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Preprint Sep 2026

Single-Exponential Algorithms for Directed Feedback Vertex Set on Planar Digraphs

We consider Directed Feedback Vertex Set on planar digraphs, parameterized by the solution size $k$. We give a randomized algorithm with one-sided error running in time $(2+\sqrt5)^k n^{O(1)}= 4.24^k n^{O(1)}$, and a deterministic algorithm running in time $8.04^k n^{O(1)}$. Both algorithms use polynomial space. To the...

D. Lokshtanov, Saket Saurabh, Jie Xue · 0 citations
Preprint Sep 2026

Counting Paths and Trees via Exterior Algebra

We give randomized approximation algorithms for counting k-paths and k-forests in a host graph. Here k denotes the number of pattern vertices, n and m denote the numbers of host vertices and edges or arcs, {\epsilon} is the relative error, and {\delta} is the failure probability. Our main results are: 1. Paths: We appr...

Fahad Panolan, Saket Saurabh, M. Zehavi et al. · 0 citations

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