Abstract
We present an approximation algorithm for detecting the number of cycles in an undirected graph, using CUDA (Compute Unified Device Architecture) technology from NVIDIA and utilizing the massively parallel multi-threaded processor; GPU (Graphics Processing Unit). Although the cycle detection is an NP-complete problem, this work reduces the execution time and the consumption of hardware resources with only a commodity GPU, such that the algorithm makes a substantial difference compared to the serial counterpart. The idea is to convert the cycle detection from adjacency matrix/list view of the graph, applying DFS (Depth First Search) to a mathematical model so that each thread in the GPU will execute a simple computation procedures and a finite number of loops in a polynomial time. The algorithm is composed of two phases, the first phase is to create a unique number of combinations of the cycle length using combinatorial mathematics. The second phase is to approximate the number of swaps (permutations) for each thread to check the possibility of cycle. An experiment was conducted to compare the results of our algorithm with the results of another algorithm based on the Donald Johnson backtracking algorithm.
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Mahdi, F., Safar, M., Mahdi, K. (2011). Detecting Cycles in Graphs Using Parallel Capabilities of GPU. In: Cherifi, H., Zain, J.M., El-Qawasmeh, E. (eds) Digital Information and Communication Technology and Its Applications. DICTAP 2011. Communications in Computer and Information Science, vol 167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22027-2_17
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DOI: https://doi.org/10.1007/978-3-642-22027-2_17
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