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- W4361003676 abstract "This chapter discusses the computational complexity of checking the necessary and sufficient conditions for membership in the pedigree polytope developed in the previous chapter. An algorithmic framework is provided in this chapter for this purpose. Each step of the algorithm is shown to be executable in time strongly polynomial in n. The number of nodes and arcs of the network in stage $$N_k$$ is bounded above by a low-order polynomial in k. So the corresponding flow problems can be solved in time strongly polynomial in k. Furthermore, the linear multi-commodity flow problem can be solved efficiently as it is a combinatorial linear programme. Thus in conclusion this chapter proves that membership checking in the pedigree polytope can be done efficiently. The algorithmic framework provided in this chapter is crucial since its complexity determines the complexity of solving the pedigree optimisation problem. The new results presented in this chapter from the author’s research do not appear elsewhere. This chapter is crucial for showing $$NP = P$$ as done in the next chapter. An illustrative example is provided." @default.
- W4361003676 created "2023-03-30" @default.
- W4361003676 creator A5014099345 @default.
- W4361003676 date "2023-01-01" @default.
- W4361003676 modified "2023-09-24" @default.
- W4361003676 title "Computational Complexity of Membership Checking" @default.
- W4361003676 doi "https://doi.org/10.1007/978-981-19-9952-9_6" @default.
- W4361003676 hasPublicationYear "2023" @default.
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