Bounding all-terminal reliability in computer networks

Many bounds for the all-terminal reliability of computer networks have been proposed. Of those computable in polynomial time, the Ball-Provan bounds and the Lomonosov Polesskii bounds provide the tightest estimates. A strategy is developed here using linear programming to obtain bounds which are tighter than both the Lomonosov-Polesskii and the Ball-Provan bounds. Computational results on these new bounds are also reported.

[1]  Eitan Zemel,et al.  Polynomial algorithms for estimating network reliability , 1982, Networks.

[2]  J. Scott Provan,et al.  Calculating bounds on reachability and connectedness in stochastic networks , 1983, Networks.

[3]  F. Boesch,et al.  Super line-connectivity properties of circulant graphs , 1986 .

[4]  W. T. Tutte,et al.  The Dissection of Rectangles Into Squares , 1940 .

[5]  Richard M. Van Slyke,et al.  Network reliability analysis: Part I , 1971, Networks.

[6]  Michael Ball,et al.  Backtracking Algorithms for Network Reliability Analysis , 1977 .

[7]  John A. Buzacott,et al.  A recursive algorithm for finding reliability measures related to the connection of nodes in a graph , 1980, Networks.

[8]  Charles J. Colbourn,et al.  The Leggett bounds for network reliability , 1985 .

[9]  R. Wilkov,et al.  Analysis and Design of Reliable Computer Networks , 1972, IEEE Trans. Commun..

[10]  W. T. Tutte.  On the Problem of Decomposing a Graph into n Connected Factors , 1961 .

[11]  Robert E. Tarjan,et al.  Network Flow and Testing Graph Connectivity , 1975, SIAM J. Comput..

[12]  T. C. Hu,et al.  Multi-Terminal Network Flows , 1961 .

[13]  Claude E. Shannon,et al.  Reliable Circuits Using Less Reliable Relays , 1956 .

[14]  S. Bedrosian,et al.  Synthesis of Reliable Networks , 1969 .

[15]  R. Stanley.  Cohen-Macaulay Complexes , 1977 .

[16]  C. Nash-Williams.  Edge-disjoint spanning trees of finite graphs , 1961 .

[17]  Irwin Mark. Jacobs,et al.  Connectivity in probabilistic graphs , 1960 .

[18]  J. S. Provan,et al.  Bounds on the reliability polynomial for shellable independence systems , 1982 .

[19]  Mark K. Chang,et al.  Network reliability and the factoring theorem , 1983, Networks.

[20]  Charles J. Colbourn,et al.  RELIABILITY BOUNDS FOR NETWORKS WITH STATISTICAL DEPENDENCE. , 1986 .

[21]  J. Scott Provan,et al.  The Complexity of Counting Cuts and of Computing the Probability that a Graph is Connected , 1983, SIAM J. Comput..

[22]  G. Kirchhoff.  Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird , 1847 .

[23]  Charles J. Colbourn,et al.  The most reliable series-parallel networks , 1985, Networks.