Joseph Kruskal

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Joseph Kruskal
Born(1928-01-29)January 29, 1928
DiedSeptember 19, 2010(2010-09-19) (aged 82)
Alma materUniversity of Chicago
Princeton University
Known forMultidimensional scaling
Kruskal's algorithm
Kruskal's tree theorem
Kruskal–Katona theorem
RelativesClyde Kruskal (nephew)
Scientific career
InstitutionsUniversity of Michigan
Bell Labs
ThesisThe Theory of Well-Partially-Ordered Sets (1954)
Doctoral advisorsRoger Lyndon
Paul Erdős

Joseph Bernard Kruskal, Jr. (/ˈkrʌskəl/; January 29, 1928 – September 19, 2010) was an American mathematician, statistician, computer scientist and psychometrician.

Personal life[edit]

Kruskal was born to a Jewish family[2] 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.

Kruskal had two notable brothers, Martin David Kruskal, co-inventor of solitons, and William Kruskal, who developed the Kruskal–Wallis one-way analysis of variance. One of Joseph Kruskal's nephews is notable computer scientist and professor Clyde Kruskal.

Education and career[edit]

He was a student at the University of Chicago earning a bachelor of science in mathematics in the year of 1948, and a master of science in mathematics in the following year 1949.[3] After his time at the University of Chicago Kruskal attended Princeton University, where he completed his Ph.D. in 1954, nominally under Albert W. Tucker and Roger Lyndon,[4] but de facto under Paul Erdős with whom he had two very short conversations.[5] Kruskal worked on well-quasi-orderings[4][6] and multidimensional scaling.[7] 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.[8]

He worked at Bell Labs from 1959 to 1993.[9]


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.

Concepts named after Joseph Kruskal[edit]


  1. ^ Carroll, J. Douglas; Arabie, Phipps (2011-12-20). "In Memoriam Joseph B. Kruskal 1928–2010". Psychometrika. 78 (2): 237–239. doi:10.1007/s11336-011-9241-5. ISSN 0033-3123. PMID 25107613.
  2. ^ American Jewish Archives: "Two Baltic Families Who Came to America The Jacobsons and the Kruskals, 1870-1970" by RICHARD D. BROWN January 24, 1972
  3. ^ J J O'Connor; E F Robertson. "Kruskal Joseph biography - University of St Andrews". University of St Andrews. Archived from the original on 7 July 2015. Retrieved 2 November 2015. He was awarded a BS in 1948 and an MS in 1949 by Chicago.
  4. ^ a b Kruskal, J. B. (May 1960). "Well-quasi-ordering, the Tree Theorem, and Vazsonyi's conjecture". Transactions of the American Mathematical Society. 95 (2). American Mathematical Society (AMS): 210–225. doi:10.1090/S0002-9947-1960-0111704-1.
  5. ^ "Reflection on the old days- by Joseph Kruskal".
  6. ^ Joseph B. Kruskal (1972). "The Theory of Well-Quasi-Ordering: A Frequently Discovered Concept". Journal of Combinatorial Theory, Series A. 13 (3): 297–305. doi:10.1016/0097-3165(72)90063-5.
  7. ^ J.B. Kruskal (1977). "Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics". Linear Algebra and Its Applications. 18 (2): 95–138. doi:10.1016/0024-3795(77)90069-6.
  8. ^ "Veterans of the Civil Rights Movement -- List of Oral Histories".
  9. ^ "Joseph B. Kruskal Jr. *54". 21 January 2016.
  10. ^ J.B. Kruskal (1977). "Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics". Linear Algebra and Its Applications. 18 (2): 95–138. doi:10.1016/0024-3795(77)90069-6.

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