TSP问题
The famous Traveling Salesperson Problem (TSP) asks for a spanning cycle of minimum length in an edge-weighted complete graph. It is not possible to approximate the TSP within any constant factor of the optimum unless P=NP; otherwise, one could solve the Hamiltonian cycle problem, one of Karp...
if m⁎ is an optimal solution for I′, then f+m⁎ is an optimal solution for I. The algorithm does not need to know F, just the value of sn(F). Proof Our algorithm begins by finding an optimal solution r to Fixed Degree Subgraph with regard to instance I using Observation 3.3....
TspGWI is a bifunctional protein comprising a tandem arrangement of Type I-like domains; particularly noticeable is the central HsdM-like module comprising a helical domain and a highly conserved S-adenosylmethionine-binding/catalytic MTase domain, containing DPAVGTG and NPPY motifs. TspGWI also pos...
Given the complete undirected graph Kn=(V,E) on n nodes with edge costs c∈RE, c≥0, the symmetric traveling salesman problem (henceforth TSP) is to find a Hamilton cycle (or tour) in Kn of minimum cost. This problem is known to be NP-hard, even in the case where the costs satis...
By adjusting the proof of Theorem 3, we can prove that the master tour problem with scenarios is NP-complete when |Sj|≤5. This is done by reducing from Set Splitting instead of Max Cut and using that 3-Set Splitting is NP-complete [24]. In 3-Set Splitting, we are given n elements...
Proof. Suppose there exists an 𝛼-approximation algorithm Alg for some 𝛼≥1. We show that algorithm Alg could be used to solve the Hamiltonian Cycle problem on an undirected graph 𝐺=(𝑉,𝐸). To this end, let 𝐷=(𝑉,𝐴) be the bidirected complete graph with costs 𝑑...
In computer science, the TSP is still an open problem to be solved in a globally optimal way due to the intractability of its inherent combinatorial nature. A problem is said to be intractable if the computational complexity is superpolynomial. The TSP is defined as an NP (Nondeterministic ...