259,605 research outputs found
Reconstructing Generalized Staircase Polygons with Uniform Step Length
Visibility graph reconstruction, which asks us to construct a polygon that
has a given visibility graph, is a fundamental problem with unknown complexity
(although visibility graph recognition is known to be in PSPACE). We show that
two classes of uniform step length polygons can be reconstructed efficiently by
finding and removing rectangles formed between consecutive convex boundary
vertices called tabs. In particular, we give an -time reconstruction
algorithm for orthogonally convex polygons, where and are the number of
vertices and edges in the visibility graph, respectively. We further show that
reconstructing a monotone chain of staircases (a histogram) is fixed-parameter
tractable, when parameterized on the number of tabs, and polynomially solvable
in time under reasonable alignment restrictions.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Routing on the Visibility Graph
We consider the problem of routing on a network in the presence of line
segment constraints (i.e., obstacles that edges in our network are not allowed
to cross). Let be a set of points in the plane and let be a set of
non-crossing line segments whose endpoints are in . We present two
deterministic 1-local -memory routing algorithms that are guaranteed to
find a path of at most linear size between any pair of vertices of the
\emph{visibility graph} of with respect to a set of constraints (i.e.,
the algorithms never look beyond the direct neighbours of the current location
and store only a constant amount of additional information). Contrary to {\em
all} existing deterministic local routing algorithms, our routing algorithms do
not route on a plane subgraph of the visibility graph. Additionally, we provide
lower bounds on the routing ratio of any deterministic local routing algorithm
on the visibility graph.Comment: An extended abstract of this paper appeared in the proceedings of the
28th International Symposium on Algorithms and Computation (ISAAC 2017).
Final version appeared in the Journal of Computational Geometr
The Partial Visibility Representation Extension Problem
For a graph , a function is called a \emph{bar visibility
representation} of when for each vertex , is a
horizontal line segment (\emph{bar}) and iff there is an
unobstructed, vertical, -wide line of sight between and
. Graphs admitting such representations are well understood (via
simple characterizations) and recognizable in linear time. For a directed graph
, a bar visibility representation of , additionally, puts the bar
strictly below the bar for each directed edge of
. We study a generalization of the recognition problem where a function
defined on a subset of is given and the question is whether
there is a bar visibility representation of with for every . We show that for undirected graphs this problem
together with closely related problems are \NP-complete, but for certain cases
involving directed graphs it is solvable in polynomial time.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Recommended from our members
Couldn't or Wouldn't? the Influence of Privacy Concerns and Self-Efficacy in Privacy Management on Privacy Protection
Sampling 515 college students, this study investigates how privacy protection, including profile visibility, self-disclosure, and friending, are influenced by privacy concerns and efficacy regarding one's own ability to manage privacy settings, a factor that researchers have yet to give a great deal of attention to in the context of social networking sites (SNSs). The results of this study indicate an inconsistency in adopting strategies to protect privacy, a disconnect from limiting profile visibility and friending to self-disclosure. More specifically, privacy concerns lead SNS users to limit their profile visibility and discourage them from expanding their network. However, they do not constrain self-disclosure. Similarly, while self-efficacy in privacy management encourages SNS users to limit their profile visibility, it facilitates self-disclosure. This suggests that if users are limiting their profile visibility and constraining their friending behaviors, it does not necessarily mean they will reduce self-disclosure on SNSs because these behaviors are predicted by different factors. In addition, the study finds an interaction effect between privacy concerns and self-efficacy in privacy management on friending. It points to the potential problem of increased risk-taking behaviors resulting from high self-efficacy in privacy management and low privacy concerns.Radio-Television-Fil
Information Gathering in Networks via Active Exploration
How should we gather information in a network, where each node's visibility
is limited to its local neighborhood? This problem arises in numerous
real-world applications, such as surveying and task routing in social networks,
team formation in collaborative networks and experimental design with
dependency constraints. Often the informativeness of a set of nodes can be
quantified via a submodular utility function. Existing approaches for
submodular optimization, however, require that the set of all nodes that can be
selected is known ahead of time, which is often unrealistic. In contrast, we
propose a novel model where we start our exploration from an initial node, and
new nodes become visible and available for selection only once one of their
neighbors has been chosen. We then present a general algorithm NetExp for this
problem, and provide theoretical bounds on its performance dependent on
structural properties of the underlying network. We evaluate our methodology on
various simulated problem instances as well as on data collected from social
question answering system deployed within a large enterprise.Comment: Longer version of IJCAI'15 pape
- …