Matching is as easy as matrix inversion
Combinatorica
Exact arborescences, matchings and cycles
Discrete Applied Mathematics
The complexity of restricted spanning tree problems
Journal of the ACM (JACM)
Approximation algorithms for the TSP with sharpened triangle inequality
Information Processing Letters
Approximation algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximations for ATSP with Parametrized Triangle Inequality
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Approximating the Pareto curve with local search for the bicriteria TSP(1,2) problem
Theoretical Computer Science
Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs
Journal of the ACM (JACM)
8/7-approximation algorithm for (1,2)-TSP
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Multicriteria Optimization
An improved approximation algorithm for the asymmetric TSP with strengthened triangle inequality
Journal of Discrete Algorithms
(Non)-approximability for the multi-criteria TSP(1, 2)
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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In multi-criteria optimization, several objective functions are to be optimized. Since the different objective functions are usually in conflict with each other, one cannot consider only one particular solution as optimal. Instead, the aim is to compute so-called Pareto curves. Since Pareto curves cannot be computed efficiently in general, we have to be content with approximations to them. We are concerned with approximating Pareto curves of multi-criteria traveling salesman problems (TSP). We provide algorithms for computing approximate Pareto curves for the symmetric TSP with triangle inequality (Δ− STSP), symmetric and asymmetric TSP with strengthened triangle inequality (Δ(γ)−STSP and Δ(γ)− ATSP), and symmetric and asymmetric TSP with weights one and two (STSP(1,2) and ATSP(1,2)). We design a deterministic polynomial-time algorithm that computes (1+γ+ ε)-approximate Pareto curves for multi-criteria Δ(γ)−STSP for $\gamma \in [\frac 12, 1]$. We also present two randomized approximation algorithms for multi-criteria Δ(γ)−STSP achieving approximation ratios of $\frac{2\gamma^3 + \gamma^2 + 2 \gamma-1}{2\gamma^2} + \varepsilon$ and $\frac{1+\gamma}{1+3 \gamma -- 4 \gamma^2}$ + ε, respectively. Moreover, we design randomized approximation algorithms for multi-criteria Δ(γ)−ATSP (ratio $\frac 12+ \frac{\gamma^3}{1-3\gamma^2}$ + ε for $\gamma The algorithms for Δ(γ)−ATSP, STSP(1,2), and ATSP(1,2) as well as one algorithm for Δ(γ)−STSP are based on cycle covers. Therefore, we design randomized approximation schemes for multi-criteria cycle cover problems by showing that multi-criteria graph factor problems admit fully polynomial-time randomized approximation schemes.