The Parameterized Complexity of Local Search for TSP, More Refined

Autor: Jiong Guo, Ondřej Suchý, Rolf Niedermeier, Sepp Hartung
Rok vydání: 2012
Předmět:
Zdroj: Algorithmica. 67:89-110
ISSN: 1432-0541
0178-4617
DOI: 10.1007/s00453-012-9685-8
Popis: We extend previous work on the parameterized complexity of local search for the Traveling Salesperson Problem (TSP). So far, its parameterized complexity has been investigated with respect to the distance measures (defining the local search area) “Edge Exchange” and “Max-Shift”. We perform studies with respect to the distance measures “Swap” and “r-Swap”, “Reversal” and “r-Reversal”, and “Edit”, achieving both fixed-parameter tractability and W[1]-hardness results. In particular, from the parameterized reduction showing W[1]-hardness we infer running time lower bounds (based on the exponential time hypothesis) for all corresponding distance measures. Moreover, we provide non-existence results for polynomial-size problem kernels and we show that some in general W[1]-hard problems turn fixed-parameter tractable when restricted to planar graphs.
Databáze: OpenAIRE