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Fault diagnosis of interconnection networks is vital to ensuring the reliability and maintenance of multiprocessor systems. Based on graph theory, diagnostic algorithms for solving the problem of fault diagnosis in interconnection networks have been widely studied. As the number of processors in multiprocessor systems has increased in recent years, fault diagnosis algorithms based on graph theory cannot meet the current diagnosis requirements of some interconnection networks, such as t-diagnosable systems. In this paper, we use the evolution diagnosis approach to study fault diagnosis in t-diagnosable systems under the PMC model. First, for a t-diagnosable system G with a syndrome σ , we use a simple centralized algorithm to generate its simplified diagnosis graph G f , which contains all the faulty nodes in G. Based on the graph, we prove that the faulty node set in G is the minimum cover set of G f . Next, we prove that the problem of computing the minimum cover set for G f is equivalent to the problem of computing the optimal solution of a zero-one integer program. Using this result, we propose a novel genetic algorithm to solve the problem of the zero-one integer program. The simulation results show that the diagnostic accuracy of our proposed algorithm is equal to or greater than 96% and that the proposed algorithm outperforms its competitors in terms of diagnostic accuracy, number of iterations and running time. [ABSTRACT FROM AUTHOR]

This paper deals with an analysis of three algorithms for the graph vertex cover problem. Certain methods for solving this problem are analyzed. In addition, different studies on the problem and some approaches to its solution are discussed as well. An exact algorithm (based on the backtracking approach) is presented. Calculating the average time for execution of this algorithm is consistent with the multitasking way of work of the operating system. For this purpose, four different starts of the algorithm are made and then the average time of all of them is calculated. The exact algorithm found the optimal solutions for all analyzed graphs. Besides this algorithm, two other heuristic algorithms for solving the problem are discussed. For this study, an interactive application is developed to visualize the performance of the three algorithms and display the obtained results. The results show that for small graphs with no more than 25 vertices, the exact algorithm can be used to solve optimally the graph vertex cover problem. For the largest graphs, none of the two heuristic algorithms found the optimal solutions, but these algorithms generated solutions that are very close to the optimal ones. In summary, when the size of the graph increases linearly, the execution time of the heuristic algorithms increases linearly, while the execution time of the exact algorithm increases exponentially. [ABSTRACT FROM AUTHOR]

Given an undirected graph G on n nodes and m edges in the form of a data stream we study the problem of finding an Euler tour in G. Our main result is the first one-pass streaming algorithm computing an Euler tour of G in the form of an edge successor function with only O (n log (n)) RAM, which is optimal for this setting (e.g. Sun and Woodruff (2015)). Since the output size can be much larger, we use a write-only tape to gradually output the solution. The previously best-known result for finding Euler tours in data streams is implicitly given by the W-stream algorithm of Demetrescu et al. (2010) using O (m / n) passes under the same RAM limitation. Our approach is to partition the edges into edge-disjoint cycles and to merge the cycles until a single Euler tour is achieved. In the streaming environment such a merging is far from being obvious as the limited RAM allows the processing of only a constant number of cycles at once. This enforces merging of cycles that partially are no longer present in RAM. We solve this problem with a new edge swapping technique, for which storing two certain edges per node is sufficient to merge tours without having all tour edges in RAM. The mathematical key is to model tours and their merging in an algebraic way, where certain equivalence classes represent subtours. This quite general approach might be of interest also in other routing problems. [ABSTRACT FROM AUTHOR]