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, mathematical structure, structure, space, Mathematica ...

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 networks. Early life and educa ...

on the

maximum flow problem In Optimization (mathematics), 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 ...

and the

Ford–Fulkerson algorithm The Ford–Fulkerson method or Ford–Fulkerson algorithm (FFA) is a greedy algorithm that computes the maximum flow in a flow network. It is sometimes called a "method" instead of an "algorithm" as the approach to finding augmenting paths in a r ...

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 ...

. 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 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 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 (graph theory), vertex to all of the other vertices in a weighted digraph. It is slower than Dijkstra's algorithm for the same problem, but more ...

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 two ...

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 foun ...

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 ...

, 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 algor ...

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 oc ...

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 is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

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

rectangle In Euclidean geometry, Euclidean plane geometry, a rectangle is a Rectilinear polygon, rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that a ...

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 small variation of the argument induces a small variation of the value of the function. This implies there are no abrupt changes in value, known as '' discontinuities''. More preci ...

s (page 10) and to describe

integrable function In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus,Inte ...

s (page 148).

Personal information

Lester was born in

Houston, Texas Houston ( ) is the List of cities in Texas by population, most populous city in the U.S. state of Texas and in the Southern United States. Located in Southeast Texas near Galveston Bay and the Gulf of Mexico, it is the county seat, seat of ...

on September 23, 1927. He learned to play

piano A piano is a keyboard instrument that produces sound when its keys are depressed, activating an Action (music), action mechanism where hammers strike String (music), strings. Modern pianos have a row of 88 black and white keys, tuned to a c ...

and the

flute The flute is a member of a family of musical instruments in the woodwind group. Like all woodwinds, flutes are aerophones, producing sound with a vibrating column of air. Flutes produce sound when the player's air flows across an opening. In th ...

and was frequently heard whistling. For higher education he considered

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

and

Oberlin Conservatory The Oberlin Conservatory of Music is a private music conservatory of Oberlin College, a private liberal arts college in Oberlin, Ohio. It was founded in 1865 and is the second oldest conservatory and oldest continually operating conservatory in ...

, but chose the

University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...

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 (UIUC, U of I, Illinois, or University of Illinois) is a public land-grant research university in the Champaign–Urbana metropolitan area, Illinois, United States. Established in 1867, it is the f ...

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

University of North Carolina The University of North Carolina is the Public university, public university system for the state of North Carolina. Overseeing the state's 16 public universities and the North Carolina School of Science and Mathematics, it is commonly referre ...

and

RAND Corporation The RAND Corporation, doing business as RAND, is an American nonprofit global policy think tank, research institute, and public sector consulting firm. RAND engages in research and development (R&D) in several fields and industries. Since the ...

. 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 200 ...

employed him for forty years as he kept pace with

digital revolution The Information Age is a History by period, historical period that began in the mid-20th century. It is characterized by a rapid shift from traditional industries, as established during the Industrial Revolution, to an economy centered on info ...

. Ford married twice. With his first wife, Janet Johnson, he had nine children, including Fred Ford, programmer of the ''

Star Control ''Star Control: Famous Battles of the Ur-Quan Conflict, Volume IV'' is an action-strategy video game developed by Toys for Bob and published by Accolade. It was originally released for MS-DOS and Amiga in 1990, followed by ports for the Sega Gene ...

'' Universe. His second wife was Naoma Gower.

References

{{DEFAULTSORT:Ford, L. R. Jr. 1927 births 2017 deaths 20th-century American mathematicians 21st-century American mathematicians 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