The cause of death was cancer, said officials at the University of Texas, where Dr. Dijkstra held the Schlumberger centennial chair in computer sciences from 1984 to 1999, when he retired.

Dr. Dijkstra is best known for his shortest-path algorithm, a method for finding the most direct route on a graph or map, and for his work as the co-designer of the first version of Algol 60, a programming language that represented one of the first compiler programs that translates human instructions.

The shortest-path algorithm, which is now widely used in global positioning systems and travel planning, came to him one morning in 1956 as he sat sipping coffee on the terrace of an Amsterdam cafe.

It took him three years to publish the method, which is now known simply as Dijkstra's algorithm. At the time, he said, algorithms were hardly considered a scientific topic.

Of even greater importance was his solution to what he originally called the dining quintuple problem, but which later became known as the dining philosophers' problem.

He conceived of the problem faced by five philosophers sitting around a table, each with a bowl of rice and a single chopstick. Because eating requires two chopsticks, the challenge was to find an equitable method that would permit all of those at the table to eat without having anyone starve or having the entire table face deadlock. Dijkstra's original solution ensured that each diner took turns using a pair of chopsticks.

The problem has applicability to both computer operating systems and to network design.

Several years after Dr. Dijkstra solved the problem, he was surprised to learn that the Massachusetts Institute of Technology designers of the pioneering Multics operating system had not grappled successfully with the issue of deadlock. The consequence was that on occasion their system would abruptly halt.

"You can hardly blame M.I.T. for not taking notice of an obscure computer scientist in a small town in the Netherlands," he was quoted as saying in "Out Of Their Minds: The Lives and Discoveries of 15 Great Computer Scientists."

Dr. Dijkstra, an advocate of an approach known as structured programming, wrote a short research note in the March 1968 edition of the journal Communications of the ACM that became legendary. Titled "The GO TO Considered Harmful," it argued against the complexity of a feature in programming languages like Fortran and Basic that permitted programmers to write convoluted programs that jump around haphazardly.

A theoretical physicist by training, early in his career he observed that many problems required extensive calculation and so in the early 1950's he taught himself how to program.

In March 1952 he took a part-time job at the Mathematical Center in Amsterdam, immersing himself in the challenges of instructing the primitive computers of the era.

When he married in 1957, the Dutch marriage rites required that he state his profession and he attempted to say he was a programmer. The municipal authorities in Amsterdam did not accept his answer on the ground that there was no such profession. As a result, his marriage certificate described his profession as "theoretical physicist."

He was born May 11, 1930, in Rotterdam, the Netherlands. His father was a chemist and his mother was a mathematician. In 1942, at 12, Dr. Dijkstra entered an elite high school where he studied classical Greek and Latin, French, German, English, biology, mathematics, physics and chemistry. During the German occupation his parents sent him away for a brief period to the countryside. He earned degrees in mathematics and theoretical physics from the University of Leyden and a Ph.D. in computing science from the University of Amsterdam.

He worked as a programmer at the Mathematical Center from 1952 to 1962, taught mathematics at Eindhoven University of Technology from 1962 to 1984 and was a research fellow at the Burroughs Corporation from 1973 to 1984.

Dr. Dijkstra was the recipient of many awards, notably the Association for Computing Machinery's prestigious Turing Award in 1972.

He is survived by his wife of more than 40 years, Maria C. Debets Dijkstra, who is known as Ria; three children, Marcus, Femke and the computer scientist Rutger M. Dijkstra; and by two grandchildren.

Throughout Dr. Dijkstra's career, his work was characterized by elegance and economy. His love affair with simplicity came at an early age and under his mother's guidance. He once said he had asked his mother whether mathematics was a difficult topic. She replied that he must learn all the formulas and that furthermore if he required more than five lines to prove something, he was on the wrong track.