Lester Randolph Ford Jr. (September 23, 1927 – February 26, 2017) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

specializing in network flow problems. He was the son of mathematician Lester R. Ford Sr. Ford's paper with

D. R. Fulkerson Delbert Ray Fulkerson (; August 14, 1924 – January 10, 1976) was an American mathematician who co-developed the FordFulkerson algorithm, one of the most well-known algorithms to solve the maximum flow problem in Flow network, networks. Early l ...

on the

maximum flow problem In optimization theory, maximum flow problems involve finding a feasible flow through a flow network that obtains the maximum possible flow rate. The maximum flow problem can be seen as a special case of more complex network flow problems, such ...

and the Ford–Fulkerson algorithm for solving it, published as a technical report in 1954 and in a journal in 1956, established the

max-flow min-cut theorem In computer science and optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the ''source'' to the ''sink'' is equal to the total weight of the edges in a minimum cut, i.e., the ...

. In 1962 they published ''Flows in Networks'' with

Princeton University Press Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial su ...

. According to the preface, it "included topics that were purely mathematically motivated, together with those that are strictly utilitarian in concept." In his review,

S.W. Golomb Solomon Wolf Golomb (; May 30, 1932 – May 1, 2016) was an American mathematician, engineer, and professor of electrical engineering at the University of Southern California, best known for his works on recreational mathematics, mathematical gam ...

wrote, "This book is an attractive, well-written account of a fairly new topic in pure and applied combinatorial analysis." As a topic of continued interest, a new edition was published in 2010 with a new foreword by

Robert G. Bland Robert Gary Bland (born February 25, 1948) is an American mathematician and operations researcher, a professor of operations research and information engineering at Cornell University.

and James B. Orlin. In 1956, Ford developed the

Bellman–Ford algorithm The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph. It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is ...

for finding

shortest path In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between tw ...

s in

graphs Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...

that have negative weights, two years before

Richard Bellman Richard Ernest Bellman (August 26, 1920 – March 19, 1984) was an American applied mathematician, who introduced dynamic programming in 1953, and made important contributions in other fields of mathematics, such as biomathematics. He founde ...

also published the algorithm. With

Selmer M. Johnson Selmer Martin Johnson (21 May 1916 – 26 June 1996) was an American mathematician, a researcher at the RAND Corporation. Biography Johnson was born on May 21, 1916, in Buhl, Minnesota. He earned a B.A. and then an M.A. in mathematics from the U ...

, he developed the

Ford–Johnson algorithm In computer science, merge-insertion sort or the Ford–Johnson algorithm is a comparison sorting algorithm published in 1959 by L. R. Ford Jr. and Selmer M. Johnson. It uses fewer comparisons in the worst case than the best previously known algori ...

for sorting, which is of theoretical interest in connection with the problem of doing

comparison sort A comparison sort is a type of sorting algorithm that only reads the list elements through a single abstract comparison operation (often a "less than or equal to" operator or a three-way comparison) that determines which of two elements should occ ...

with the fewest comparisons. For 20 years, this algorithm required the minimum number of comparisons. In 1963 along with his father Lester R. Ford, he published an innovative textbook on

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...

. For a given function ''f'' and point ''x'', they defined a ''frame'' as a

rectangle In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containi ...

containing (''x'', ''f''(''x'')) with sides parallel to the axes of the plane (page 9). Frames are then exploited to define

continuous function In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value ...

s (page 10) and to describe

integrable function In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with ...

s (page 148).

Personal information

Lester was born in

Houston, Texas Houston (; ) is the most populous city in Texas, the most populous city in the Southern United States, the fourth-most populous city in the United States, and the sixth-most populous city in North America, with a population of 2,304,580 in ...

on September 23, 1927. He learned to play

piano The piano is a stringed keyboard instrument in which the strings are struck by wooden hammers that are coated with a softer material (modern hammers are covered with dense wool felt; some early pianos used leather). It is played using a keyboa ...

and the

flute The flute is a family of classical music instrument in the woodwind group. Like all woodwinds, flutes are aerophones, meaning they make sound by vibrating a column of air. However, unlike woodwind instruments with reeds, a flute is a reedless ...

and was frequently heard whistling. For higher education he considered

Harvard Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

and

Oberlin Conservatory The Oberlin Conservatory of Music is a private music conservatory in Oberlin College in Oberlin, Ohio. It was founded in 1865 and is the second oldest conservatory and oldest continually operating conservatory in the United States. It is one of t ...

, but chose the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

which provided him a scholarship. He earned his bachelor's degree in 1949 and a masters in 1950. Ford continued his studies at

University of Illinois at Urbana-Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Univ ...

where he earned a Ph.D. in mathematics in 1953. Ford's employers included the

U. S. Army The United States Army (USA) is the land service branch of the United States Armed Forces. It is one of the eight U.S. uniformed services, and is designated as the Army of the United States in the U.S. Constitution.Article II, section 2, cla ...

University of North Carolina The University of North Carolina is the multi-campus public university system for the state of North Carolina. Overseeing the state's 16 public universities and the NC School of Science and Mathematics, it is commonly referred to as the UNC Sy ...

and

RAND Corporation The RAND Corporation (from the phrase "research and development") is an American nonprofit global policy think tank created in 1948 by Douglas Aircraft Company to offer research and analysis to the United States Armed Forces. It is financed ...

. The Defense Research Corporation of

Goleta, California Goleta (; ; Spanish for "Schooner") is a city in southern Santa Barbara County, California, United States. It was incorporated as a city in 2002, after a long period as the largest unincorporated populated area in the county. As of the 2000 c ...

employed him for forty years as he kept pace with digital revolution. Ford married twice. His first wife, Janet Johnson, gave him nine children, including Fred Ford, programmer of the Star Control Universe. His second wife was Naoma Gower.

References

{{DEFAULTSORT:Ford, L. R. Jr. 20th-century American mathematicians 1927 births 2017 deaths American operations researchers American textbook writers University of Chicago alumni University of Illinois Urbana-Champaign alumni People from Houston People from Goleta, California RAND Corporation people