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About 708 papers for “Topological sorting”
Taras Zakharko · 2023
Flexible and ergonomic topological sorting implementation for R. Supports a variety of input data encoding (lists of edges or adjacency matrices, graphs edge direction), stable sort variants as well as cycle detection with detailed diagnosis.
Cited by 0Open access
Maxim Arnold, Christian Kondor · arXiv (Cornell University) · 2021
In this note we investigate finite-type invariants of the pure braids arising from signed sorting networks.
Cited by 0Open access
Philipp Woelfel · Journal of Discrete Algorithms · 2005
Cited by 43
Antoine Amarilli, Charles Paperman · SPIRE - Sciences Po Institutional REpository · 2018
International audience
Cited by 6Open access
I. Dochviri, James F. Peters · Mathematics in Computer Science · 2016
Cited by 5
Perayil, Aneena Rinu, Kuświk, Piotr, Urbaniak, Maciej et al. · arXiv (Cornell University) · 2025
Topologically nontrivial adiabatic loops of the orientation of a homogeneous external magnetic field drive the walking of paramagnetic colloidal bipeds above a deformed quasi-periodic magnetic square pattern. Depending on the topological properties of the loop we can simultaneously control the walking directions of colloidal bipeds as a function of their size and as a function of the size of a deformed unit cell of the pattern. The bipeds walk performing steps with their two feet alternatingly grounding one foot and lifting the other. The step width of the bipeds is given by a set of winding numbers $(w_x,w_{y})\in Z^2$ -- a set of topological invariants -- that can only change by integers as we continuously increase the length of the bipeds. We experimentally use this discrete size dependence for the robust sorting of bipeds according to their length.
Cited by 0Open access
Chen, Ho-Lin, Lin, Peng-Ting, Tsai, Meng-Tsung · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2025
Computing a topological ordering for an n-node directed acyclic graph (DAG) G is computationally challenging in streaming models. Chakrabarti et al. {[}SODA 2020{]} showed that in the insertion-only streaming model, every single-pass algorithm requires Ω(n²) space, and every k-pass algorithm requires n^{1+Ω(1/k)} space for any constant k ≥ 1. We study the parameterized complexity of streaming algorithms for topological sorting, considering two parameters: the independence number α and the maximum displacement δ. Our results include an O(1/ε)-pass O(α n^{1+ε})-space streaming algorithm and an O(n^{1/2})-pass O(n+δ²)-space streaming algorithm. For dense random DAGs, both α and δ are small, allowing us to improve the state-of-the-art for topological sorting in random DAGs. As applications, we show that strongly connected components (SCC) decomposition and 2-satisfiability (2-SAT) can be solved in O(1/ε) passes using O(α n^{1+ε}) space and O(α_I n^{1+ε}) space, respectively, where α_I denotes the independence number of the implication graph induced by the input 2-SAT instance.
Cited by 0Open access
Aneena Rinu Rinu Perayil, Piotr Kuświk, M. Urbaniak et al. · Soft Matter · 2025
Topologically nontrivial adiabatic loops of the orientation of a homogeneous external magnetic field drive the walking of paramagnetic colloidal bipeds above a deformed quasi-periodic magnetic square pattern. Depending on the topological properties of the loop we can simultaneously control the walking directions of colloidal bipeds as a function of their size and as a function of the size of a deformed unit cell of the pattern. The bipeds walk performing steps with their two feet alternatingly grounding one foot and lifting the other. The step width of the bipeds is given by a set of winding numbers (<i>w</i><sub><i>x</i></sub>, <i>w</i><sub><i>y</i></sub>) ∈ <sup>2</sup> - a set of topological invariants - that can only change by integers as we continuously increase the length of the bipeds. We experimentally use this discrete size dependence for the robust sorting of bipeds according to their length.
