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arXiv · 2609.11160

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Tomohiro Koana·Soh Kumabe
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Abstract

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

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Tomohiro Koana, Soh Kumabe. 2026-09-10. Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation. https://arxiv.org/abs/2609.11160

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