519 research outputs found
Interactive Camera Network Design using a Virtual Reality Interface
Traditional literature on camera network design focuses on constructing
automated algorithms. These require problem specific input from experts in
order to produce their output. The nature of the required input is highly
unintuitive leading to an unpractical workflow for human operators. In this
work we focus on developing a virtual reality user interface allowing human
operators to manually design camera networks in an intuitive manner. From real
world practical examples we conclude that the camera networks designed using
this interface are highly competitive with, or superior to those generated by
automated algorithms, but the associated workflow is much more intuitive and
simple. The competitiveness of the human-generated camera networks is
remarkable because the structure of the optimization problem is a well known
combinatorial NP-hard problem. These results indicate that human operators can
be used in challenging geometrical combinatorial optimization problems given an
intuitive visualization of the problem.Comment: 11 pages, 8 figure
Half-integrality, LP-branching and FPT Algorithms
A recent trend in parameterized algorithms is the application of polytope
tools (specifically, LP-branching) to FPT algorithms (e.g., Cygan et al., 2011;
Narayanaswamy et al., 2012). However, although interesting results have been
achieved, the methods require the underlying polytope to have very restrictive
properties (half-integrality and persistence), which are known only for few
problems (essentially Vertex Cover (Nemhauser and Trotter, 1975) and Node
Multiway Cut (Garg et al., 1994)). Taking a slightly different approach, we
view half-integrality as a \emph{discrete} relaxation of a problem, e.g., a
relaxation of the search space from to such that
the new problem admits a polynomial-time exact solution. Using tools from CSP
(in particular Thapper and \v{Z}ivn\'y, 2012) to study the existence of such
relaxations, we provide a much broader class of half-integral polytopes with
the required properties, unifying and extending previously known cases.
In addition to the insight into problems with half-integral relaxations, our
results yield a range of new and improved FPT algorithms, including an
-time algorithm for node-deletion Unique Label Cover with
label set and an -time algorithm for Group Feedback Vertex
Set, including the setting where the group is only given by oracle access. All
these significantly improve on previous results. The latter result also implies
the first single-exponential time FPT algorithm for Subset Feedback Vertex Set,
answering an open question of Cygan et al. (2012).
Additionally, we propose a network flow-based approach to solve some cases of
the relaxation problem. This gives the first linear-time FPT algorithm to
edge-deletion Unique Label Cover.Comment: Added results on linear-time FPT algorithms (not present in SODA
paper
Discovering Reliable Dependencies from Data: Hardness and Improved Algorithms
The reliable fraction of information is an attractive score for quantifying
(functional) dependencies in high-dimensional data. In this paper, we
systematically explore the algorithmic implications of using this measure for
optimization. We show that the problem is NP-hard, which justifies the usage of
worst-case exponential-time as well as heuristic search methods. We then
substantially improve the practical performance for both optimization styles by
deriving a novel admissible bounding function that has an unbounded potential
for additional pruning over the previously proposed one. Finally, we
empirically investigate the approximation ratio of the greedy algorithm and
show that it produces highly competitive results in a fraction of time needed
for complete branch-and-bound style search.Comment: Accepted to Proceedings of the IEEE International Conference on Data
Mining (ICDM'18
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