Representations of task assignments in distributed systems using Young tableaux and symmetric groups

Details Representations of task assignments in distributed systems using Young tableaux and symmetric groups Representations of task assignments in distributed systems using Young tableaux and symmetric groups

2010-12-06

arxiv.org/abs/1012.1288v3

Computer Science

Distributed, Parallel, and Cluster Computing

37 pages. Removal of the second author. Supposed to be reviewed by the second author, but cancelled by mutual agreement betwee

Scientific paper

In this paper we present a novel approach to representing task assignments for partitioned processors (respectively, tasks) in distributed systems. A partition of processors (respectively, tasks) is represented by a Young tableau, which is one of the main tools in studying symmetric groups and their representations. We propose a task, processor, and assignment tableau in order to represent a task assignment for partitioned processors (respectively, tasks) in distributed systems. Due to their simplicity and tight relationship to symmetric groups, we mainly focus on n-task-n-processor assignments in distributed systems. A certain set of n-task-n-processor assignments is represented by a k-assignments vector in the k-assignments vector space. We present some examples of the dual space and vector space model for the vector space of k-assignments vectors in distributed systems. We concern representations of task assignments rather than finding approximate or near optimal solutions for task assignments. A Young tableau approach allows us to raise the expressiveness of partitioned processors (respectively, tasks) and their task assignments.

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