Implementing discrete mathematics: combinatorics and graph theory with Mathematica
Implementing discrete mathematics: combinatorics and graph theory with Mathematica
A reliable multicast framework for light-weight sessions and application level framing
IEEE/ACM Transactions on Networking (TON)
Viceroy: a scalable and dynamic emulation of the butterfly
Proceedings of the twenty-first annual symposium on Principles of distributed computing
Scalable Stability Detection Using Logical Hypercube
IEEE Transactions on Parallel and Distributed Systems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Gossip versus Deterministically Constrained Flooding on Small Networks
DISC '00 Proceedings of the 14th International Conference on Distributed Computing
Pastry: Scalable, Decentralized Object Location, and Routing for Large-Scale Peer-to-Peer Systems
Middleware '01 Proceedings of the IFIP/ACM International Conference on Distributed Systems Platforms Heidelberg
Graph-theoretic analysis of structured peer-to-peer systems: routing distances and fault resilience
Proceedings of the 2003 conference on Applications, technologies, architectures, and protocols for computer communications
Building Low-Diameter P2P Networks
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
ICDCSW '01 Proceedings of the 21st International Conference on Distributed Computing Systems
Lightweight probabilistic broadcast
ACM Transactions on Computer Systems (TOCS)
Araneola: A Scalable Reliable Multicast System for Dynamic Environments
NCA '04 Proceedings of the Network Computing and Applications, Third IEEE International Symposium
Overcast: reliable multicasting with on overlay network
OSDI'00 Proceedings of the 4th conference on Symposium on Operating System Design & Implementation - Volume 4
Hybrid dissemination: adding determinism to probabilistic multicasting in large-scale P2P systems
Proceedings of the ACM/IFIP/USENIX 2007 International Conference on Middleware
Scribe: a large-scale and decentralized application-level multicast infrastructure
IEEE Journal on Selected Areas in Communications
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This paper studies the existence and the regularity of Logarithmic Harary Graphs (LHGs). This study is motivated by the fact that these graphs are employed for modeling the communication topology to support efficient flooding in the presence of link and node failures when considering an initial arbitrary number of nodes n. Therefore, the capability to identify graph constraints that allow the construction of LHGs for the largest number of pairs (n,k) (where k is the desired degree of connectivity to be tolerant to failures) becomes of primary importance. The paper presents several results in that direction. We introduce a graph constraint, namely K-PASTED-TREE, that allows the construction of a LHG for every pair (n,k) such that n=2k. Secondly we present another graph constraint for LHG, namely K-DIAMOND, which is equivalent to K-PASTED-TREE in terms of capability to construct LHGs for any pair (n,k). The interest of K-DIAMOND lies in the fact that, for a given k, K-DIAMOND allows us to construct more regular graphs than K-PASTED-TREE does. A k-regular graph shows the minimal number of links required by a k-connected graph, leading to minimal flooding cost. The paper formally shows, in particular, that there are an infinite number of pairs (n,k), such that there exists a k-regular LHG for the pair (n,k) that satisfies K-DIAMOND and does not satisfy K-PASTED-TREE.