12. A method of phrase-based statistical machine translation (PBSMT), comprising: defining a PBSMT task as a generalized traveling salesman problem (GTSP); generating a graph of the GTSP comprising a plurality of nodes; generating an optimal tour of the graph; computing a true cost C t of the optimal tour; computing an apparent cost C a of the optimal tour; determining a difference D between the true cost C t and an apparent cost C a ; determining whether the difference D is less than a predetermined threshold ε; outputting the optimal tour as a solution to the GSTP if D is less than the predetermined threshold ε; and translating an input sentence from a first language to a second language using the output GSTP solution; wherein the true cost C t of the optimal tour is computed using n-gram costs, where n is an integer greater than or equal to 3.
12. A method of phrase-based statistical machine translation (PBSMT), comprising: defining a PBSMT task as a generalized traveling salesman problem (GTSP); generating a graph of the GTSP comprising a plurality of nodes; generating an optimal tour of the graph; computing a true cost C t of the optimal tour; computing an apparent cost C a of the optimal tour; determining a difference D between the true cost C t and an apparent cost C a ; determining whether the difference D is less than a predetermined threshold ε; outputting the optimal tour as a solution to the GSTP if D is less than the predetermined threshold ε; and translating an input sentence from a first language to a second language using the output GSTP solution; wherein the true cost C t of the optimal tour is computed using n-gram costs, where n is an integer greater than or equal to 3. 13. The method of claim 12 , further comprising refining at least one node in the graph if D is greater than or equal to the predetermined threshold ε, and generating a refined graph comprising the refined node.