On a Labeled Vehicle Routing Problem
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Approximation and hardness results for label cut and related problems
Journal of Combinatorial Optimization
Approximating minimum label s-t cut via linear programming
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Labeled Traveling Salesman Problems: Complexity and approximation
Discrete Optimization
Comparison of heuristics for the colourful travelling salesman problem
International Journal of Metaheuristics
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We consider labeled Traveling Salesman Problems, defined upon acomplete graph of n vertices with colored edges. Theobjective is to find a tour of maximum (or minimum) number ofcolors. We derive results regarding hardness of approximation, andanalyze approximation algorithms for both versions of the problem.For the maximization version we give a $\frac{1}{2}$-approximationalgorithm and show that it is APX-hard. For the minimizationversion, we show that it is not approximable within n1-ε for every ε 0.When every color appears in the graph at most r times andr is an increasing function of n the problem isnot O(r1-ε)-approximable. For fixed constantr we analyze a polynomial-time (r + Hr)/2-approximation algorithm (Hr is the r-th harmonic number), andprove APX-hardness. Analysis of the studied algorithms isshown to be tight.