@inproceedings{EbertMasingLindneretal.2025, author = {Ebert, Patricia and Masing, Berenike and Lindner, Niels and Gleixner, Ambros}, title = {Sorting Criteria for Line-based Periodic Timetabling Heuristics}, booktitle = {Operations Research Proceedings 2024. OR 2024}, pages = {348 -- 354}, year = {2025}, abstract = {It is well-known that optimal solutions are notoriously hard to find for the Periodic Event Scheduling Problem (PESP), which is the standard mathematical formulation to optimize periodic timetables in public transport. We consider a class of incremental heuristics that have been demonstrated to be effective by Lindner and Liebchen (2023), however, for only one fixed sorting strategy of lines along which a solution is constructed. Thus, in this paper, we examine a variety of sortings based on the number, weight, weighted span, and lower bound of arcs, and test for each setting various combinations of the driving, dwelling, and transfer arcs of lines. Additionally, we assess the impact on the incremental extension of the event-activity network by minimizing resp. maximizing a connectivity measure between subsets of lines. We compare our 27 sortings on the railway instances of the benchmarking library PESPlib within the ConcurrentPESP solver framework. We are able to find five new incumbent solutions, resulting in improvements of up to 2\%.}, language = {en} } @inproceedings{FrankeHamacherManns2026, author = {Franke, Paula and Hamacher, Kay and Manns, Paul}, title = {Minimizing and Maximizing the Shannon Entropy for Fixed Marginals}, booktitle = {Operations Research Proceedings 2025}, year = {2026}, abstract = {The mutual information (MI) between two random variables is an important correlation measure in data analysis. The Shannon entropy of a joint probability distri- bution is the variable part under fixed marginals. We aim to minimize and maximize it to obtain the largest and smallest MI possible in this case, leading to a scaled MI ratio for better comparability. We present algorithmic approaches and optimal solutions for a set of problem instances based on data from molecular evolution. We show that this allows us to construct a sensible, systematic correction to raw MI values.}, language = {en} } @inproceedings{RiccardiLindner2026, author = {Riccardi, Gabor and Lindner, Niels}, title = {On The Minimum-Weight Forward (Weakly) Fundamental Cycle Basis Problem in Directed Graphs}, booktitle = {International Network Optimization Conference 2026 (INOC 2026)}, year = {2026}, abstract = {The cycle space of a directed graph is generated by a cycle basis, where, in general, cycles are allowed to have both forward and backward arcs. In a forward cycle, all arcs have to follow the given direction. We study the existence, structure, and computational complexity of minimum-weight forward cycle bases in directed graphs. We give a complete structural characterization of digraphs that admit weakly fundamental (and hence integral) forward cycle bases, showing that this holds if and only if every block is either strongly connected or a single arc. We further provide an easily verifiable characterization of when a strongly connected digraph admits a forward fundamental cycle basis, proving that such a basis exists if and only if the set of directed cycles has cardinality equal to the cycle rank; in this case, the basis is unique and computable in polynomial time, and nonexistence can likewise be certified efficiently. Lastly, we show that while minimum-weight forward fundamental cycle bases can be found in polynomial time whenever they exist, the minimum-weight forward weakly fundamental cycle basis problem is NP-hard via a polynomial-time reduction from the minimum-weight weakly fundamental cycle basis problem on digraphs with metric weights.}, language = {en} }