PASS approximation: a framework for analyzing and designing heuristics
The authors introduce a new framework for designing and analyzing algorithms. Their framework applies best to problems that are inapproximable according to the standard worst-case analysis. They circumvent such negative results by designing guarantees for classes of instances, parameterized according to properties of the optimal solution. Given their parameterized approximation, called parametrized by the signature of the solution (PASS) approximation, the authors design algorithms with optimal approximation ratios for problems with additive and submodular objective functions such as the capacitated maximum facility location problems. The authors consider two types of algorithms for these problems. For Greedy algorithms, their framework provides a justification for preferring a certain natural greedy rule over some alternative Greedy rules that have been used in similar contexts. For LP-based algorithms, they show that the natural LP relaxation for these problems is not optimal in our framework. We design a new LP relaxation and show that this LP relaxation coupled with a new randomized rounding technique is optimal in our framework.
scientific article; zbMATH DE number 6162390
scientific article