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Electronic Colloquium on Computational Complexity

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Reports tagged with Traveling Salesman Problem:
TR96-046 | 27th August 1996
Luca Trevisan

On the Approximability of the Multi-dimensional Euclidean TSP

Revisions: 1

We consider the Traveling Salesperson Problem (TSP) restricted
to Euclidean spaces of dimension at most k(n), where n is the number of
cities. We are interested in the relation between the asymptotic growth of
k(n) and the approximability of the problem. We show that the problem is ... more >>>

TR98-024 | 28th April 1998
Wenceslas Fernandez de la Vega, Marek Karpinski

On Approximation Hardness of Dense TSP and other Path Problems

TSP(1,2), the Traveling Salesman Problem with distances 1 and 2, is
the problem of finding a tour of minimum length in a complete
weighted graph where each edge has length 1 or 2. Let $d_o$ satisfy
$0<d_o<1/2$. We show that TSP(1,2) has no PTAS on the set ... more >>>

TR99-031 | 2nd September 1999
Hans-Joachim Böckenhauer, Juraj Hromkovic, Ralf Klasing, Sebastian Seibert, Walter Unger

Towards the Notion of Stability of Approximation for Hard Optimization Tasks and the Traveling Salesman Problem

The investigation of the possibility to efficiently compute
approximations of hard optimization problems is one of the central
and most fruitful areas of current algorithm and complexity theory.
The aim of this paper is twofold. First, we introduce the notion of
stability of approximation algorithms. This notion is shown to ... more >>>

TR01-042 | 31st May 2001
Marek Karpinski

Approximating Bounded Degree Instances of NP-Hard Problems

We present some of the recent results on computational complexity
of approximating bounded degree combinatorial optimization problems. In
particular, we present the best up to now known explicit nonapproximability
bounds on the very small degree optimization problems which are of
particular importance on the intermediate stages ... more >>>

TR13-045 | 26th March 2013
Marek Karpinski, Michael Lampis, Richard Schmied

New Inapproximability Bounds for TSP

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 >>>

TR13-066 | 25th April 2013
Marek Karpinski, Richard Schmied

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 ... more >>>

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