Dr. Dijkstra was trained as a theoretical physicist, but taught himself to program in the early 1950s when he observed that many problems required extensive calculation.

In March 1952 he took a challengingg job at the Mathematical Center in Amsterdam, finding ways to program the primitive computers of the time.

One morning in 1956, while sipping coffee in an Amsterdam café, he devised the shortest-path algorithm, now widely used in global positioning systems and travel planning. Three years later, he published the method, which is now known just as Dijkstra's algorithm.

When he married in 1957, Dijkstra tried to list himself on the marriage certificate as a programmer. The Dutch authorities would not allow it, on grounds that there was no such profession. He finally gave in and was listed as a "theoretical physicist."

One of his most important accomplishments was the solution he devised to what is now called the dining philosophers' problem. He conceived of the problem faced by five philosophers sitting around a table, each with a bowl of rice and one chopstick. Because two chopsticks are required to eat, the problem is to find a fair method that would allow all to eat without having anyone starve or the entire table become deadlocked. Dijkstra's solution had each diner taking turns using a pair of chopsticks.

Several years later, he discovered that the M.I.T. creators of Multics, a pioneering operating system, had not solved the deadlock problem and their system periodically came to an abrupt halt.

In 1968 he published a legendary short essay arguing against the complexity of the "GO TO" command in languages like Fortran and Basic. The article was called "The GO TO Considered Harmful."

Dijkstra earned degrees in mathematics and theoretical physics from the University of Leyden and a Ph.D. in computting science from the University of Amsterdam.

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

He held the Schlumberger centennial chair in computer sciences at the University of Texas from 1984 to 1999, when he retired.

Throughout his career he won numerous awards, including the Association for Computing Machinery's prestigious Turing Award in 1972.

Mr. Nygaard worked in operations research while employed at the Norwegian Defense Research Establishment from 1948 to 1960. Using ideas from that work, he and a co-worker, Ole-Johan Dahl, designed Simula, a programming language designed to simulate real-world problems. Simula pioneered the concept of object-oriented programming. Previously, programming was seen as software instructions and data. Simula introduced the idea of objects and classes of objects, which could be re-used many times, dramatically increasing efficiency and productivity.

Originally Simula was intended as a physics simulation for a military laboratory. But workers in the Norwegian Iron and Metal Union approached Mr. Nygaard in the late 1960s, asking for help in dealing with displacement by computers. Mr. Nygaard worked with them and developed an approach known as participatory design. Originally seen as a socialistic movement, it has become widespread because large corporations saw value in it.

Simula influenced many computer scientists, including Alan Kay, who helped develop Smalltalk at Xerox's Palo Alto Research Center. Dr. Kay began thinking of software in biological terms because of the attributes he found in Simula.

Bjarne Stroustrup, a Danish programmer who studied at Cambridge and worked at Bell Laboratories, also discovered Simula, and used many of its innovations in designing the C++ programming language.

In addition to his work in the field of computer science, Mr. Nygaard took great interest in the impact of technology on the labor movement and became involved in political, social, and environmental issues.

He was the first chairman of the environment protection committee of the Norwegian Association for the Protection of Nature. He also helped run an experimental program to create humane living conditions for alcoholics. In 1968 he became chairman of a group that successfully opposed Norway's membership in the European Union.

This year, with Ole-Johan Dahl, Mr. Nygaard shared both the Turing Award from the Association of Computing Machinery, and the von Neumann Medal from the Institute for Electrical and Electronics Engineers (IEEE).

Shortly after AOL employee Richard Frankel released Gnutella, Kan and some friends set up a portal site to provide information to Gnutella developers. It quickly became a stopping point for journalists and others, and Kan's talent for communicating technical information in concise, colorful phrases made him the principal spokesperson for the Gnutella movement.

After writing their own version of Gnutella—designed to work on Unix and Linux—Kan and his friends developed a new kind of search engine, based on the file-sharing technology, which they called InfraSearch.

The company was later acquired by Sun Microsystems, who folded it into their own peer-to-peer project, called Jxta (pronounced Jux-ta). Kan became one of the key members of the Jxta team.

"Gene contributed much to the industry, specifically in the peer-to-peer (P2P) space," Sun said in a statement. "Gene brought new ideas to the organization and stretched our thinking. Gene was a trusted friend and colleague, and we will miss him greatly."

Kan graduated from U.C. Berkeley in 1997 with degrees in electrical engineering and computer science.