The probabilistic relationship between the assignment and asymmetric traveling salesman problems
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On the b-Partite Random Asymmetric Traveling Salesman Problem and Its Assignment Relaxation
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
On the relationship between ATSP and the cycle cover problem
Theoretical Computer Science
Are Stacker Crane Problems easy? A statistical study
Computers and Operations Research
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We consider the probabilistic relationship between the value of a random asymmetric traveling salesman problem $ATSP(M)$ and the value of its assignment relaxation $AP(M)$. We assume here that the costs are given by an $n\times n$ matrix $M$ whose entries are independently and identically distributed. We focus on the relationship between $Pr(ATSP(M)=AP(M))$ and the probability $p_n$ that any particular entry is zero. If $np_n\rightarrow \infty$ with $n$ then we prove that $ATSP(M)=AP(M)$ with probability 1-o(1). This is shown to be best possible in the sense that if $np(n)\rightarrow c$, $c0$ and constant, then $Pr(ATSP(M)=AP(M))