Solving Connectivity Problems Parameterized by Treedepth in Single-Exponential Time and Polynomial Space

A breakthrough result of Cygan et al. (FOCS 2011) showed that connectivity problems parameterized by treewidth can be solved much faster than the previously best known time ?^*(2^{?(twlog tw)}). Using their inspired Cut&Count technique, they obtained ?^*(?^tw) time algorithms for many such problems. Moreover, they proved these running times to be optimal assuming the Strong Exponential-Time Hypothesis. Unfortunately, like other dynamic programming algorithms on tree decompositions, these algorithms also require exponential space, and this is widely believed to be unavoidable. In contrast, for the slightly larger parameter called treedepth, there are already several examples of matching the time bounds obtained for treewidth, but using only polynomial space. Nevertheless, this has remained open for connectivity problems. In the present work, we close this knowledge gap by applying the Cut&Count technique to graphs of small treedepth. While the general idea is unchanged, we have to design novel procedures for counting consistently cut solution candidates using only polynomial space. Concretely, we obtain time ?^*(3^d) and polynomial space for Connected Vertex Cover, Feedback Vertex Set, and Steiner Tree on graphs of treedepth d. Similarly, we obtain time ?^*(4^d) and polynomial space for Connected Dominating Set and Connected Odd Cycle Transversal

Analyze Large Multidimensional Datasets Using Algebraic Topology

This paper presents an efficient algorithm to extract knowledge from high-dimensionality, high- complexity datasets using algebraic topology, namely simplicial complexes. Based on concept of isomorphism of relations, our method turn a relational table into a geometric object (a simplicial complex is a polyhedron). So, conceptually association rule searching is turned into a geometric traversal problem. By leveraging on the core concepts behind Simplicial Complex, we use a new technique (in computer science) that improves the performance over existing methods and uses far less memory. It was designed and developed with a strong emphasis on scalability, reliability, and extensibility. This paper also investigate the possibility of Hadoop integration and the challenges that come with the framework

Dynamic Graph Generation Network: Generating Relational Knowledge from Diagrams

In this work, we introduce a new algorithm for analyzing a diagram, which contains visual and textual information in an abstract and integrated way. Whereas diagrams contain richer information compared with individual image-based or language-based data, proper solutions for automatically understanding them have not been proposed due to their innate characteristics of multi-modality and arbitrariness of layouts. To tackle this problem, we propose a unified diagram-parsing network for generating knowledge from diagrams based on an object detector and a recurrent neural network designed for a graphical structure. Specifically, we propose a dynamic graph-generation network that is based on dynamic memory and graph theory. We explore the dynamics of information in a diagram with activation of gates in gated recurrent unit (GRU) cells. On publicly available diagram datasets, our model demonstrates a state-of-the-art result that outperforms other baselines. Moreover, further experiments on question answering shows potentials of the proposed method for various applications