Computing a Feedback Arc Set Using PageRank

Geladaris, Vasileios; Lionakis, Panagiotis; Tollis, Ioannis G.

doi:10.48550/arxiv.2208.09234

Cited by 1 publication

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References 12 publications

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“…The problem belongs to the large class of problems known as 'integer programs' or 'combinatorial optimization' which in general are NP-complete [42]. Therefore, various heuristic approaches have been taken such as the FAS algorithm [28][29][30][31][32], the Cuthill-McKee algorithm [25] or page-rank algorithms [33] (for review, see [17,34,35]). Depending on the particular objective and the specific algorithm, they are based on reordering the graph nodes according to their degree, i.e.…”

Section: Discussionmentioning

confidence: 99%

Connectivity Matrix Seriation via Relaxation

Borst

2024

PLoS Comput Biol

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Volume electron microscopy together with computer-based image analysis are yielding neural circuit diagrams of ever larger regions of the brain. These datasets are usually represented in a cell-to-cell connectivity matrix and contain important information about prevalent circuit motifs allowing to directly test various theories on the computation in that brain structure. Of particular interest are the detection of cell assemblies and the quantification of feedback, which can profoundly change circuit properties. While the ordering of cells along the rows and columns doesn’t change the connectivity, it can make special connectivity patterns recognizable. For example, ordering the cells along the flow of information, feedback and feedforward connections are segregated above and below the main matrix diagonal, respectively. Different algorithms are used to renumber matrices such as to minimize a given cost function, but either their performance becomes unsatisfying at a given size of the circuit or the CPU time needed to compute them scales in an unfavorable way with increasing number of neurons. Based on previous ideas, I describe an algorithm which is effective in matrix reordering with respect to both its performance as well as to its scaling in computing time. Rather than trying to reorder the matrix in discrete steps, the algorithm transiently relaxes the integer program by assigning a real-valued parameter to each cell describing its location on a continuous axis (‘smooth-index’) and finds the parameter set that minimizes the cost. I find that the smooth-index algorithm outperforms all algorithms I compared it to, including those based on topological sorting.

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Section: Discussionmentioning

confidence: 99%

Connectivity Matrix Seriation via Relaxation

Borst

2024

PLoS Comput Biol

View full text Add to dashboard Cite

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Computing a Feedback Arc Set Using PageRank

Cited by 1 publication

References 12 publications

Connectivity Matrix Seriation via Relaxation

Connectivity Matrix Seriation via Relaxation

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