# Joseph Bernard Kruskal

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**Joseph Bernard Kruskal, Jr.** (born January 29, 1928) is an American mathematician, statistician, computer scientist and psychometrician. He was a student at the University of Chicago and at Princeton University, where he completed his Ph.D. in 1954, nominally under Albert W. Tucker and Roger Lyndon, but de facto under Paul Erdős with whom he had two very short conversations^{[How to reference and link to summary or text]}. Kruskal has worked on well-quasi-orderings and multidimensional scaling.

He is a Fellow of the American Statistical Association, former president of the Psychometric Society, and former president of the Classification Society of North America. He also initiated and was first president of the Fair Housing Council of South Orange and Maplewood in 1963, and actively supported civil rights in several other organizations.

In statistics, Kruskal's most influential work is his seminal contribution to the formulation of multidimensional scaling. In computer science, his best known work is Kruskal's algorithm for computing the minimal spanning tree (MST) of a weighted graph. The algorithm first orders the edges by weight and then proceeds through the ordered list adding an edge to the partial MST provided that adding the new edge does not create a cycle. Minimal spanning trees have applications to the construction and pricing of communication networks. In combinatorics, he is known for Kruskal's tree theorem (1960), which is also interesting from a mathematical logic perspective since it can only be proved nonconstructively. Kruskal also applied his work in linguistics, in an experimental lexicostatistical study of Indo-European languages, together with the linguists Isidore Dyen and Paul Black. Their database is still widely-used (available at the link below).

Kruskal was born in New York City to a successful fur wholesaler, Joseph B. Kruskal, Sr. His mother, Lillian Rose Vorhaus Kruskal Oppenheimer, became a noted promoter of Origami during the early era of television.

Joseph Kruskal should not be confused with his two brothers Martin David Kruskal (1925-2006; co-inventor of solitons and of surreal numbers) and William Kruskal (1919–2005; developed the Kruskal-Wallis one-way analysis of variance).

## Concepts named after Joseph KruskalEdit

- Kruskal's algorithm (1956)
- Kruskal's tree theorem (1960)
- Kruskal–Katona theorem (1963)

## External linksEdit

- The Dyen, Kruskal and Black lexicostatistical database : the 200-meaning Swadesh lists for 95 Indo-European languages.

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