The least weight subsequence problem
SIAM Journal on Computing
Algorithms for two bottleneck optimization problems
Journal of Algorithms
The concave least-weight subsequence problem revisited
Journal of Algorithms
Efficiently solvable special cases of bottleneck travelling salesman problems
Discrete Applied Mathematics
Finding a minimum weight K-link path in graphs with Monge property and applications
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
On the recognition of permuted bottleneck Monge matrices
Discrete Applied Mathematics
Perspectives of Monge properties in optimization
Discrete Applied Mathematics
Selection in Monotone Matrices and Computing kth Nearest Neighbors
SWAT '94 Proceedings of the 4th Scandinavian Workshop on Algorithm Theory
The Knuth-Yao quadrangle-inequality speedup is a consequence of total monotonicity
ACM Transactions on Algorithms (TALG)
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We give algorithmic results for combinatorial problems with cost arrays possessing certain algebraic Monge properties. We extend Monge-array results for two shortest path problems to a general algebraic setting, with values in an ordered commutative semigroup, if the semigroup operator is strictly compatible with the order relation.We show how our algorithms can be modified to solve bottleneck shortest path problems, even though strict compatibility does not hold in that case. For example, we give a linear time algorithm for the unrestricted shortest path bottleneck problem on n nodes, also O(kn) and O(n3/2 log5/2 n) time algorithms for the k-shortest path bottleneck problem.