13 research outputs found
Subexponential Parameterized Algorithms for Cut and Cycle Hitting Problems on H-Minor-Free Graphs
We design the first subexponential-time (parameterized) algorithms for
several cut and cycle-hitting problems on -minor free graphs. In particular,
we obtain the following results (where is the solution-size parameter).
1. time algorithms for Edge
Bipartization and Odd Cycle Transversal;
2. a time algorithm for Edge
Multiway Cut and a time algorithm for
Vertex Multiway Cut, where is the number of terminals to be separated;
3. a time algorithm for Edge
Multicut and a time algorithm
for Vertex Multicut, where is the number of terminal pairs to be separated;
4. a time algorithm for
Group Feedback Edge Set and a time
algorithm for Group Feedback Vertex Set, where is the size of the group.
5. In addition, our approach also gives time algorithms for
all above problems with the exception of time for
Edge/Vertex Multicut and time for Group Feedback
Edge/Vertex Set.
We obtain our results by giving a new decomposition theorem on graphs of
bounded genus, or more generally, an -almost-embeddable graph for any fixed
constant . In particular we show the following. Let be an
-almost-embeddable graph for a constant . Then for every
, there exist disjoint sets such
that for every and every , the treewidth
of is . Here is the
graph obtained from by contracting edges with both endpoints in .Comment: A preliminary version appears in SODA'2
A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms
Parameterization and approximation are two popular ways of coping with
NP-hard problems. More recently, the two have also been combined to derive many
interesting results. We survey developments in the area both from the
algorithmic and hardness perspectives, with emphasis on new techniques and
potential future research directions
Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization
International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM
Learning-based Segmentation for Connectomics
Recent advances in electron microscopy techniques make it possible to acquire highresolution, isotropic volume images of neural circuitry. In connectomics, neuroscientists seek to obtain the circuit diagram involving all neurons and synapses in such a volume image. Mapping neuron connectivity requires tracing each and every neural process through terabytes of image data. Due to the size and complexity of these volume images, fully automated analysis methods are desperately needed. In this thesis, I consider automated, machine learning-based neurite segmentation approaches based on a simultaneous merge decision of adjacent supervoxels.
- Given a learned likelihood of merging adjacent supervoxels, Chapter 4 adapts a probabilistic graphical model which ensures that merge decisions are consistent
and the surfaces of final segments are closed. This model can be posed as a multicut optimization problem and is solved with the cutting-plane method. In order to scale to large datasets, a fast search for (and good choice of) violated cycle constraints is crucial. Quantitative experiments show that the proposed closed-surface regularization significantly improves segmentation performance.
- In Chapter 5, I investigate whether the edge weights of the previous model can be chosen to minimize the loss with respect to non-local segmentation quality measures (e.g. Rand Index). Suitable w are obtained from a structured learning approach. In the Structured Support Vector Machine formulation, a novel fast enumeration scheme is used to find the most violated constraint. Quantitative experiments show that structured learning can improve upon unstructured methods. Furthermore, I introduce a new approximate, hierarchical and blockwise optimization approach for large-scale multicut segmentation. Using this method, high-quality approximate solutions for large problem instances are found quickly.
- Chapter 6 introduces another novel approximate scheme for multicut segmentation -- Cut, Glue&Cut -- which is based on the move-making paradigm. First, the graph is recursively partitioned into small regions (cut phase). Then, for any two adjacent regions, alternative cuts of these two regions define possible moves (glue&cut phase). The proposed algorithm finds segmentations that are { as measured by a loss function { as close to the ground-truth as the global optimum found by exact solvers, while being significantly faster than existing methods.
- In order to jointly label resulting segments as well as to label the boundaries between segments, Chapter 7 proposes the Asymmetric Multi-way Cut model, a variant of Multi-way Cut. In this new model, within-class cuts are allowed for some labels, while being forbidden for other labels. Qualitative experiments show when such a formulation can be beneficial. In particular, an application to joint neurite and cell organelle labeling in EM volume images is discussed.
- Custom software tools that can cope with the large data volumes common in the field of connectomics are a prerequisite for the implementation and evaluation of novel segmentation techniques. Chapter 3 presents version 1.0 of ilastik, a joint effort of multiple researchers. I have co-written its volume viewing component, volumina. ilastik provides an interactive pixel classification work
ow on largerthan-RAM datasets as well as a semi-automated segmentation module useful for acquiring gold standard segmentations. Furthermore, I describe new software for
dealing with hierarchies of cell complexes as well as for blockwise image processing operations on large datasets.
The different segmentation methods presented in this thesis provide a promising direction towards reaching the required reliability as well as the required data throughput
necessary for connectomics applications
LIPIcs, Volume 248, ISAAC 2022, Complete Volume
LIPIcs, Volume 248, ISAAC 2022, Complete Volum
Networks, Communication, and Computing Vol. 2
Networks, communications, and computing have become ubiquitous and inseparable parts of everyday life. This book is based on a Special Issue of the Algorithms journal, and it is devoted to the exploration of the many-faceted relationship of networks, communications, and computing. The included papers explore the current state-of-the-art research in these areas, with a particular interest in the interactions among the fields
A Near-Linear Approximation Scheme for Multicuts of Embedded Graphs with a Fixed Number of Terminals
International audienc
A Near-Linear Approximation Scheme for Multicuts of Embedded Graphs with a Fixed Number of Terminals
International audienc