Approximability of Connected Factors

Finding a d-regular spanning subgraph (or d-factor) of a graph is easy by Tutte's reduction to the matching problem. By the same reduction, it is easy to find a minimal or maximal d-factor of a graph. However, if we require that the d-factor is connected, these problems become NP-hard - finding a minimal connected 2-factor is just the traveling salesman problem (TSP). Given a complete graph with edge weights that satisfy the triangle inequality, we consider the problem of finding a minimal connected $d$-factor. We give a 3-approximation for all $d$ and improve this to an (r+1)-approximation for even d, where r is the approximation ratio of the TSP. This yields a 2.5-approximation for even d. The same algorithm yields an (r+1)-approximation for the directed version of the problem, where r is the approximation ratio of the asymmetric TSP. We also show that none of these minimization problems can be approximated better than the corresponding TSP. Finally, for the decision problem of deciding whether a given graph contains a connected d-factor, we extend known hardness results.Comment: To appear in the proceedings of WAOA 201

Hypergraph Acyclicity and Propositional Model Counting

We show that the propositional model counting problem #SAT for CNF- formulas with hypergraphs that allow a disjoint branches decomposition can be solved in polynomial time. We show that this class of hypergraphs is incomparable to hypergraphs of bounded incidence cliquewidth which were the biggest class of hypergraphs for which #SAT was known to be solvable in polynomial time so far. Furthermore, we present a polynomial time algorithm that computes a disjoint branches decomposition of a given hypergraph if it exists and rejects otherwise. Finally, we show that some slight extensions of the class of hypergraphs with disjoint branches decompositions lead to intractable #SAT, leaving open how to generalize the counting result of this paper

CIDI-Lung-Seg: A Single-Click Annotation Tool for Automatic Delineation of Lungs from CT Scans

Accurate and fast extraction of lung volumes from computed tomography (CT) scans remains in a great demand in the clinical environment because the available methods fail to provide a generic solution due to wide anatomical variations of lungs and existence of pathologies. Manual annotation, current gold standard, is time consuming and often subject to human bias. On the other hand, current state-of-the-art fully automated lung segmentation methods fail to make their way into the clinical practice due to their inability to efficiently incorporate human input for handling misclassifications and praxis. This paper presents a lung annotation tool for CT images that is interactive, efficient, and robust. The proposed annotation tool produces an "as accurate as possible" initial annotation based on the fuzzy-connectedness image segmentation, followed by efficient manual fixation of the initial extraction if deemed necessary by the practitioner. To provide maximum flexibility to the users, our annotation tool is supported in three major operating systems (Windows, Linux, and the Mac OS X). The quantitative results comparing our free software with commercially available lung segmentation tools show higher degree of consistency and precision of our software with a considerable potential to enhance the performance of routine clinical tasks.Comment: 4 pages, 6 figures; to appear in the proceedings of 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC 2014