The traveling salesman problem on cubic and subcubic graphs
نویسندگان
چکیده
منابع مشابه
The traveling salesman problem on cubic and subcubic graphs
We study the Travelling Salesman Problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NPhard. The problem is of interest because of its relation to the famous 4/3 conjecture for metric TSP, which says that the integrality gap, i.e., the worst case ratio between the optimal values of the TSP and its linear programming relaxation (the subtour elimination relax...
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We show how to find a Hamiltonian cycle in a graph of degree at most three with n vertices, in time O(2) ≈ 1.260 and linear space. Our algorithm can find the minimum weight Hamiltonian cycle (traveling salesman problem), in the same time bound. We can also count or list all Hamiltonian cycles in a degree three graph in time O(2) ≈ 1.297. We also solve the traveling salesman problem in graphs of...
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We study the Travelling Salesman Problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NP-hard. The problem is of interest because of its relation to the famous 4/3 conjecture for metric TSP, which says that the integrality gap, i.e., the worst case ratio between the optimal values of the TSP and its linear programming relaxation, is 4/3. Using polyhedral tec...
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Let tsp(G) denote the length of a shortest travelling salesman tour in a graph G. We prove that for any ε > 0, there exists a simple 2-connected planar cubic graph G1 such that tsp(G1) ≥ (1.25 − ε) · |V (G1)|, a simple 2-connected bipartite cubic graph G2 such that tsp(G2) ≥ (1.2 − ε) · |V (G2)|, and a simple 3-connected cubic graph G3 such that tsp(G3) ≥ (1.125− ε) · |V (G3)|.
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2012
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-012-0620-1