Approximation Hardness of TSP with Bounded Metrics ( Revised
نویسندگان
چکیده
The general asymmetric TSP with triangle inequality is known to be approximable only to within an O(log n) factor, and is also known to be approximable within a constant factor as soon as the metric is bounded. In this paper we study the asymmetric and symmetric TSP problems with bounded metrics and prove approximation lower bounds of 131=130 and 174=173, respectively, for these problems, improving over the previous best lower bounds of 2805=2804 and 3813=3812 by an order of magnitude. Our bound 174=173 for the symmetric TSP with bounded metric is also the currently best known approximation lower bound for the general metric symmetric TSP problem. We prove also approximation lower bounds of 321=320 and 743=742 for the asymmetric and symmetric TSP with distances one and two, improving over the previous best lower bounds of 2805=2804 and 5381=5380.
منابع مشابه
TSP with bounded metrics
The general asymmetric TSP with triangle inequality is known to be approximable only within logarithmic factors. In this paper we study the asymmetric and symmetric TSP problems with bounded metrics, i.e., metrics where the distances are integers between one and some constant upper bound. In this case, the problem is known to be approximable within a constant factor. We prove that it is NP-hard...
متن کاملApproximation Hardness of TSP with Bounded Metrics
The general asymmetric TSP with triangle inequality is known to be approximable only within an O(log n) factor, and is also known to be approximable within a constant factor as soon as the metric is bounded. In this paper we study the asymmetric and symmetric TSP problems with bounded metrics, i.e., metrics where the distances are integers between one and some upper bound B. We first prove appr...
متن کاملOn Approximability of Bounded Degree Instances of Selected Optimization Problems
In order to cope with the approximation hardness of an underlying optimization problem, it is advantageous to consider specific families of instances with properties that can be exploited to obtain efficient approximation algorithms for the restricted version of the problem with improved performance guarantees. In this thesis, we investigate the approximation complexity of selected NP-hard opti...
متن کاملOn Approximation Lower Bounds for TSP with Bounded Metrics
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 bounded metrics for the metric bound equal to 4.
متن کاملImproved Inapproximability Results for the Shortest Superstring and the Bounded Metric TSP
We present a new method for proving explicit approximation lower bounds for the Shortest Superstring problem, the Maximum Compression problem, Maximum Asymmetric TSP problem, the (1, 2)–ATSP problem, the (1, 2)–TSP problem, the (1, 4)–ATSP problem and the (1, 4)–TSP problem improving on the best up to now known approximation lower bounds for those problems.
متن کامل