Revisiting a simple algorithm for the planar multiterminal cut problem

Yeh (2001) [W.-C. Yeh, A simple algorithm for the planar multiway cut problem, J. Algorithms 39 (2001) 68–77] described a simple algorithm with time complexity O ( ( k − 3 2 ) k − 1 ( n − k ) 2 k − 4 ( n k − 3 2 k 2 + 1 2 k ) log ( n − k ) ) for the planar minimum k -terminal cut problem. In this paper, an example showing that the algorithm could fail to return a minimum k -cut is given.