4,708 research outputs found
Fully-dynamic Planarity Testing in Polylogarithmic Time
Given a dynamic graph subject to insertions and deletions of edges, a natural
question is whether the graph presently admits a planar embedding. We give a
deterministic fully-dynamic algorithm for general graphs, running in amortized
time per edge insertion or deletion, that maintains a bit
indicating whether or not the graph is presently planar. This is an exponential
improvement over the previous best algorithm [Eppstein, Galil, Italiano,
Spencer, 1996] which spends amortized time per update.Comment: Updated version of paper submitted to STOC'20. This version features
a complete rewrite of section 4.4 (do-separation-flips). The new version
fixes an overlooked case in the previous version (the two fundamental cycles
we find do not necessarily share an edge) and contains a detailed
case-by-case proof of correctnes
Dynamic Planar Embeddings of Dynamic Graphs
We present an algorithm to support the dynamic embedding in the plane of a
dynamic graph. An edge can be inserted across a face between two vertices on
the face boundary (we call such a vertex pair linkable), and edges can be
deleted. The planar embedding can also be changed locally by flipping
components that are connected to the rest of the graph by at most two vertices.
Given vertices , linkable decides whether and are
linkable in the current embedding, and if so, returns a list of suggestions for
the placement of in the embedding. For non-linkable vertices , we
define a new query, one-flip-linkable providing a suggestion for a flip
that will make them linkable if one exists. We support all updates and queries
in O(log) time. Our time bounds match those of Italiano et al. for a
static (flipless) embedding of a dynamic graph.
Our new algorithm is simpler, exploiting that the complement of a spanning
tree of a connected plane graph is a spanning tree of the dual graph. The
primal and dual trees are interpreted as having the same Euler tour, and a main
idea of the new algorithm is an elegant interaction between top trees over the
two trees via their common Euler tour.Comment: Announced at STACS'1
Lower bounds for fully dynamic connectivity problems in graphs
We prove lower bounds on the complexity of maintaining fully dynamic k-edge or k-vertex connectivity in plane graphs and in (k - 1)-vertex connected graphs. We show an amortized lower bound of _0_(log n/k(log log n + log b)) per edge insertion, deletion, or query operation in the cell probe model, where b is the word size of the machine and n is the number of vertices in G. We also show an amortized lower bound of _0_(log n/(log log n + log b)) per operation for fully dynamic planarity testing in embedded graphs. These are the first lower bounds for fully dynamic connectivity problems
PQ TREES, CONSECUTIVE ONES PROBLEM AND APPLICATIONS
A PQ tree is an advanced treeâbased data structure, which represents a family of permutations on a set of elements. In this research article, we considered the significance of PQ trees and the Consecutive ones Problem to Computer Science and bioinformatics and their various applications.
We also went further to demonstrate the operations of the characteristics of the Consecutive ones property by simulation, using high level programming languages. Attempt was also made at developing a PQ treeâConsecutive Ones analyzer, which could be instrumental not only as an
educative tool to inquisitive students, but also serve as an important tool in developing clustering software in the field of bioinformatics and other application domains, with respect to solving real life problems
Folding Large Antenna Tape Spring
This paper presents a novel concept for a low-mass, 50-m^2-deployable, P-band dual polarization antenna that can measure terrestrial biomass levels from a spacecraft in a low Earth orbit. A monolithic array of feed and radiating patches is bonded to a transversally curved structure consisting of two Kevlar sheets. The first sheet supports the array and the other sheet supports a ground plane. The two sheets are connected by a compliant Kevlar core that allows the whole structure to be folded elastically and to spring back to its original, undamaged shape. Test pieces have been made to demonstrate both the radio frequency and mechanical aspects of the design, particularly the radio frequency performance before and after folding the structure. It is concluded that the proposed design concept has high potential for large, low-frequency antennas for low-cost missions
Dynamic Planar Embeddings of Dynamic Graphs
We present an algorithm to support the dynamic embedding in the plane
of a dynamic graph. An edge can be inserted across a face between two vertices on the boundary (we call such a vertex pair linkable), and edges can be deleted. The planar embedding can also be changed locally by flipping components that are connected to the rest of the graph by at most two vertices. Given vertices u,v, linkable(u,v) decides whether u and v are linkable, and if so, returns a list of suggestions for the placement of (u,v) in the embedding. For non-linkable vertices u,v, we define a new query, one-flip-linkable(u,v) providing a suggestion for a flip that will make them linkable if one exists. We will support all updates and queries in O(log^2 n) time. Our time bounds match those of Italiano et al. for a static (flipless) embedding of a dynamic graph.
Our new algorithm is simpler, exploiting that the complement of a spanning tree of a connected plane graph is a spanning tree of the dual graph. The primal and dual trees are interpreted as having the same Euler tour, and a main idea of the new algorithm is an elegant
interaction between top trees over the two trees via their common Euler tour
Fast Dynamic Graph Algorithms for Parameterized Problems
Fully dynamic graph is a data structure that (1) supports edge insertions and
deletions and (2) answers problem specific queries. The time complexity of (1)
and (2) are referred to as the update time and the query time respectively.
There are many researches on dynamic graphs whose update time and query time
are , that is, sublinear in the graph size. However, almost all such
researches are for problems in P. In this paper, we investigate dynamic graphs
for NP-hard problems exploiting the notion of fixed parameter tractability
(FPT).
We give dynamic graphs for Vertex Cover and Cluster Vertex Deletion
parameterized by the solution size . These dynamic graphs achieve almost the
best possible update time and the query time
, where is the time complexity of any static
graph algorithm for the problems. We obtain these results by dynamically
maintaining an approximate solution which can be used to construct a small
problem kernel. Exploiting the dynamic graph for Cluster Vertex Deletion, as a
corollary, we obtain a quasilinear-time (polynomial) kernelization algorithm
for Cluster Vertex Deletion. Until now, only quadratic time kernelization
algorithms are known for this problem.
We also give a dynamic graph for Chromatic Number parameterized by the
solution size of Cluster Vertex Deletion, and a dynamic graph for
bounded-degree Feedback Vertex Set parameterized by the solution size. Assuming
the parameter is a constant, each dynamic graph can be updated in
time and can compute a solution in time. These results are obtained by
another approach.Comment: SWAT 2014 to appea
Correlations between cancellous bone architecture and its dynamic behaviour
Previous studies showed that in vivo evaluation of the fracture risk of cancellous bone can be assessed by identifying the relationships between its microarchitecture description extracted from clinical imaging and its mechanical properties. The mechanical properties under dynamic loadings (with and without confinement) were obtained and compared to quasi-static ones. The architectural parameters of each specimen were extracted from pQCT images and split into four groups: geometry, topology, connectivity and anisotropy. Results show that architectural parameters are strong determinants of mechanical behaviour for the different applied boundary conditions.http://icills2014.org/wp-content/uploads/2014/01/Marrianne-Prot.pd
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