Mathematics – Optimization and Control
Scientific paper
2011-01-21
Mathematics
Optimization and Control
22 pages
Scientific paper
This paper addresses the problem of decomposing a numerical semigroup into m-irreducible numerical semigroups. The problem originally stated in algebraic terms is translated, introducing the so called Kunz-coordinates, to resolve a series of several discrete optimization problems. First, we prove that finding a minimal m-irreducible decomposition is equivalent to solve a multiobjective linear integer problem. Then, we restate that problem as the problem of finding all the optimal solutions of a finite number of single objective integer linear problems plus a set covering problem. Finally, we prove that there is a suitable transformation that reduces the original problem to find an optimal solution of a compact integer linear problem. This result ensures a polynomial time algorithm for each given multiplicity m. We have implemented the different algorithms and have performed some computational experiments to show the efficiency of our methodology.
Blanco Víctor
Puerto Justo
No associations
LandOfFree
Integer Programming and m-irreducibility of numerical semigroups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Integer Programming and m-irreducibility of numerical semigroups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Integer Programming and m-irreducibility of numerical semigroups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-18997