Abstract
We present a new class of integer extended ABS algorithms for solving linear Diophantine systems. The proposed class contains the integer ABS (the so-called EMAS and our proposed MEMAS) algorithms and the generalized Rosser’s algorithm as its members. After an application of each member of the class a particular solution of the system and an integer basis for the null space of the coefficient matrix are at hand. We show that effective algorithms exist within this class by appropriately setting the parameters of the members of the new class to control the growth of intermediate results. Finally, we propose two effective heuristic rules for selecting certain parameters in the new class of integer extended ABS algorithms.
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Khorramizadeh, M., Mahdavi-Amiri, N. Integer extended ABS algorithms and possible control of intermediate results for linear Diophantine systems. 4OR-Q J Oper Res 7, 145–167 (2009). https://doi.org/10.1007/s10288-008-0082-8
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DOI: https://doi.org/10.1007/s10288-008-0082-8
Keywords
- Linear Diophantine systems
- Integer ABS algorithms
- EMAS algorithms
- Generalized Rosser’s algorithm
- Expression swell