Compact enumeration for scheduling one machine
Nodari Vakhania

TL;DR
This paper introduces variable parameter analysis for scheduling on a single machine, providing algorithms with complexity depending only on specific problem parameters, and demonstrates the practical efficiency of these methods.
Contribution
It presents two VP-algorithms for a strongly NP-hard scheduling problem, including an implicit enumeration and a polynomial-time approximation scheme, with complexity depending on problem-specific parameters.
Findings
Partial solutions are polynomial-time computable without special jobs.
Exponential complexity depends only on a small set of variable parameters.
Experimental results suggest variable parameters are significantly fewer than total jobs.
Abstract
A Variable Parameter (VP) analysis, that we introduce here, aims to give a precise algorithm time complexity expression in which an exponent appears solely in terms of a variable parameter. A variable parameter is the number of objects with specific problem-dependent properties. Here we describe two VP-algorithms, an implicit enumeration algorithm and a polynomial-time approximation scheme for a strongly -hard problem of scheduling independent jobs with release and due times on one machine to minimize the maximum job lateness. For the problem considered, a variable parameter is the number of a special kind of the so-called ``emerging'' jobs. A partial solution without these jobs is constructed in a low degree polynomial time, and an exponential time procedure (in the number of variable parameters) is carried out to augment it to a complete optimal solution. In the alternative…
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Taxonomy
TopicsScheduling and Optimization Algorithms · Optimization and Search Problems · Optimization and Packing Problems
