Graphic TSP in Cubic Graphs
نویسندگان
چکیده
We present a polynomial-time 9/7-approximation algorithm for the graphic TSP for cubic graphs, which improves the previously best approximation factor of 1.3 for 2-connected cubic graphs and drops the requirement of 2-connectivity at the same time. To design our algorithm, we prove that every simple 2-connected cubic n-vertex graph contains a spanning closed walk of length at most 9n/7− 1, and that such a walk can be found in polynomial time. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems
منابع مشابه
Approximation hardness of graphic TSP on cubic graphs
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 in the paper could be also of independent interest.
متن کاملGraphic TSP in 2-connected cubic graphs
We prove that every simple 2-connected cubic n-vertex graph contains a spanning closed walk of length at most 9n/7 − 1, and that such a walk can be found in polynomial time. This yields a polynomial-time 9/7-approximation algorithm for the graphic TSP for 2-connected cubic graphs, which improves the previously known approximation factor of 1.3 for 2-connected cubic graphs. On the negative side,...
متن کاملA -approximation algorithm for Graphic TSP in cubic bipartite graphs
We prove new results for approximating Graphic TSP. Specifically, we provide a polynomialtime 9 7 -approximation algorithm for cubic bipartite graphs and a ( 9 7 + 1 21(k−2) )-approximation algorithm for k-regular bipartite graphs, both of which are improved approximation factors compared to previous results. Our approach involves finding a cycle cover with relatively few cycles, which we are a...
متن کاملA 9/7 -Approximation Algorithm for Graphic TSP in Cubic Bipartite Graphs
We prove new results for approximating Graphic TSP. Specifically, we provide a polynomial-time 9 7 -approximation algorithm for cubic bipartite graphs and a ( 9 7 + 1 21(k−2) )-approximation algorithm for k-regular bipartite graphs, both of which are improved approximation factors compared to previous results. Our approach involves finding a cycle cover with relatively few cycles, which we are ...
متن کاملAn improved upper bound for the TSP in cubic 3-edge-connected graphs
We consider the travelling salesman problem (TSP) problem on (the metric completion of) 3-edge-connected cubic graphs. These graphs are interesting because of the connection between their optimal solutions and the subtour elimination LP relaxation. Our main result is an approximation algorithm better than the 3/2-approximation algorithm for TSP in general. © 2004 Elsevier B.V. All rights reserved.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017