Abstract
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+γ,2γ2/2γ2−2γ+1}+ε and a randomized approximation algorithm that achieves a ratio of 2γ3+2γ2/3γ2−2γ+1+ε. 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 1+γ/1+3γ−4γ2+ε), asymmetric TSP (ATSP) with γ-triangle inequality (ratio 1/2+γ3/1−3γ2+ε ), STSP with weights one and two (ratio 4/3) and ATSP with weights one and two (ratio 3/2).
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 1+γ/1+3γ−4γ2+ε), asymmetric TSP (ATSP) with γ-triangle inequality (ratio 1/2+γ3/1−3γ2+ε ), STSP with weights one and two (ratio 4/3) and ATSP with weights one and two (ratio 3/2).
Original language | English |
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Pages (from-to) | 69-88 |
Number of pages | 20 |
Journal | Algorithmica |
Volume | 53 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 2009 |
Keywords
- Approximation algorithms
- Multi-criteria optimization
- Traveling salesman problem