Searching the k-change neighborhood for TSP is W[1]-hard

Authors:
DáNiel Marx
Affiliations:
Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
Venue:
Operations Research Letters
Year:
2008

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Abstract

We show that searching the k-change neighborhood is W[1]-hard for metric TSP, which means that finding the best tour in the k-change neighborhood essentially requires complete search (modulo some complexity-theoretic assumptions).