Providing successful data collection and aggregation is a primary goal for a broad spectrum of critical applications of wireless sensor networks. Unfortunately, the problem of connectivity loss, which may occur when a network suffers from natural disasters or human sabotages, may cause failure in data aggregation. To tackle this issue, plenty of strategies that deploy relay devices on target areas to restore connectivity have been devised. However, all of them assume that either the landforms of target areas are flat or there are sufficient relay devices. In real scenarios, such assumptions are not realistic. In this paper, we propose a hybrid recovery strategy based on random terrain (simply, HRSRT) that takes both realistic terrain influences and quantitative limitations of relay devices into consideration. HRSRT is proved to accomplish the biconnectivity restoration and meanwhile minimize the energy cost for data collection and aggregation. In addition, both of complexity and approximation ratio of HRSRT are explored. The simulation results show that HRSRT performs well in terms of overall/maximum energy cost.

In wireless sensor networks (WSNs), connecting disjoint segments is significant for network restoration, especially in some mission critical applications. However, the variability of distances between disjoint segments has tremendous influence on relay nodes deployment. In fact, finding the optimal solution for connecting disjoint segments in terms of the number and positions of relay nodes is NP-hard. To address this issue, plenty of heuristics, such as STP-MSP (Cheng et al., 2008), MST-1tRN (Lloyd et al., 2007), and CORP (Lee and Younis, 2010) are deeply pursued. In this paper, we propose a distributed restoration algorithm based on optimal relay node placement (simply, ORNP). It aims at federating separated segments by populating the minimum number of relay nodes in a WSN that has suffered a significant damage. In addition, both of complexity and upper bound of the relay count for ORNP are explored. The simulation results show that ORNP performs better than STP-MSP, MST-1tRN, and CORP in terms of relay count and the connectivity of resulting topology.

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The growing size of the multiprocessor system increases its vulnerability to component failures. It is crucial to locate and to replace the faulty processors to maintain a system's high reliability. The fault diagnosis is the process of identifying faulty processors in a system through testing. This paper shows that the largest connected component of the survival graph contains almost all remaining vertices in the (n, k)-arrangement graph A n,k when the number of moved faulty vertices is up to twice or three times the traditional connectivity. Based on this fault resiliency, we establishes that the conditional diagnosability of A n,k under the comparison model. We prove that for k ≥ 4, n ≥ k + 2, the conditional diagnosability of A n,k is (3k − 2)(n − k) − 3; the conditional diagnosability of A n,n−1 is 3n − 7 for n ≥ 5.

The growing size of the multiprocessor systems increases their vulnerability to component failures. It is crucial to locate and replace the faulty processors to maintain the system's high reliability. The fault diagnosis is the process of identifying faulty processors in a system through testing. The conditional diagnosis requires that for each processor v in a system, all the processors that are directly connected to v do not fail simultaneously. In this paper, we show that the conditional diagnosability of the crossed cubes CQ n under the comparison diagnosis model is 3n − 5 when n ≥ 7. Hence, the conditional diagnosability of CQ n is three times larger than its classical diagnosability.

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