The Fourth International Workshop on Computational Social Choice COMSOC 2012

We consider a setting in which a single divisible good (“cake”) needs to be dividedbetween n players, each with a possibly different valuation function over pieces of thecake. For this setting, we address the problem of finding divisions that maximize thesocial welfare, focusing on divisions where each player needs to get one contiguouspiece of the cake. We show that for both the utilitarian and the egalitarian socialwelfare functions it is NP-hard to find the optimal division. For the utilitarianwelfare, we provide a constant factor approximation algorithm, and prove that noFPTAS is possible unless P=NP. For egalitarian welfare, we prove that it is NP-hardto approximate the optimum to any factor smaller than 2. For the case where thenumber of players is small, we provide an FPT (fixed parameter tractable) FPTASfor both the utilitarian and the egalitarian welfare objectives.