International Society of Science and Applied Technologies |
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A Novel Approach to Search for All Solutions of a Non-Negative Linear Diophantine Equation | ||||
Author | Shin-Guang Chen
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Abstract | Solving non-negative linear Diophantine equation is the basis for solving most optimization problems. A typical form of such equation is expressed as: a1x1 + a2x2 + : : : + anxn = k. When ai = 1 for all i, the mathematical results show that the number of solutions for such equation is equivalent to the number of distinct terms in a multinomial equation, which would be (kn+k-1). Therefore, the optimal complexity for such search is of O((kn+k-1)). However, there are very limited methods existed in the literature to tackle such kind of problems. This paper proposes a novel and efficient approach to search for all solutions of a non-negative linear Diophantine equation. The complexity of the proposed approach would be no greater than O((kn+k-1)). Several examples are explored to show the application of the proposed approach.
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Keywords | Linear equation, network reliability, minimal path, fast enumeration, backtrack | |||
Article #: 2455 |
August 2-4, 2018 - Toronto, Ontario, Canada |