We present a numerical study of multicommodity transport in a noisy, nonlinear network. The nonlinearity determines the dynamics of the edge capacities, which can be amplified or suppressed depending on the local curr...
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We present a numerical study of multicommodity transport in a noisy, nonlinear network. The nonlinearity determines the dynamics of the edge capacities, which can be amplified or suppressed depending on the local current flowing across an edge. We consider network self-organization for three different nonlinear functions: For all three we identify parameter regimes where noise leads to self-organization into more robust topologies, that are not found by the sole noiseless dynamics. Moreover, the interplay between noise and specific functional behavior of the nonlinearity gives rise to different features, such as (i) continuous or discontinuous responses to the demand strength and (ii) either single or multistable solutions. Our study shows the crucial role of the activation function on noise-assisted phenomena.
networkX is a well-established Python library for network analysis. With gdMetriX, we aim to extend the functionality of networkX and provide common quality metrics used in the field of graph drawing, such as the numb...
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The constraint satisfaction problem (CSP) is among the most studied computational problems. While NP-hard, many tractable subproblems have been identified (Bulatov 2017, Zuk 2017). Backdoors, introduced by Williams, G...
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For several decades, much effort has been put into identifying classes of CNF formulas whose satisfiability can be decided in polynomial time. Classic results are the linear-time tractability of Horn formulas (Aspvall...
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A book embedding of a graph is a drawing that maps vertices onto a line and edges to simple pairwise non-crossing curves drawn into "pages", which are half-planes bounded by that line. Two-page book embeddin...
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Boundary labeling is a well-known method for displaying short textual labels for a set of point features in a figure alongside the boundary of that figure. Labels and their corresponding points are connected via cross...
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The labeling of point features on a map is a well-studied topic. In a static setting, the goal is to find a non-overlapping label placement for (a subset of) point features. In a dynamic setting, the set of point feat...
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The approximate computation of twin-width has attracted significant attention already since the moment the parameter was introduced. A recently proposed approach (STACS 2024) towards obtaining a better understanding o...
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Tree-cut width is a parameter that has been introduced as an attempt to obtain an analogue of treewidth for edge cuts. Unfortunately, in spite of its desirable structural properties, it turned out that tree-cut width ...
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The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is the most prominent multi-objective evolutionary algorithm for real-world applications. While it performs evidently well on bi-objective optimization problems...
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