[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 …

Deterministic and Las Vegas Algorithms for Sparse Nonnegative Convolution∗

K Bringmann, N Fischer, V Nakos - Proceedings of the 2022 Annual ACM …, 2022 - SIAM
Computing the convolution A∗ B of two length-n integer vectors A, B is a core problem in
several disciplines. It frequently comes up as a subroutine in various problem domains, eg in …

On minimizing tardy processing time, max-min skewed convolution, and triangular structured ILPs

KM Klein, A Polak, L Rohwedder - Proceedings of the 2023 Annual ACM …, 2023 - SIAM
The starting point of this paper is the problem of scheduling n jobs with processing times and
due dates on a single machine so as to minimize the total processing time of tardy jobs, ie …

Minimizing the Weighted Number of Tardy Jobs is W [1]-hard

K Heeger, D Hermelin - arXiv preprint arXiv:2401.01740, 2024 - arxiv.org
We consider the $1||\sum w_J U_j $ problem, the problem of minimizing the weighted
number of tardy jobs on a single machine. This problem is one of the most basic and …

Minimizing the weighted number of tardy jobs via (max,+)-convolutions

D Hermelin, H Molter… - INFORMS Journal on …, 2024 - pubsonline.informs.org
In this paper we consider the fundamental scheduling problem of minimizing the weighted
number of tardy jobs on a single machine. We present a simple pseudo polynomial-time …

Minimizing Tardy Processing Time on a Single Machine in Near-Linear Time

N Fischer, L Wennmann - arXiv preprint arXiv:2402.13357, 2024 - arxiv.org
In this work we revisit the elementary scheduling problem $1||\sum p_j U_j $. The goal is to
select, among $ n $ jobs with processing times and due dates, a subset of jobs with …

Quick minimization of tardy processing time on a single machine

B Schieber, P Sitaraman - Algorithms and Data Structures Symposium, 2023 - Springer
We consider the problem of minimizing the total processing time of tardy jobs on a single
machine. This is a classical scheduling problem, first considered by [Lawler and Moore …

Does Subset Sum Admit Short Proofs?

M Włodarczyk - arXiv preprint arXiv:2409.03526, 2024 - arxiv.org
We investigate the question whether Subset Sum can be solved by a polynomial-time
algorithm with access to a certificate of length poly (k) where k is the maximal number of bits …

Single-machine scheduling to minimize the number of tardy jobs with release dates

M Kaul, M Mnich, H Molter - arXiv preprint arXiv:2408.12967, 2024 - arxiv.org
We study the fundamental scheduling problem $1\mid r_j\mid\sum w_j U_j $: schedule a set
of $ n $ jobs with weights, processing times, release dates, and due dates on a single …

Algorithms for sparse convolution and sublinear edit distance

N Fischer - 2023 - publikationen.sulb.uni-saarland.de
In this PhD thesis on fine-grained algorithm design and complexity, we investigate output-
sensitive and sublinear-time algorithms for two important problems.(1) Sparse Convolution …