Improved Bounds for Minimum Fault-Tolerant Gossip Graphs
Conference paper
Abstract
A k-fault-tolerant gossip graph is a (multiple) graph whose edges are linearly ordered such that for any ordered pair of vertices u and v, there are k + 1 edge-disjoint ascending paths from u to v. Let τ(n,k) denote the minimum number of edges in a k-fault-tolerant gossip graph with n vertices. In this paper, we present upper and lower bounds on τ(n,k) which improve the previously known bounds. In particular, from our upper bounds, it follows that \(\tau(n,k) \leq \frac{nk}{2} + O(n\log{n})\). Previously, it has been shown that this upper bound holds only for the case that n is a power of two.
Keywords
Telephone Call Exchange Path Small Factor Center Vertex Circulant Graph
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References
- 1.Baker, B., Shostak, R.: Gossips and telephones. Discrete Math. 2, 191–193 (1972)MathSciNetCrossRefMATHGoogle Scholar
- 2.Berman, K.A., Hawrylycz, M.: Telephone problems with failures. SIAM J. Alg. Disc. Meth. 7, 13–17 (1986)MathSciNetCrossRefMATHGoogle Scholar
- 3.Berman, K.A., Paul, J.L.: Verifiable broadcasting and gossiping in communication networks. Discrete Applied Math 118, 293–298 (2002)MathSciNetCrossRefMATHGoogle Scholar
- 4.Bumby, R.T.: A problem with telephones. SIAM J. Alg. Disc. Meth. 2, 13–18 (1981)MathSciNetCrossRefMATHGoogle Scholar
- 5.Haddad, R.W., Roy, S., Schäffer, A.A.: On gossiping with faulty telephone lines. SIAM J. Alg. Disc. Meth. 8, 439–445 (1987)MathSciNetCrossRefMATHGoogle Scholar
- 6.Hajnal, A., Milner, E.C., Szemerédi, E.: A cure for the telephone disease. Canad. Math. Bull. 15, 447–450 (1976)MathSciNetCrossRefMATHGoogle Scholar
- 7.Hedetniemi, S.M., Hedetniemi, S.T., Liestman, A.L.: A survey of gossiping and broadcasting in communication networks. Networks 18, 319–349 (1988)MathSciNetCrossRefMATHGoogle Scholar
- 8.Hou, Z., Shigeno, M.: New bounds on the minimum number of calls in failure-tolerant gossiping. Networks 53, 35–38 (2009)MathSciNetCrossRefMATHGoogle Scholar
- 9.Pelc, A.: Fault-tolerant broadcasting and gossiping in communication networks. Networks 28, 143–156 (1996)MathSciNetCrossRefMATHGoogle Scholar
- 10.Seress, Á.: Quick gossiping by conference calls. SIAM J. Disc. Math. 1, 109–120 (1988)MathSciNetCrossRefMATHGoogle Scholar
- 11.Tijdeman, R.: On a telephone problem. Nieuw Arch. Wisk. 3, 188–192 (1971)MathSciNetMATHGoogle Scholar
- 12.West, D.B.: Gossiping without duplicate transmissions. SIAM J. Alg. Disc. Meth. 3, 418–419 (1982)MathSciNetCrossRefMATHGoogle Scholar
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