A Note on Hardness of Multiprocessor Scheduling with Scheduling Solution Space Tree
Debasis Dwibedy, Rakesh Mohanty

TL;DR
This paper investigates the complexity of non-preemptive multiprocessor scheduling, introduces the Scheduling Solution Space Tree data structure, and presents the first non-deterministic polynomial-time algorithm for the problem.
Contribution
It defines the SSST data structure, proves NP-hardness using SSST and WSSST, and develops the first non-deterministic polynomial-time scheduling algorithm.
Findings
Proves the problem is NP-hard using SSST and WSSST.
Introduces the Magic Scheduling (MS) algorithm.
Defines a new scheduling variant with an additional user parameter.
Abstract
We study the computational complexity of the non-preemptive scheduling problem of a list of independent jobs on a set of identical parallel processors with a makespan minimization objective. We make a maiden attempt to explore the combinatorial structure showing the exhaustive solution space of the problem by defining the \textit{Scheduling Solution Space Tree (SSST)} data structure. The properties of the \textit{SSST} are formally defined and characterized through our analytical results. We develop a unique technique to show the problem using the SSST and the \textit{Weighted Scheduling Solution Space Tree (WSSST)} data structures. We design the first non-deterministic polynomial-time algorithm named \textit{Magic Scheduling (MS)} for the problem based on the reduction framework. We also define a new variant of multiprocessor scheduling by including the user as an…
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Taxonomy
TopicsScheduling and Optimization Algorithms · Optimization and Search Problems · Interconnection Networks and Systems
