Problems on multivariate reliability polynomial

The original results include: (i) homogenization of a reliability polynomial; (ii) compact hypersurfaces attached to homogeneous polynomials; (iii) an affine diffeomorphism that preserves a reliability polynomial; (iv) duality of networks via a diffeomorphism; (v) straight line segments in constant level sets associated to a reliability polynomial.

[1]  V. Balan,et al.  Reliability extrema of a complex circuit on bi-variate slice classes , 2015 .

[2]  C. Udriste,et al.  Geometric properties of reliability polynomials , 2015, 1507.02122.

[3]  Z. Hassan,et al.  Equivalent reliability polynomials modeling EAS and their geometries , 2015 .

[4]  Jean-François Aubry,et al.  Systems Dependability Assessment: Modeling with Graphs and Finite State Automata , 2015 .

[5]  C. Udriste,et al.  Geometric Modeling in Probability and Statistics , 2014 .

[6]  Wei Zhou,et al.  An Inclusion-Exclusion Algorithm for Network Reliability with Minimal Cutsets , 2012 .

[7]  Nicolae Jula,et al.  Methods for Analyzing the Reliability of Electrical Systems Used Inside Aircrafts , 2012 .

[8]  Yoseph Shpungin,et al.  Network Reliability and Resilience , 2011, Springer Briefs in Electrical and Computer Engineering.

[9]  Daoud Ait-Kadi,et al.  A Practical Algorithm for Network Reliability Evaluation Based on the Factoring Theorem-A Case Study of a Generic Radiocommunication System , 2009 .

[10]  A. Sokal,et al.  The Brown-Colbourn conjecture on zeros of reliability polynomials is false , 2003, J. Comb. Theory B.

[11]  Min-Sheng Lin,et al.  A linear-time algorithm for computing K-terminal reliability on proper interval graphs , 2002, IEEE Trans. Reliab..

[12]  R. K. Wood,et al.  Note on "A Linear-Time Algorithm for Computing K-Terminal Reliability in a Series-Parallel Network" , 1996, SIAM J. Comput..

[13]  C. Udriste,et al.  Convex Functions and Optimization Methods on Riemannian Manifolds , 1994 .

[14]  A. Satyanarayana,et al.  A Unified Formula for Analysis of Some Network Reliability Problems , 1982, IEEE Transactions on Reliability.

[15]  A. Prabhakar,et al.  New Topological Formula and Rapid Algorithm for Reliability Analysis of Complex Networks , 1978, IEEE Transactions on Reliability.

[16]  Yuji Nakagawa,et al.  Optimal Reliability Allocation by Branch-and-Bound Technique , 1978, IEEE Transactions on Reliability.

[17]  Ionel,et al.  GEOMETRIC PROGRAMMING APPROACHES OF RELIABILITY ALLOCATION , 2017 .

[18]  Ammar M. Sarhan,et al.  Equivalence factors of a parallel-series system , 2008 .

[19]  Zhang Xiang-de,et al.  An Inclusion-exclusion Algorithm for Network Reliability , 2007 .

[20]  Charles J. Colbourn,et al.  The Combinatorics of Network Reliability , 1987 .

[21]  Appajosyula Satyanarayana,et al.  A Linear-Time Algorithm for Computing K-Terminal Reliability in Series-Parallel Networks , 1985, SIAM J. Comput..