An Analysis of Dinkelbach's Algorithm for 0-1 Fractional Programming Problems

The 0-1 fractional programming problem minimizes the fractional objective function (c1x1 + c2x2 + + cnxn)=(d1x1 + d2x2 + + dnxn) = cx=dx under the condition that x = (x1; ; xn) 2 f0; 1g; where is the set of feasible solutions. For a fractional programming problem, Dinkelbach developed an algorithm which obtains an optimal solution of the given problem by solving a sequence of subproblems Q( ), in which the linear objective function cx dx is minimized under the same condition x 2 : In this paper, we show that Dinkelbach's algorithm solves at most O(log(nM)) subproblems in the worst case, where M = maxf max i=1;2; ;n jcij; max i=1;2; ;n jdij; 1g:

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