752 research outputs found
Linear-Time Algorithms for Geometric Graphs with Sublinearly Many Edge Crossings
We provide linear-time algorithms for geometric graphs with sublinearly many
crossings. That is, we provide algorithms running in O(n) time on connected
geometric graphs having n vertices and k crossings, where k is smaller than n
by an iterated logarithmic factor. Specific problems we study include Voronoi
diagrams and single-source shortest paths. Our algorithms all run in linear
time in the standard comparison-based computational model; hence, we make no
assumptions about the distribution or bit complexities of edge weights, nor do
we utilize unusual bit-level operations on memory words. Instead, our
algorithms are based on a planarization method that "zeroes in" on edge
crossings, together with methods for extending planar separator decompositions
to geometric graphs with sublinearly many crossings. Incidentally, our
planarization algorithm also solves an open computational geometry problem of
Chazelle for triangulating a self-intersecting polygonal chain having n
segments and k crossings in linear time, for the case when k is sublinear in n
by an iterated logarithmic factor.Comment: Expanded version of a paper appearing at the 20th ACM-SIAM Symposium
on Discrete Algorithms (SODA09
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
Prioritized Metric Structures and Embedding
Metric data structures (distance oracles, distance labeling schemes, routing
schemes) and low-distortion embeddings provide a powerful algorithmic
methodology, which has been successfully applied for approximation algorithms
\cite{llr}, online algorithms \cite{BBMN11}, distributed algorithms
\cite{KKMPT12} and for computing sparsifiers \cite{ST04}. However, this
methodology appears to have a limitation: the worst-case performance inherently
depends on the cardinality of the metric, and one could not specify in advance
which vertices/points should enjoy a better service (i.e., stretch/distortion,
label size/dimension) than that given by the worst-case guarantee.
In this paper we alleviate this limitation by devising a suit of {\em
prioritized} metric data structures and embeddings. We show that given a
priority ranking of the graph vertices (respectively,
metric points) one can devise a metric data structure (respectively, embedding)
in which the stretch (resp., distortion) incurred by any pair containing a
vertex will depend on the rank of the vertex. We also show that other
important parameters, such as the label size and (in some sense) the dimension,
may depend only on . In some of our metric data structures (resp.,
embeddings) we achieve both prioritized stretch (resp., distortion) and label
size (resp., dimension) {\em simultaneously}. The worst-case performance of our
metric data structures and embeddings is typically asymptotically no worse than
of their non-prioritized counterparts.Comment: To appear at STOC 201
Advance of the Access Methods
The goal of this paper is to outline the advance of the access methods in the last ten years as well as
to make review of all available in the accessible bibliography methods
Convexity-Increasing Morphs of Planar Graphs
We study the problem of convexifying drawings of planar graphs. Given any
planar straight-line drawing of an internally 3-connected graph, we show how to
morph the drawing to one with strictly convex faces while maintaining planarity
at all times. Our morph is convexity-increasing, meaning that once an angle is
convex, it remains convex. We give an efficient algorithm that constructs such
a morph as a composition of a linear number of steps where each step either
moves vertices along horizontal lines or moves vertices along vertical lines.
Moreover, we show that a linear number of steps is worst-case optimal.
To obtain our result, we use a well-known technique by Hong and Nagamochi for
finding redrawings with convex faces while preserving y-coordinates. Using a
variant of Tutte's graph drawing algorithm, we obtain a new proof of Hong and
Nagamochi's result which comes with a better running time. This is of
independent interest, as Hong and Nagamochi's technique serves as a building
block in existing morphing algorithms.Comment: Preliminary version in Proc. WG 201
Survey on model-based manipulation planning of deformable objects
A systematic overview on the subject of model-based manipulation planning of deformable objects is presented. Existing modelling techniques of volumetric, planar and linear deformable objects are described, emphasizing the different types of deformation. Planning strategies are categorized according to the type of manipulation goal: path planning, folding/unfolding, topology modifications and assembly. Most current contributions fit naturally into these categories, and thus the presented algorithms constitute an adequate basis for future developments.Preprin
From Frequency to Meaning: Vector Space Models of Semantics
Computers understand very little of the meaning of human language. This
profoundly limits our ability to give instructions to computers, the ability of
computers to explain their actions to us, and the ability of computers to
analyse and process text. Vector space models (VSMs) of semantics are beginning
to address these limits. This paper surveys the use of VSMs for semantic
processing of text. We organize the literature on VSMs according to the
structure of the matrix in a VSM. There are currently three broad classes of
VSMs, based on term-document, word-context, and pair-pattern matrices, yielding
three classes of applications. We survey a broad range of applications in these
three categories and we take a detailed look at a specific open source project
in each category. Our goal in this survey is to show the breadth of
applications of VSMs for semantics, to provide a new perspective on VSMs for
those who are already familiar with the area, and to provide pointers into the
literature for those who are less familiar with the field
Sequential Principal-Agent Problems with Communication: Efficient Computation and Learning
We study a sequential decision making problem between a principal and an
agent with incomplete information on both sides. In this model, the principal
and the agent interact in a stochastic environment, and each is privy to
observations about the state not available to the other. The principal has the
power of commitment, both to elicit information from the agent and to provide
signals about her own information. The principal and the agent communicate
their signals to each other, and select their actions independently based on
this communication. Each player receives a payoff based on the state and their
joint actions, and the environment moves to a new state. The interaction
continues over a finite time horizon, and both players act to optimize their
own total payoffs over the horizon. Our model encompasses as special cases
stochastic games of incomplete information and POMDPs, as well as sequential
Bayesian persuasion and mechanism design problems. We study both computation of
optimal policies and learning in our setting. While the general problems are
computationally intractable, we study algorithmic solutions under a conditional
independence assumption on the underlying state-observation distributions. We
present an polynomial-time algorithm to compute the principal's optimal policy
up to an additive approximation. Additionally, we show an efficient learning
algorithm in the case where the transition probabilities are not known
beforehand. The algorithm guarantees sublinear regret for both players
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