Unconstrained traveling tournament problem is APX-complete

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Salomon Bendayan, Joseph Cheriyan, Kevin K. H. Cheung

Published: 2023, Last Modified: 07 Nov 2025Oper. Res. Lett. 2023EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: We show that the Unconstrained Traveling Tournament Problem (UTTP) is APX-complete by giving an L-reduction from the following version of (1,2)-TSP: Given a complete graph on m nodes with edge costs of one or two, find a Hamiltonian cycle C that minimizes the objective m(m+1)∑{cost(ij):ij∈C}. Our analysis gives an inapproximability threshold of 1+((α−1)/200) for UTTP, where α denotes the inapproximability threshold for (1,2)-TSP.