We prove explicit approximation hardness results for the Graphic TSP on cubic and subcubic graphs as well as the new inapproximability bounds for the corresponding instances of the (1,2)-TSP. The proof technique uses new modular constructions of simulating gadgets for the restricted cubic and subcubic instances. The modular constructions used ... more >>>

In this paper, we study the approximability of the metric Traveling Salesman Problem, one of the most widely studied problems in combinatorial optimization. Currently, the best known hardness of approximation bounds are 185/184 for the symmetric case (due to Lampis) and 117/116 for the asymmetric case (due to Papadimitriou and ... more >>>

We develop a new method for proving explicit approximation lower bounds for TSP problems with bounded metrics improving on the best up to now known bounds. They almost match the best known bounds for unbounded metric TSP problems. In particular, we prove the best known lower bound for TSP with ... more >>>

We study the approximation hardness of the Shortest Superstring, the Maximal Compression and
the Maximum Asymmetric Traveling Salesperson (MAX-ATSP) problem.
We introduce a new reduction method that produces strongly restricted instances of
the Shortest Superstring problem, in which the maximal orbit size is eight
(with no ... more >>>

We establish almost tight upper and lower approximation bounds for the Vertex Cover problem on dense k-partite hypergraphs.