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cs.DS2023
Max -Flow Oracles and Negative Cycle Detection in Planar Digraphs
Adam Karczmarz
We study the maximum -flow oracle problem on planar directed graphs where the goal is to design a data structure answering max -flow value (or equivalently, min -cut…
cs.DS2023
Deterministic Fully Dynamic SSSP and More
Jan van den Brand, Adam Karczmarz
We present the first non-trivial fully dynamic algorithm maintaining exact single-source distances in unweighted graphs. This resolves an open problem stated by Sankowski [COCOON 2…
cs.DS2023
Sensitivity and Dynamic Distance Oracles via Generic Matrices and Frobenius Form
Adam Karczmarz, Piotr Sankowski
Algebraic techniques have had an important impact on graph algorithms so far. Porting them, e.g., the matrix inverse, into the dynamic regime improved best-known bounds for various…