Joseph Bernard Kruskal, Jr. (//; January 29, 1928 – September 19, 2010) was 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. Kruskal has worked on well-quasi-orderings and multidimensional scaling.
He was 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 such as CORE.
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 to a Jewish family 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. He worked at Bell Labs from 1959 to 1993.
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), or his nephew Clyde Kruskal.
Concepts named after Joseph Kruskal
- Kruskal's algorithm (1956)
- Kruskal's tree theorem (1960)
- Kruskal–Katona theorem (1963)
- Kruskal rank or k-rank (1997)
- Veterans of the Civil Rights Movement
- American Jewish Archives: "Two Baltic Families Who Came to America The Jacobsons and the Kruskals, 1870-1970" by RICHARD D. BROWN January 24, 1972
- Joseph Kruskal at the Mathematics Genealogy Project
- The Dyen, Kruskal and Black lexicostatistical database : the 200-meaning Swadesh lists for 95 Indo-European languages.
- http://cm.bell-labs.com/cm/ms/departments/sia/kruskal/ : his Bell Labs page