A Distributed Search Program for the 3x + 1 Problem

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1989-11-01
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Leavens, Gary
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Computer Science

Computer Science—the theory, representation, processing, communication and use of information—is fundamentally transforming every aspect of human endeavor. The Department of Computer Science at Iowa State University advances computational and information sciences through; 1. educational and research programs within and beyond the university; 2. active engagement to help define national and international research, and 3. educational agendas, and sustained commitment to graduating leaders for academia, industry and government.

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The Computer Science Department was officially established in 1969, with Robert Stewart serving as the founding Department Chair. Faculty were composed of joint appointments with Mathematics, Statistics, and Electrical Engineering. In 1969, the building which now houses the Computer Science department, then simply called the Computer Science building, was completed. Later it was named Atanasoff Hall. Throughout the 1980s to present, the department expanded and developed its teaching and research agendas to cover many areas of computing.

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1969-present

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This report describes the design of a distributed program that searched for peaks in certain measures related to the 3x+1 problem. The searches for peaks in the number of steps taken, the maximum value reached, and the number of steps before the values of the iterates fall below the starting value exhibit a great deal of parallelism, but there is also some small amount of synchronization necessary. The design of a reliable and long-lived distributed system that searched for such peaks is discussed from the partitioning of the search to more detailed design issues such as ways to limit the search. The search was implemented in the distributed programming language Argus, and a few observations about Argus programming are included. An appendix includes tables of various results from the three years that the search program was running on six or more computers.

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© Gary T. Leavens, 1989. All rights reserved.

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