53 research outputs found
Locked and unlocked smooth embeddings of surfaces
We study the continuous motion of smooth isometric embeddings of a planar
surface in three-dimensional Euclidean space, and two related discrete
analogues of these embeddings, polygonal embeddings and flat foldings without
interior vertices, under continuous changes of the embedding or folding. We
show that every star-shaped or spiral-shaped domain is unlocked: a continuous
motion unfolds it to a flat embedding. However, disks with two holes can have
locked embeddings that are topologically equivalent to a flat embedding but
cannot reach a flat embedding by continuous motion.Comment: 8 pages, 8 figures. To appear in 34th Canadian Conference on
Computational Geometr
Robust Geometric Spanners
Highly connected and yet sparse graphs (such as expanders or graphs of high
treewidth) are fundamental, widely applicable 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 removes a few vertices from a robust
spanner, this harms only a small number of other vertices. We show that robust
spanners must have a superlinear number of edges, even in one dimension. On the
positive side, we give constructions, for any dimension, of robust spanners
with a near-linear number of edges.Comment: 18 pages, 8 figure
Arboricity, h-Index, and Dynamic Algorithms
In this paper we present a modification of a technique by Chiba and Nishizeki
[Chiba and Nishizeki: Arboricity and Subgraph Listing Algorithms, SIAM J.
Comput. 14(1), pp. 210--223 (1985)]. Based on it, we design a data structure
suitable for dynamic graph algorithms. We employ the data structure to
formulate new algorithms for several problems, including counting subgraphs of
four vertices, recognition of diamond-free graphs, cop-win graphs and strongly
chordal graphs, among others. We improve the time complexity for graphs with
low arboricity or h-index.Comment: 19 pages, no figure
Degree Constrained Triangulation of Annular Regions and Point Sites
Generating constrained triangulations of point sites distributed in the plane is a significant problem in computational geometry. We present theoretical and experimental investigation results for generating triangulations for polygons and point sites that address node degree constraints. We characterize point sites that have almost all vertices of odd degree. We present experimental results on the node degree distribution of Delaunay triangulations of point sites generated randomly. Additionally, we present a heuristic algorithm for triangulating a given normal annular region with an increment of even degree nodes
Representation transformations of ordered lists
Search and update operations of dictionaries have been well studied, due
to their practical significance. There are many different representations of
them, and some applications prefer this, the others that representation. A
main point is the size of the dictionary: for a small one a sorted array can
be the best representation, while for a bigger one an AVL tree or a red-black
tree might be the optimal choice (depending on the necessary operations and
their frequencies), and for an extra large one we may prefer a B+-tree, for
example.
Consequently it can be desirable to transform such a collection of data
from one representation into another, efficiently. There is a common feature
of the data structures mentioned: they can be considered strictly ordered
lists. Thus in this paper we start a new topic of interest: How to transform a
strictly ordered list form one representation into another, efficiently? What
about the time and space complexities of such transformations?
Keywords: strictly increasing list, representation-transformation, data structure
(DS), linear, array, binary tree (BT), balanced, search tre
An Improved Upper Bound for SAT
We show that the CNF satisfiability problem can be solved
time, where is the number of clauses in the formula, improving the known
upper bounds given by Yamamoto 15 years ago and
given by Hirsch 22 years ago. By using an amortized technique and careful case
analysis, we successfully avoid the bottlenecks in previous algorithms and get
the improvement
- …