[PDF][PDF] 0-1 knapsack in nearly quadratic time

C Jin - Proceedings of the 56th Annual ACM Symposium on …, 2024 - dl.acm.org
We study pseudo-polynomial time algorithms for the fundamental 0-1 Knapsack problem.
Recent research interest has focused on its fine-grained complexity with respect to the …

Breaking the cubic barrier for all-pairs max-flow: Gomory-hu tree in nearly quadratic time

A Abboud, R Krauthgamer, J Li… - 2022 IEEE 63rd …, 2022 - ieeexplore.ieee.org
In 1961, Gomory and Hu showed that the All-Pairs Max-Flow problem of computing the max-
flow between all n\2 pairs of vertices in an undirected graph can be solved using only n-1 …

Faster algorithms for bounded knapsack and bounded subset sum via fine-grained proximity results

L Chen, J Lian, Y Mao, G Zhang - Proceedings of the 2024 Annual ACM-SIAM …, 2024 - SIAM
We investigate pseudopolynomial-time algorithms for Bounded Knapsack and Bounded
Subset Sum. Recent years have seen a growing interest in settling their fine-grained …

On integer programming, discrepancy, and convolution

K Jansen, L Rohwedder - Mathematics of Operations …, 2023 - pubsonline.informs.org
Integer programs with a fixed number of constraints are solvable in pseudo-polynomial time
in the largest coefficient of any constraint. We give a new algorithm which improves the …

Approximating knapsack and partition via dense subset sums

M Deng, C Jin, X Mao - Proceedings of the 2023 Annual ACM-SIAM …, 2023 - SIAM
Knapsack and Partition are two important additive problems whose fine-grained
complexities in the (1—ε)-approximation setting are not yet settled. In this work, we make …

Faster knapsack algorithms via bounded monotone min-plus-convolution

K Bringmann, A Cassis - arXiv preprint arXiv:2205.08493, 2022 - arxiv.org
We present new exact and approximation algorithms for 0-1-Knapsack and Unbounded
Knapsack:* Exact Algorithm for 0-1-Knapsack: 0-1-Knapsack has known algorithms running …

On integer programming, discrepancy, and convolution

K Jansen, L Rohwedder - arXiv preprint arXiv:1803.04744, 2018 - arxiv.org
Integer programs with m constraints are solvable in pseudo-polynomial time in $\Delta $, the
largest coefficient in a constraint, when m is a fixed constant. We give a new algorithm with a …

On the fine-grained complexity of one-dimensional dynamic programming

M Künnemann, R Paturi, S Schneider - arXiv preprint arXiv:1703.00941, 2017 - arxiv.org
In this paper, we investigate the complexity of one-dimensional dynamic programming, or
more specifically, of the Least-Weight Subsequence (LWS) problem: Given a sequence of …

Monochromatic triangles, triangle listing and APSP

VV Williams, Y Xu - 2020 IEEE 61st Annual Symposium on …, 2020 - ieeexplore.ieee.org
All-Pairs Shortest Paths (APSP) is one of the most basic problems in graph algorithms.
Given an n-node directed or undirected graph with integer weights in {-nc,..., nc} and no …

Knapsack and subset sum with small items

A Polak, L Rohwedder, K Węgrzycki - arXiv preprint arXiv:2105.04035, 2021 - arxiv.org
Knapsack and Subset Sum are fundamental NP-hard problems in combinatorial
optimization. Recently there has been a growing interest in understanding the best possible …