Path and cycle sub-Ramsey numbers and an edge-colouring conjecture
Discrete Mathematics
The traveling salesman problem with distances one and two
Mathematics of Operations Research
Discrete Mathematics
The minimum labeling spanning trees
Information Processing Letters
On the minimum label spanning tree problem
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Discrete Applied Mathematics
On Labeled Traveling Salesman Problems
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
The labeled perfect matching in bipartite graphs
Information Processing Letters
The complexity of bottleneck labeled graph problems
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Traveling salesman problem under categorization
Operations Research Letters
Erratum: On: Travelling salesman problem under categorization
Operations Research Letters
| Hi-index | 0.00 |
We consider labeled Traveling Salesman Problems, defined upon a complete graph of n vertices with colored edges. The objective is to find a tour of maximum or minimum number of colors. We derive results regarding hardness of approximation and analyze approximation algorithms, for both versions of the problem. For the maximization version we give a 12-approximation algorithm based on local improvements and show that the problem is APX-hard. For the minimization version, we show that it is not approximable within n^1^-^@e for any fixed @e0. When every color appears in the graph at most r times and r is an increasing function of n, the problem is shown not to be approximable within factor O(r^1^-^@e). For fixed constant r we analyze a polynomial-time (r+H"r)/2-approximation algorithm, where H"r is the rth harmonic number, and prove APX-hardness for r=2. For all of the analyzed algorithms we exhibit tightness of their analysis by provision of appropriate worst-case instances.