Expander Properties in Random Regular Graphs with Edge Faults

Let H be an undirected graph. A random graph of type-H is obtained by selecting edges of H independently and with probability p. We can thus represent a communication network H in which the links fail independently and with probability f=1−p. A fundamental type of H is the clique of n nodes (leading to the well-known random graph G n,p ). Another fundamental type of H is a random member of the set G n d of all regular graphs of degree d (leading to a new type of random graphs, of the class G n,p d ). Note that G n,p =G n,p n−1 . The G n,p d model was introduced in ([11]).

[1]  Svante Janson,et al.  The Birth of the Giant Component , 1993, Random Struct. Algorithms.

[2]  Eli Upfal,et al.  Constructing disjoint paths on expander graphs , 1987, STOC '87.

[3]  Frank Thomson Leighton,et al.  Fast Computation Using Faulty Hypercubes (Extended Abstract) , 1989, Symposium on the Theory of Computing.

[4]  Michael O. Rabin,et al.  Efficient dispersal of information for security, load balancing, and fault tolerance , 1989, JACM.

[5]  Frank Thomson Leighton,et al.  Fast computation using faulty hypercubes , 1989, STOC '89.

[6]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[7]  Leslie G. Valiant,et al.  A bridging model for parallel computation , 1990, CACM.

[8]  Endre Szemerédi,et al.  On the second eigenvalue of random regular graphs , 1989, STOC '89.

[9]  Paul G. Spirakis,et al.  Efficient robust parallel computations , 2018, STOC '90.

[10]  Z. M. Kedem,et al.  Combining tentative and definite executions for very fast dependable parallel computing , 1991, STOC '91.

[11]  Charles E. Leiserson,et al.  Fat-trees: Universal networks for hardware-efficient supercomputing , 1985, IEEE Transactions on Computers.

[12]  Béla Bollobás,et al.  Random Graphs , 1985 .

[13]  Paul G. Spirakis,et al.  Short Vertex Disjoint Paths and Multiconnectivity in Random Graphs: Reliable Network Computing , 1994, ICALP.

[14]  Stefan Burr,et al.  The Mathematics of networks , 1982 .

[15]  Andrei Z. Broder,et al.  On the second eigenvalue of random regular graphs , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).