92,320 research outputs found
Semi-dynamic connectivity in the plane
Motivated by a path planning problem we consider the following procedure.
Assume that we have two points and in the plane and take
. At each step we add to a compact convex
set that does not contain nor . The procedure terminates when the sets
in separate and . We show how to add one set to
in amortized time plus the time needed to find
all sets of intersecting the newly added set, where is the
cardinality of , is the number of sets in
intersecting the newly added set, and is the inverse of the
Ackermann function
Connectivity Oracles for Graphs Subject to Vertex Failures
We introduce new data structures for answering connectivity queries in graphs
subject to batched vertex failures. A deterministic structure processes a batch
of failed vertices in time and thereafter
answers connectivity queries in time. It occupies space . We develop a randomized Monte Carlo version of our data structure
with update time , query time , and space
for any failure bound . This is the first connectivity oracle for
general graphs that can efficiently deal with an unbounded number of vertex
failures.
We also develop a more efficient Monte Carlo edge-failure connectivity
oracle. Using space , edge failures are processed in time and thereafter, connectivity queries are answered in
time, which are correct w.h.p.
Our data structures are based on a new decomposition theorem for an
undirected graph , which is of independent interest. It states that
for any terminal set we can remove a set of
vertices such that the remaining graph contains a Steiner forest for with
maximum degree
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A design representation model for high-level synthesis
Design tools share and exchange various types of information pertaining to the design. The identification of a uniform design representation to capture this information is essential for the development of a successful design environment. We have done an extensive study on the representation needs of existing database tools in the UCI CADLAB; examples of which are graph compilers for high-level hardware specifications, state schedulers, hardware allocators, and microarchitecture optimizers. The result of this study is the development of a design representation model that will serve as a common internal representation (DDM) for all system and behavioral synthesis tools. DDM thus builds the foundation for a CAD Framework in which design tools can communicate via operating on this common representation. The design information is composed of three separate graph models: the conceptual model, the behavioral model and the structural model. The conceptual model (represented by a Design Entity Graph) captures the overall organization of the design information, such as, versions and configurations. The behavioral model (represented by an Augmented Control/Data Flow Graph) describes the design behavior. The structural model (represented by an Annotated Component Graph) captures the hierarchical data path structure and its geometric information. In this paper, we define the last two graph models. They both capture the actual design data of the application domain. Since VHDL has gained increasing popularity as hardware description language for synthesis, we give numerous examples throughout this report that show how the proposed design representation model can be used to represent VHDL specifications
Decentralized Connectivity-Preserving Deployment of Large-Scale Robot Swarms
We present a decentralized and scalable approach for deployment of a robot
swarm. Our approach tackles scenarios in which the swarm must reach multiple
spatially distributed targets, and enforce the constraint that the robot
network cannot be split. The basic idea behind our work is to construct a
logical tree topology over the physical network formed by the robots. The
logical tree acts as a backbone used by robots to enforce connectivity
constraints. We study and compare two algorithms to form the logical tree:
outwards and inwards. These algorithms differ in the order in which the robots
join the tree: the outwards algorithm starts at the tree root and grows towards
the targets, while the inwards algorithm proceeds in the opposite manner. Both
algorithms perform periodic reconfiguration, to prevent suboptimal topologies
from halting the growth of the tree. Our contributions are (i) The formulation
of the two algorithms; (ii) A comparison of the algorithms in extensive
physics-based simulations; (iii) A validation of our findings through
real-robot experiments.Comment: 8 pages, 8 figures, submitted to IROS 201
A New Perspective on Clustered Planarity as a Combinatorial Embedding Problem
The clustered planarity problem (c-planarity) asks whether a hierarchically
clustered graph admits a planar drawing such that the clusters can be nicely
represented by regions. We introduce the cd-tree data structure and give a new
characterization of c-planarity. It leads to efficient algorithms for
c-planarity testing in the following cases. (i) Every cluster and every
co-cluster (complement of a cluster) has at most two connected components. (ii)
Every cluster has at most five outgoing edges.
Moreover, the cd-tree reveals interesting connections between c-planarity and
planarity with constraints on the order of edges around vertices. On one hand,
this gives rise to a bunch of new open problems related to c-planarity, on the
other hand it provides a new perspective on previous results.Comment: 17 pages, 2 figure
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
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