Computing Network Reliability in Time Polynomial in the Number of Cuts

Article Abstract:

The probability that there is an operating path between two given nodes is calculated. The modes reside in a stochastic network. The computation time is bounded by a polynomial in the number of cuts in the network. It is shown that an algorithm with a time bound that is polynomial in network size and the number of (S,T)-paths cannot exist unless P=NP. Other algorithms enumerate pathsets and cutsets in the network. Diagrams illustrate portions of networks.

Reliability (Trustworthiness), Network analyzers, Graph theory, LAN Monitor, Reliability, Stochastic Model, Algorithm Analysis, Probability, Polynomial Time, Execution Time

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A Polynomial Simplex Method for the Assignment Problem

Article Abstract:

A polynomial primal simplex method algorithm for the assignment problem is presented. For an nXn assignment problem with integer cost coefficients, the algorithm generates at most n cubed natural log delta bases prior to reaching the optimal basis. Delta is the difference in objective value between an initial extreme point and the optimal extreme point.

Linear programming, Polynomials, Numerical analysis, Simplexes (Mathematics), Mathematical Programming, Simplex Method

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The Secretary Problem with Optimal Assignment

Article Abstract:

The classical secretary problem is described. Each applicant is ranked according to some quality. Applicants appear in order; their ranks are observed relative to those preceding them. They are selected or rejected with the objective of selecting the best applicant. The 3-problem is solved.

Scientific Research, Theory, Searching

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