Abstract
In this paper, we introduce the 1 − K robotic-cell scheduling problem, whose solution can be reduced to solving a TSP on specially structured permuted Monge matrices, we call b-decomposable matrices. We also review a number of other scheduling problems which all reduce to solving TSP-s on permuted Monge matrices. We present the important insight that the TSP on b-decomposable matrices can be solved in polynomial time by a special adaptation of the well-known subtour-patching technique. We discuss efficient implementations of this algorithm on newly defined subclasses of permuted Monge matrices.
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Deineko, V.G., Steiner, G. & Xue, Z. Robotic-Cell Scheduling: Special Polynomially Solvable Cases of the Traveling Salesman Problem on Permuted Monge Matrices. J Comb Optim 9, 381–399 (2005). https://doi.org/10.1007/s10878-005-1778-8
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DOI: https://doi.org/10.1007/s10878-005-1778-8