Quick Minimization of Tardy Processing Time on a Single Machine
Baruch Schieber, Pranav Sitaraman

TL;DR
This paper presents an improved algorithm for minimizing total tardy processing time on a single machine, reducing computational complexity by introducing a job bundling technique and leveraging skewed-convolutions.
Contribution
The authors develop a faster algorithm for tardy processing time minimization by applying job bundling and advanced convolution techniques, improving previous time complexity bounds.
Findings
Achieved a $ ilde{O}(P^{7/5})$ time algorithm for the problem.
Introduced a job bundling technique to optimize computation.
Improved upon the previous $ ilde{O}(P^{5/3})$ algorithm.
Abstract
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 1969], that also generalizes the Subset Sum problem. Recently, it was shown that this problem can be solved efficiently by computing -skewed-convolutions. The running time of the resulting algorithm is equivalent, up to logarithmic factors, to the time it takes to compute a -skewed-convolution of two vectors of integers whose sum is , where is the sum of the jobs' processing times. We further improve the running time of the minimum tardy processing time computation by introducing a job ``bundling'' technique and achieve a running time, where is the running time of a -skewed-convolution of…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsScheduling and Optimization Algorithms · Optimization and Search Problems · Computability, Logic, AI Algorithms
