Synthesizing partial orders given comparability information: Partitive sets and slack in critical path networks
type: Item
instance of: scholarly article
title: Synthesizing partial orders given comparability information: Partitive sets and slack in critical path networks
zbMATH Open document ID: 0538.92025
DOI: 10.1016/0022-2496(83)90010-X
author: Richard Schweickert
published in: Journal of Mathematical Psychology
publication date: 1983-01-01T00:00:00Z
review text: Critical path networks are used here to model complex cognitive tasks; the set of mental activities of a task can be represented as a partially ordered set of arcs in a directed acyclic graph (critical path network), the nonnegative real number associated with each arc being the duration of the corresponding activity. Suppose the critical path network underlying a task is unknown; analyzing the reaction times it is possible to distinguish comparable (sequential) pairs of activities from incomparable (concurrent) ones, and then this information can be represented in a comparability graph. A partial order compatible with this graph can be constructed using the transitive orientation algorithm, summarized in the first part of this paper; the uniqueness of the partial order depends on the presence of partitive sets. The author gives a characterization of weakly connected subgraphs (of a directed acyclic graph) generated by partitive sets of arcs as those subgraphs having a unique source, a unique sink, and no vertices of attachment other than these. Then, the main result of this paper shows that there is a close relationship between partitive sets of activities and slacks in critical path networks.
Mathematics Subject Classification ID: 91E99
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 3856896
zbMATH Keywords: cognitive tasks
zbMATH Keywords: mental activities
zbMATH Keywords: directed acyclic graph
zbMATH Keywords: critical path network
zbMATH Keywords: reaction times
zbMATH Keywords: comparability graph
zbMATH Keywords: transitive orientation algorithm
zbMATH Keywords: partitive sets
zbMATH Keywords: characterization of weakly connected subgraphs
zbMATH Keywords: slacks
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3856896