A fault-free cycle in the n-dimensional hypercube Qn with f faulty vertices is long if it has length at least 2 − 2f . If all faulty vertices are from the same bipartite class of Qn, such length is the best possible. We prove a conjecture of Castañeda and Gotchev [2] asserting that fn = ( n 2 ) −2 where fn is the largest integer such that for every set of at most fn faulty vertices, there exist...

Nodes in distributed systems can become faulty due to multiple reasons: software or hardware bug, node misconfiguration or node being compromised by an attacker. Often such faulty nodes can be difficult to detect and localize. An approach to solve this problem is to hold each node accountable for its actions i.e. each node is required to provide verifiable evidence for its actions and detect a ...

In this paper, we present a strongly fault-tolerant design for the l-level k-ary tree multiprocessor and examine its reconfigurability. Our design assigns one spare node to the regular nodes of each subtree with lc levels. Moreover, spare nodes are interconnected to form a spare tree. Our approach utilizes the circuit-switched capabilities of the communication modules of the spare nodes to tole...

In this paper, we present a strongly fault-tolerant design for a d-dimensional hypercube multiprocessor and examine its reconfigurability. The augmented hypercube has a spare node connected to each node of an i-cube and the spare nodes are also connected as a (d i)-dimensional hypercube. By utilizing the circuit-switched capabilities of the communication modules of the spare nodes, large number...

The star graph interconnection network has been recognized as an attractive alternative to the hypercube network. Previously, the star graph has been shown to contain a Hamiltonian cycle. In this paper, we consider an injured star graph with some faulty links and nodes. We show that even with fe £ n 3 faulty links, a Hamiltonian cycle still can be found in an n-star, and that with fv £ n 3 faul...

We consider the problem of simulating a PRAM on a faulty distributed memory machine (DMM). We focus on dynamic faults, i.e. each processor or memory module independently fails during the simulation of a PRAM step with fixed probability and remains faulty for the rest of the simulation. We build upon randomized hashing-based simulations on non-faulty DMMs from [14], which achieve delay O(log log...