The paper presents an improved algorithm for solving the Pigeonhole Equal Sums problem, which is a variant of the Subset Sum problem.
The key insights are:
Structural characterization of instances with few non-subset-sums: The algorithm exploits a rigid structure of the input numbers when the number of non-subset-sums (parameter d) is small. This allows improving the naive meet-in-middle approach.
Subsampling approach for instances with many solutions: When d is large, there are many solutions, which enables a subsampling technique combined with modular dynamic programming to speed up the search.
The paper provides two algorithms:
Combining these two algorithms gives an overall O*(2^0.4n) time randomized algorithm for Pigeonhole Equal Sums.
The paper also presents a polynomial-space algorithm that runs in O*(2^0.75n) time.
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by Ce Jin,Hongx... pada arxiv.org 03-29-2024
https://arxiv.org/pdf/2403.19117.pdfPertanyaan yang Lebih Dalam