Kemeny aggregation, one-sided crossing minimization, parameterized complexity, subexponential-time algorithms, social choice theory, graph drawing, directed feedback arc set
We analyze a common feature of p-Kemeny AGGregation (p-KAGG) and p-One-Sided Crossing Minimization (p-OSCM) to provide new insights and findings of interest to both the graph drawing community and the social choice community. We obtain parameterized subexponential-time algorithms for p-KAGG—a problem in social choice theory—and for p-OSCM—a problem in graph drawing. These algorithms run in time O*(2O(klogk)), where k is the parameter, and significantly improve the previous best algorithms with running times ��*(1.403k) and ��*(1.4656k), respectively. We also study natural "above-guarantee" versions of these problems and show them to be fixed parameter tractable. In fact, we show that the above-guarantee versions of these problems are equivalent to a weighted variant of p-directed feedback arc set. Our results for the above-guarantee version of p-KAGG reveal an interesting contrast. We show that when the number of "votes" in the input to p-KAGG is odd the above guarantee version can still be solved in time O*(2O(klogk)), while if it is even then the problem cannot have a subexponential time algorithm unless the exponential time hypothesis fails (equivalently, unless FPT=M).
Tsinghua University Press
Henning Fernau, Fedor V. Fomin, Daniel Lokshtanov et al. Social Choice Meets Graph Drawing: How to Get Subexponential Time Algorithms for Ranking and Drawing Problems. Tsinghua Science and Technology 2014, 19(04): 374-386.