time. We hope that the techniques we used shed some light on solving the more general conjecture that a unit tree in two dimensions can always be straightened. 1
unknown title
"... We consider the problem of unfolding lattice polygons embedded on the surface of some classes of lattice polyhedra. We show that an unknotted lattice polygon embedded on a lattice orthotube or orthotree can be convexified in O(n) moves and time, and a lattice polygon embedded on a lattice Tower of H ..."
Abstract
 Add to MetaCart
We consider the problem of unfolding lattice polygons embedded on the surface of some classes of lattice polyhedra. We show that an unknotted lattice polygon embedded on a lattice orthotube or orthotree can be convexified in O(n) moves and time, and a lattice polygon embedded on a lattice Tower of Hanoi or Manhattan Tower can be convexified in O(n 2) moves and time. 1
Labeling Points with Weights
, 2001
"... . Annotating maps, graphs, and diagrams with pieces of text is an important step in information visualization that is usually referred to as label placement. We define nine labelplacement models for labeling points with axisparallel rectangles given a weight for each point. There are two group ..."
Abstract

Cited by 15 (3 self)
 Add to MetaCart
. Annotating maps, graphs, and diagrams with pieces of text is an important step in information visualization that is usually referred to as label placement. We define nine labelplacement models for labeling points with axisparallel rectangles given a weight for each point. There are two groups; fixedposition models and slider models. We aim to maximize the weight sum of those points that receive a label. We first compare our models by giving bounds for the ratios between the weights of maximumweight labelings in di#erent models. Then we present algorithms for labeling n points with unitheight rectangles. We show how an O(n log n)time factor2 approximation algorithm and a PTAS for fixedposition models can be extended to handle the weighted case. Our main contribution is the first algorithm for weighted sliding labels. Its approximation factor is (2 + ε), it runs in O(n 2/ε) time and uses O(n²/#) space. We also investigate some special cases.
Few Optimal Foldings of HP Protein Chains on Various Lattices∗
"... We consider whether or not protein chains in the HP model have unique or few optimal foldings. We solve the conjecture proposed by Aichholzer et al. that the open chain L2k−1 = (HP)k(PH)k−1 for k ≥ 3 has exactly two optimal foldings on the square lattice. We show that some closed and open chains ha ..."
Abstract
 Add to MetaCart
We consider whether or not protein chains in the HP model have unique or few optimal foldings. We solve the conjecture proposed by Aichholzer et al. that the open chain L2k−1 = (HP)k(PH)k−1 for k ≥ 3 has exactly two optimal foldings on the square lattice. We show that some closed and open chains have unique optimal foldings on the hexagonal and triangular lattices, respectively. 1
Abstract Few Optimal Foldings of HP Protein Chains on Various Lattices ∗
"... We consider whether or not protein chains in the HP model have unique or few optimal foldings. We solve the conjecture proposed by Aichholzer et al. that the open chain L2k−1 = (HP) k (P H) k−1 for k ≥ 3 has exactly two optimal foldings on the square lattice. We show that some closed and open chains ..."
Abstract
 Add to MetaCart
We consider whether or not protein chains in the HP model have unique or few optimal foldings. We solve the conjecture proposed by Aichholzer et al. that the open chain L2k−1 = (HP) k (P H) k−1 for k ≥ 3 has exactly two optimal foldings on the square lattice. We show that some closed and open chains have unique optimal foldings on the hexagonal and triangular lattices, respectively. 1
Abstract Few Optimal Foldings of HP Protein Chains on Various Lattices ∗
"... We consider whether or not protein chains in the HP model have unique or few optimal foldings. We solve the conjecture proposed by Aichholzer et al. that the open chain L2k−1 = (HP) k (P H) k−1 for k ≥ 3 has exactly two optimal foldings on the square lattice. We show that some closed and open chains ..."
Abstract
 Add to MetaCart
We consider whether or not protein chains in the HP model have unique or few optimal foldings. We solve the conjecture proposed by Aichholzer et al. that the open chain L2k−1 = (HP) k (P H) k−1 for k ≥ 3 has exactly two optimal foldings on the square lattice. We show that some closed and open chains have unique optimal foldings on the hexagonal and triangular lattices, respectively. 1
Results 1  10
of
75