Approximating Multi-criteria Max-TSP
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Deterministic algorithms for multi-criteria TSP
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
On approximating multicriteria TSP
ACM Transactions on Algorithms (TALG)
Multi-Criteria TSP: min and max combined
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Single approximation for biobjective max TSP
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Deterministic algorithms for multi-criteria Max-TSP
Discrete Applied Mathematics
Fair solutions for some multiagent optimization problems
Autonomous Agents and Multi-Agent Systems
Single approximation for the biobjective Max TSP
Theoretical Computer Science
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We analyze approximation algorithms for several variants of the traveling salesman problem with multiple objective functions. First, we consider the symmetric TSP (STSP) with γ-triangle inequality. For this problem, we present a deterministic polynomial-time algorithm that achieves an approximation ratio of $\min\{1+\gamma,\frac{2\gamma^{2}}{2\gamma^{2}-2\gamma +1}\}+\varepsilon$and a randomized approximation algorithm that achieves a ratio of $\frac{2\gamma^{3}+2\gamma^{2}}{3\gamma^{2}-2\gamma +1}+\varepsilon$. In particular, we obtain a 2+ε approximation for multi-criteria metric STSP. Then we show that multi-criteria cycle cover problems admit fully polynomial-time randomized approximation schemes. Based on these schemes, we present randomized approximation algorithms for STSP with γ-triangle inequality (ratio $\frac{1+\gamma}{1+3\gamma -4\gamma^{2}}+\varepsilon$), asymmetric TSP (ATSP) with γ-triangle inequality (ratio $\frac{1}{2}+ \frac{\gamma^{3}}{1-3\gamma^{2}}+\varepsilon$), STSP with weights one and two (ratio 4/3) and ATSP with weights one and two (ratio 3/2).