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Bipartite-Based 2-Approximation for Dominating Sets in General Graphs
- The article presents an algorithm for computing dominating sets in general graphs with a 2-approximation guarantee, aiming to achieve a set size at most twice the size of the optimal set.
- The algorithm transforms the problem into a bipartite graph setting and utilizes a greedy approach to find dominating sets efficiently.
- Handling isolated nodes and constructing a bipartite graph are initial steps in the algorithm to prepare for the dominating set computation.
- The algorithm's correctness is analyzed, demonstrating that every vertex in the graph is either in the dominating set or adjacent to a dominating vertex.
- An approximation analysis using the 'Du' charging scheme showcases that the algorithm guarantees a 2-approximation bound for the dominating set problem.
- Runtime analysis reveals the algorithm's time complexity of O(nlogn+m) and space complexity of O(n+m), making it efficient and scalable for large graphs.
- Experimental results show the algorithm's competitive runtime performance and approximation quality, highlighting its effectiveness and potential for real-world applications.
- Future work aims to optimize the algorithm's runtime performance, extend it to handle weighted instances, and evaluate its performance on real-world graph datasets.
- The impact of this work lies in offering theoretical insights, practical utility, and implications for the complexity class P=NP, with transformative implications.
- The algorithms contribute to the field of approximation algorithms by providing efficient solutions with improved solution quality, paving the way for various applications in network optimization.
- The findings and algorithms presented in the article showcase the potential for significant advancements in solving NP-hard problems efficiently, with implications across various domains.
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