Title

The Euclidean distance completion problem: cycle completability

Department/School

Mathematics

Date

1-1-1995

Document Type

Article

Keywords

Euclidean distance completion problem, matrix completion

DOI

https://doi.org/10.1080/03081089508818392

Abstract

The Euclidean distance matrix completion problem asks when a partial distance matrix has a distance matrix completion, in the event that the graph of the specified data is chordal no additional information is needed. If the graph is not chordal, more must be known about the data. In the event the data comprises a full cycle, the additional conditions are quite simple. We characterize those graphs such that the "cycle conditions" on all minimal cycles imply that a partial distance matrix has a distance matrix completion. One description of these graphs is that they have chordal supergraphs in which no 4-clique includes an added edge, the same condition that appeared in the corresponding question about positive definite completions.

Published in

Linear and Multilinear Algebra

Citation/Other Information

Johnson, C. R., Jones, C. A., & Kroschel, B. K. (1995). The Euclidean distance completion problem: cycle completability. Linear & Multilinear Algebra, 39, 195-207. https://doi.org/10.1080/03081089508818392

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