• Management Science and Financial Engineering
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• v.15 no.2
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• pp.119-123
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• 2009

The minimum multicut problem on a cycle is to find a multicut on an undirected cycle such that the sum of weights is minimized, which is known to be polynomially solvable. This paper shows that there exists a compact polyhedral description of the set of feasible solutions to the problem whose number of variables and constraints is O($\upsilon\kappa$).

• East Asian mathematical journal
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• v.15 no.1
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• pp.147-151
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• 1999

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.235-247
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• 2012

We study sufficient conditions for function algebras generated by four smooth functions on a small closed bidisk near the origin in $\mathbb{C}$ to coincide with the space of continuous functions on the bidisk. This problem in one dimension has been studied by De Paepe and the second name author.

• Management Science and Financial Engineering
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• v.22 no.1
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• pp.5-12
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• 2016

We consider a time-cost tradeoff problem with multiple milestones under a chain precedence graph. In the problem, some penalty occurs unless a milestone is completed before its appointed date. This can be avoided through compressing the processing time of the jobs with additional costs. We describe the compression cost as the convex or the concave function. The objective is to minimize the sum of the total penalty cost and the total compression cost. It has been known that the problems with the concave and the convex cost functions for the compression are NP-hard and polynomially solvable, respectively. Thus, we consider the special cases such that the cost functions or maximal compression amounts of each job are identical. When the cost functions are convex, we show that the problem with the identical costs functions can be solved in strongly polynomial time. When the cost functions are concave, we show that the problem remains NP-hard even if the cost functions are identical, and develop the strongly polynomial approach for the case with the identical maximal compression amounts.