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In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view.Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B involve ...
We consider high-dimensional random optimization problems where the dynamical variables are subjected to nonconvex excluded volume constraints. We focus on the case in which the cost function is a simple quadratic cost and the excluded volume constraints a ...
Many transportation markets are characterized by oligopolistic competition. In these markets customers, suppliers and regulators make decisions that are influenced by the preferences and the decisions of all other agents. In particular, capturing and under ...
Pearl's do calculus is a complete axiomatic approach to learn the identifiable causal effects from observational data. When such an effect is not identifiable, it is necessary to perform a collection of often costly interventions in the system to learn the ...
Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the filter graph dis ...
Many robotics problems are formulated as optimization problems. However, most optimization solvers in robotics are locally optimal and the performance depends a lot on the initial guess. For challenging problems, the solver will often get stuck at poor loc ...
We solve the Bin Packing problem in O^*(2^k) time, where k is the number of items less or equal to one third of the bin capacity. This parameter measures the distance from the polynomially solvable case of only large (i.e., greater than one third) items. O ...
Schloss Dagstuhl – Leibniz-Zentrum fur Informatik2022
In this paper, we formulate a mixed integer linear program (MILP) for the simulated maximum likelihood estimation (MLSE) problem and devise a Benders decomposition approach to speed up the solution process. This framework can be applied to any advanced dis ...
We present the design of a motion planning algorithm that ensures safety for an autonomous vehicle. In particular, we consider a multimodal distribution over uncertainties; for example, the uncertain predictions of future trajectories of surrounding vehicl ...
In this paper, we formulate a mixed integer linear program (MILP) for the simulated maximum likelihood estimation (MLSE) problem and devise a Benders decomposition approach to speed up the solution process. This framework can be applied to any advanced dis ...