Cited by 1Open access
Deepak Ajwani, Adan Cosgaya-Lozano, Norbert Zeh · ACM Journal of Experimental Algorithmics · 2012
We present an I/O-efficient algorithm for topologically sorting directed acyclic graphs, called IterTS. In the worst case, our algorithm is extremely inefficient and performs O( n ċ sort( m )) I/Os. However, our experiments show that IterTS achieves good performance in practice. To evaluate IterTS, we compared its running time to those of three competitors: PeelTS, an I/O-efficient implementation of the standard strategy of iteratively removing sources and sinks; ReachTS, an I/O-efficient implementation of a recent parallel divide-and-conquer algorithm based on reachability queries; and SeTS, a standard DFS-based topological sorting built on top of a semiexternal DFS algorithm. In our evaluation on various types of input graphs, IterTS consistently outperformed PeelTS and ReachTS by at least an order of magnitude in most cases. SeTS outperformed IterTS on most graphs whose vertex sets fit in memory. However, IterTS often came close to the running time of SeTS on these inputs and, more importantly, SeTS was not able to process graphs whose vertex sets were beyond the size of main memory, while IterTS was able to process such inputs efficiently.
Cited by 16
Christoph Weber, Marc Stamminger · Eurographics · 2016
We present a preprocessing pipeline for triangle meshes that topologically sorts all triangles for a given camera and scene animation in front-to-back or back-to-front order. This allows us to efficiently render a given animation without depth buffer, and to include transparency. We also remove non-contributing triangles, thus improving render time, especially when applying anti-aliasing. To this end we first record the visible triangles of a sequence of frames. For every frame we create a directed graph storing occlusion information. After a topological sort of this graph, all triangles are sorted properly. The contribution of this paper is the reduction of redundancy by merging the graphs of all frames. The result of our pipeline is a single sorted index buffer, over which we slide a window that yields sorted index buffers for each single frame. Circular dependencies are broken by placing duplicates of the affected triangles in the index buffer. Our sliding window then displays only frame specific triangles in their proper order. We conclude by demonstrating the benefits of removing invisible triangles and disabling the hardware visibility test.
Cited by 2Open access
G. Yuval · Information Processing Letters · 1973
Cited by 0
Philipp Woelfel · 2012
We present a symbolic OBDD algorithm for topological sorting which requires O(log² N) OBDD operations. Then we analyze its true runtime for the directed grid graph and show an upper bound of O(log⁴ N). This is the first true runtime analysis of a symbolic OBDD algorithm for a fundamental graph problem, and it demonstrates that one can hope that the algorithm behaves well for sufficiently structured inputs.
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2025
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2025
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2025
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Lars Arge, et al. · 2003
We present algorithms that solve a number of fundamental problems on planar directed graphs (planar digraphs) in O(sort(N)) I/Os, where sort(N) is the number of I/Os needed to sort N elements. The problems we consider are breadth-first search, the single-source shortest path problem, computing a directed ear decomposition of a strongly connected planar digraph, computing an open directed ear decomposition of a strongly connected biconnected planar digraph, and topologically sorting a planar directed acyclic graph.
Cited by 0
Lars Arge, Laura Toma, Norbert Zeh · 2003
We present algorithms that solve a number of fundamental problems on planar directed graphs (planar digraphs) in O((N)) I/Os, where (N) is the number of I/Os needed to sort N elements. The problems we consider are breadth-first search, the single-source shortest path problem, computing a directed ear decomposition of a strongly connected planar digraph, computing an open directed ear decomposition of a strongly connected biconnected planar digraph, and topologically sorting a planar directed acyclic graph.
Cited by 28
Andrew R. Curtis, et al. · 2004
Cited by 0
2025
Cited by 0
Lars Arge, Laura Toma, Norbert Zeh · 2003
We present algorithms that solve a number of fundamental problems on planar directed graphs (planar digraphs) in O((N)) I/Os, where (N) is the number of I/Os needed to sort N elements. The problems we consider are breadth-first search, the single-source shortest path problem, computing a directed ear decomposition of a strongly connected planar digraph, computing an open directed ear decomposition of a strongly connected biconnected planar digraph, and topologically sorting a planar directed acyclic graph.
Cited by 4