[PDF][PDF] Shaving Logs via Large Sieve Inequality: Faster Algorithms for Sparse Convolution and More
In sparse convolution-type problems, a common technique is to hash the input integers
modulo a random prime p∈[Q/2, Q] for some parameter Q, which reduces the range of the …
modulo a random prime p∈[Q/2, Q] for some parameter Q, which reduces the range of the …
3SUM in Preprocessed Universes: Faster and Simpler
We revisit the 3SUM problem in the\emph {preprocessed universes} setting. We present an
algorithm that, given three sets $ A $, $ B $, $ C $ of $ n $ integers, preprocesses them in …
algorithm that, given three sets $ A $, $ B $, $ C $ of $ n $ integers, preprocesses them in …
A Fine-grained Classification of Subquadratic Patterns for Subgraph Listing and Friends
K Bringmann, E Gorbachev - arXiv preprint arXiv:2404.04369, 2024 - arxiv.org
In an $ m $-edge host graph $ G $, all triangles can be listed in time $ O (m^{1.5}) $[Itai,
Rodeh'78], and all $ k $-cycles can be listed in time $ O (m^{2-1/{\lceil k/2\rceil}}+ t) $ where …
Rodeh'78], and all $ k $-cycles can be listed in time $ O (m^{2-1/{\lceil k/2\rceil}}+ t) $ where …
Worst-Case to Expander-Case Reductions: Derandomized and Generalized
A Abboud, N Wallheimer - arXiv preprint arXiv:2403.08394, 2024 - arxiv.org
A recent paper by Abboud and Wallheimer [ITCS 2023] presents self-reductions for various
fundamental graph problems, that transform worst-case instances to expanders, thus …
fundamental graph problems, that transform worst-case instances to expanders, thus …
[PDF][PDF] Exact and Parameterized Algorithms for Subset Sum Problems
T Randolph - 2024 - twrand.github.io
We present a variety of exact and parameterized algorithms for Subset Sum and other
related problems. The major contributions of this thesis include: 1. Average-case algorithms …
related problems. The major contributions of this thesis include: 1. Average-case algorithms …