Improved update/query algorithms for the interval valuation problem
Information Processing Letters
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
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When restricted to cost arrays possessing the sum Monge property, many combinatorial optimization problems with sum objective functions become significantly easier to solve. The more general algebraic assignment and transportation problems are similarly easier to solve given cost arrays possessing the corresponding algebraic Monge property. We show that Monge-array results for two sum-of-edge-costs shortest-path problems can likewise be extended to a general algebraic setting, provided the problems' ordered commutative semigroup satisfies one additional restriction. In addition to this general result, we also show how our algorithms can be modified to solve certain bottleneck shortestpath problems, even though the ordered commutative semigroup naturally associated with bottleneck problems does not satisfy our additional restriction. We show how our bottleneck shortest-path techniques can be used to obtain fast algorithms for a variant of Hirschberg and Larmore's optimal paragraph formation problem, and a special case of the bottleneck traveling-salesman problem.