Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
On an instance of the inverse shortest paths problem
Mathematical Programming: Series A and B
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
A class of bottleneck expansion problems
Computers and Operations Research
Computation of the Reverse Shortest-Path Problem
Journal of Global Optimization
An inverse model for the most uniform problem
Operations Research Letters
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In this paper, we first discuss a class of inverse dominant problems under weighted l驴 norm, which is how to change the original weights of elements with bounds in a finite ground set so that a given set becomes a weakly dominant set with respect to a given collection of subsets under the new weights and the largest change of the weights is minimum. This model includes a large class of improvement problems in combinatorial optimization. We propose a Newton-type algorithm for the model. This algorithm can solve the model in strongly polynomial time if the subproblem involved is solvable in strongly polynomial time. In the second part of the paper, we improve the complexity bound for Radzik's Newton-type method which is designed to solve linear fractional combinatorial optimization problems. As Radzik's method is closely related to our algorithm, this bound also estimates the complexity of our algorithm.