Zhu, YuSegarra, Santiago2022-08-042022-08-042022Zhu, Yu and Segarra, Santiago. "Hypergraph cuts with edge-dependent vertex weights." <i>Applied Network Science,</i> 7, (2022) Springer Nature: https://doi.org/10.1007/s41109-022-00483-x.https://hdl.handle.net/1911/112981We develop a framework for incorporating edge-dependent vertex weights (EDVWs) into the hypergraph minimum s-t cut problem. These weights are able to reflect different importance of vertices within a hyperedge, thus leading to better characterized cut properties. More precisely, we introduce a new class of hyperedge splitting functions that we call EDVWs-based, where the penalty of splitting a hyperedge depends only on the sum of EDVWs associated with the vertices on each side of the split. Moreover, we provide a way to construct submodular EDVWs-based splitting functions and prove that a hypergraph equipped with such splitting functions can be reduced to a graph sharing the same cut properties. In this case, the hypergraph minimum s-t cut problem can be solved using well-developed solutions to the graph minimum s-t cut problem. In addition, we show that an existing sparsification technique can be easily extended to our case and makes the reduced graph smaller and sparser, thus further accelerating the algorithms applied to the reduced graph. Numerical experiments using real-world data demonstrate the effectiveness of our proposed EDVWs-based splitting functions in comparison with the all-or-nothing splitting function and cardinality-based splitting functions commonly adopted in existing work.engThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.Journal articles41109-022-00483-xhttps://doi.org/10.1007/s41109-022-00483-x