# Questions tagged [fine-grained]

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### Barriers and ETH, or its variants

ETH (Exponential Time Hypothesis) or its variants SETH(Strong ETH), NSETH(Non Deterministic SETH) haven't been resolved as yet. But resolution to any of the above hypotheses could lead to interesting ...
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### Lower-bounds under SETH

After reading a bit about SETH (the strong exponential time hypothesis), I see that a lot of lower bounds for problems in P can be proven if we assume SETH. But I notice that most of the ones that are ...
• 161
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### Solving All-Pairs Shortest Paths using a distance matrix in sub-cubic time

I'm working on a project centered around the All-Pairs Shortest Paths (APSP) problem. Common algorithms to APSP (Floyd-Warshall, Bellman-Ford, Johnson's) work with the standard definition of the ...
• 61
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### Fine-Grained Hardness for Undirected Hamiltonicity

The fastest known algorithm for detecting Hamiltonian cycles in directed graphs on $n$ nodes runs in essentially $2^n\text{poly}(n)$ time. However, for undirected graphs on $n$ nodes, there is an ...
• 686
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### Is APSP verification easier than APSP?

In APSP, the input is an $n$-node directed weighted graph $G$, and the output is an $n \times n$ matrix holding pairwise shortest path distances between nodes in $G$. Define "APSP-Verification" as ...
• 2,403
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### Does small circuits for a NP-complete problem contradict ETH?

The remarks of the Theorem 4 in the paper "On the complexity of circuit satisfiability" claims that: if circuit satisfiability (CktSat) problem can be decided by deterministic circuits of $2^{o(n)}$ ...
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