Efficient certification of feasibility and objective value of linear programs and its applications

The use of linear programming in various areas has increased with the significant improvement of specialized solvers. Linear programs are used as such to model practical problems, or as subroutines in algorithms such as formal proofs or branch-and-cut frameworks. In many situations a certified answer is needed, for example the guarantee that the linear program is feasible or infeasible, or a provably safe bound on its objective value. Most of the available solvers work with floating-point arithmetic and are thus subject to its shortcomings such as rounding errors or underflow, therefore they can deliver incorrect answers. While adequate for some applications, this is unacceptable for critical applications like flight controlling or nuclear plant management due to the potential catastrophic consequences. We propose a method that gives a certified answer whether a linear program is feasible or infeasible, or returns unknown'. The advantage of our method is that it is reasonably fast and rarely answers unknown'. It works by computing a safe solution that is in some way the best possible in the relative interior of the feasible set. To certify the relative interior, we employ exact arithmetic, whose use is nevertheless limited in general to critical places, allowing us to rnremain computationally efficient. Moreover, when certain conditions are fulfilled, our method is able to deliver a provable bound on the objective value of the linear program. We test our algorithm on typical benchmark sets and obtain higher rates of success compared to previous approaches for this problem, while keeping the running times acceptably small. The computed objective value bounds are in most of the cases very close to the known exact objective values. We prove the usability of the method we developed by additionally employing a variant of it in a different scenario, namely to improve the results of a Satisfiability Modulo Theories solver. Our method is used as a black box in the nodes of a branch-and-bound tree to implement conflict learning based on the certificate of infeasibility for linear programs consisting of subsets of linear constraints. The generated conflict clauses are in general small and give good rnprospects for reducing the search space. Compared to other methods we obtain significant improvements in the running time, especially on the large instances.

Content extraction: Identifying the main content in HTML documents

Except the article forming the main content most HTML documents on the WWW contain additional contents such as navigation menus, design elements or commercial banners. In the context of several applications it is necessary to draw the distinction between main and additional content automatically. Content extraction and template detection are the two approaches to solve this task. This thesis gives an extensive overview of existing algorithms from both areas. It contributes an objective way to measure and evaluate the performance of content extraction algorithms under different aspects. These evaluation measures allow to draw the first objective comparison of existing extraction solutions. The newly introduced content code blurring algorithm overcomes several drawbacks of previous approaches and proves to be the best content extraction algorithm at the moment. An analysis of methods to cluster web documents according to their underlying templates is the third major contribution of this thesis. In combination with a localised crawling process this clustering analysis can be used to automatically create sets of training documents for template detection algorithms. As the whole process can be automated it allows to perform template detection on a single document, thereby combining the advantages of single and multi document algorithms.