Stochastic Analysis of a Churn-Tolerant Structured Peer-to-Peer Scheme

We present and analyze a simple and general scheme to build a churn (fault)-tolerant structured Peer-to-Peer (P2P) network. Our scheme shows how to "convert" a static network into a dynamic distributed hash table(DHT)-based P2P network such that all the good properties of the static network are guaranteed with high probability (w.h.p). Applying our scheme to a cube-connected cycles network, for example, yields a $O(\log N)$ degree connected network, in which every search succeeds in $O(\log N)$ hops w.h.p., using $O(\log N)$ messages, where $N$ is the expected stable network size. Our scheme has an constant storage overhead (the number of nodes responsible for servicing a data item) and an $O(\log N)$ overhead (messages and time) per insertion and essentially no overhead for deletions. All these bounds are essentially optimal. While DHT schemes with similar guarantees are already known in the literature, this work is new in the following aspects: (1) It presents a rigorous mathematical analysis of the scheme under a general stochastic model of churn and shows the above guarantees; (2) The theoretical analysis is complemented by a simulation-based analysis that validates the asymptotic bounds even in moderately sized networks and also studies performance under changing stable network size; (3) The presented scheme seems especially suitable for maintaining dynamic structures under churn efficiently. In particular, we show that a spanning tree of low diameter can be efficiently maintained in constant time and logarithmic number of messages per insertion or deletion w.h.p. Keywords: P2P Network, DHT Scheme, Churn, Dynamic Spanning Tree, Stochastic Analysis

Wildcard dimensions, coding theory and fault-tolerant meshes and hypercubes

Hypercubes, meshes and tori are well known interconnection networks for parallel computers. The sets of edges in those graphs can be partitioned to dimensions. It is well known that the hypercube can be extended by adding a wildcard dimension resulting in a folded hypercube that has better fault-tolerant and communication capabilities. First we prove that the folded hypercube is optimal in the sense that only a single wildcard dimension can be added to the hypercube. We then investigate the idea of adding wildcard dimensions to d-dimensional meshes and tori. Using techniques from error correcting codes we construct d-dimensional meshes and tori with wildcard dimensions. Finally, we show how these constructions can be used to tolerate edge and node faults in mesh and torus networks

Embedding cube-connected cycles graphs into faulty hypercubes

We consider the problem of embedding a cube-connected cycles graph (CCC) into a hypercube with edge faults. Our main result is an algorithm that, given a list of faulty edges, computes an embedding of the CCC that spans all of the nodes and avoids all of the faulty edges. The algorithm has optimal running time and tolerates the maximum number of faults (in a worst-case setting). Because ascend-descend algorithms can be implemented efficiently on a CCC, this embedding enables the implementation of ascend-descend algorithms, such as bitonic sort, on hypercubes with edge faults. We also present a number of related results, including an algorithm for embedding a CCC into a hypercube with edge and node faults and an algorithm for embedding a spanning torus into a hypercube with edge faults

Constructing Two Edge-Disjoint Hamiltonian Cycles in Locally Twisted Cubes

The $n$-dimensional hypercube network $Q_n$ is one of the most popular interconnection networks since it has simple structure and is easy to implement. The $n$-dimensional locally twisted cube, denoted by $LTQ_n$, an important variation of the hypercube, has the same number of nodes and the same number of connections per node as $Q_n$. One advantage of $LTQ_n$ is that the diameter is only about half of the diameter of $Q_n$. Recently, some interesting properties of $LTQ_n$ were investigated. In this paper, we construct two edge-disjoint Hamiltonian cycles in the locally twisted cube $LTQ_n$, for any integer $n\geqslant 4$. The presence of two edge-disjoint Hamiltonian cycles provides an advantage when implementing algorithms that require a ring structure by allowing message traffic to be spread evenly across the locally twisted cube.Comment: 7 pages, 4 figure

Parallel Architectures for Planetary Exploration Requirements (PAPER)

The Parallel Architectures for Planetary Exploration Requirements (PAPER) project is essentially research oriented towards technology insertion issues for NASA's unmanned planetary probes. It was initiated to complement and augment the long-term efforts for space exploration with particular reference to NASA/LaRC's (NASA Langley Research Center) research needs for planetary exploration missions of the mid and late 1990s. The requirements for space missions as given in the somewhat dated Advanced Information Processing Systems (AIPS) requirements document are contrasted with the new requirements from JPL/Caltech involving sensor data capture and scene analysis. It is shown that more stringent requirements have arisen as a result of technological advancements. Two possible architectures, the AIPS Proof of Concept (POC) configuration and the MAX Fault-tolerant dataflow multiprocessor, were evaluated. The main observation was that the AIPS design is biased towards fault tolerance and may not be an ideal architecture for planetary and deep space probes due to high cost and complexity. The MAX concepts appears to be a promising candidate, except that more detailed information is required. The feasibility for adding neural computation capability to this architecture needs to be studied. Key impact issues for architectural design of computing systems meant for planetary missions were also identified