503 research outputs found
FPT Algorithms for Plane Completion Problems
The Plane Subgraph (resp. Topological Minor) Completion problem asks, given a (possibly disconnected) plane (multi)graph Gamma and a connected plane (multi)graph Delta, whether it is possible to add edges in Gamma without violating the planarity of its embedding so that it contains some subgraph (resp. topological minor) that is topologically isomorphic to Delta. We give FPT algorithms that solve both problems in f(|E(Delta)|)*|E(Gamma)|^{2} steps. Moreover, for the Plane Subgraph Completion problem we show that f(k)=2^{O(k*log(k))}
Variants of Plane Diameter Completion
The {\sc Plane Diameter Completion} problem asks, given a plane graph and
a positive integer , if it is a spanning subgraph of a plane graph that
has diameter at most . We examine two variants of this problem where the
input comes with another parameter . In the first variant, called BPDC,
upper bounds the total number of edges to be added and in the second, called
BFPDC, upper bounds the number of additional edges per face. We prove that
both problems are {\sf NP}-complete, the first even for 3-connected graphs of
face-degree at most 4 and the second even when on 3-connected graphs of
face-degree at most 5. In this paper we give parameterized algorithms for both
problems that run in steps.Comment: Accepted in IPEC 201
A Polynomial-time Algorithm for Outerplanar Diameter Improvement
The Outerplanar Diameter Improvement problem asks, given a graph and an
integer , whether it is possible to add edges to in a way that the
resulting graph is outerplanar and has diameter at most . We provide a
dynamic programming algorithm that solves this problem in polynomial time.
Outerplanar Diameter Improvement demonstrates several structural analogues to
the celebrated and challenging Planar Diameter Improvement problem, where the
resulting graph should, instead, be planar. The complexity status of this
latter problem is open.Comment: 24 page
A survey of parameterized algorithms and the complexity of edge modification
The survey is a comprehensive overview of the developing area of parameterized algorithms for graph modification problems. It describes state of the art in kernelization, subexponential algorithms, and parameterized complexity of graph modification. The main focus is on edge modification problems, where the task is to change some adjacencies in a graph to satisfy some required properties. To facilitate further research, we list many open problems in the area.publishedVersio
Enroute flight planning: Evaluating design concepts for the development of cooperative problem-solving concepts
The goals of this research were to develop design concepts to support the task of enroute flight planning. And within this context, to explore and evaluate general design concepts and principles to guide the development of cooperative problem solving systems. A detailed model is to be developed of the cognitive processes involved in flight planning. Included in this model will be the identification of individual differences of subjects. Of particular interest will be differences between pilots and dispatchers. The effect will be studied of the effect on performance of tools that support planning at different levels of abstraction. In order to conduct this research, the Flight Planning Testbed (FPT) was developed, a fully functional testbed environment for studying advanced design concepts for tools to aid in flight planning
Refined Complexity of PCA with Outliers
Principal component analysis (PCA) is one of the most fundamental procedures
in exploratory data analysis and is the basic step in applications ranging from
quantitative finance and bioinformatics to image analysis and neuroscience.
However, it is well-documented that the applicability of PCA in many real
scenarios could be constrained by an "immune deficiency" to outliers such as
corrupted observations. We consider the following algorithmic question about
the PCA with outliers. For a set of points in , how to
learn a subset of points, say 1% of the total number of points, such that the
remaining part of the points is best fit into some unknown -dimensional
subspace? We provide a rigorous algorithmic analysis of the problem. We show
that the problem is solvable in time . In particular, for constant
dimension the problem is solvable in polynomial time. We complement the
algorithmic result by the lower bound, showing that unless Exponential Time
Hypothesis fails, in time , for any function of , it is
impossible not only to solve the problem exactly but even to approximate it
within a constant factor.Comment: To be presented at ICML 201
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