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What is the time complexity of adding an edge to doubly connected edge list ?

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The time complexity of adding an edge to a doubly connected edge list can vary based on the specific problem being addressed. In the context of graph theory, the addition of an edge to a graph can impact various algorithms and problems. For instance, in the study of the minimum completion problem for a $P_4$-sparse graph with an added edge, a polynomial-time algorithm is presented, indicating efficient processing . Additionally, the conversion of edge lists to adjacency lists in large-scale graphs using distributed-memory parallel algorithms showcases efficient processing, with a time complexity of O(m/p + n + P) and optimal space complexity of O(m/p) for handling massive graphs with billions of nodes and edges . These insights highlight the importance of considering the specific context and problem domain when determining the time complexity of adding an edge to a doubly connected edge list.

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Open access•Proceedings Article•DOI Fast parallel conversion of edge list to adjacency list for large-scale graphs Shaikh Arifuzzaman, Maleq Khan - Show less +1 more 12 Apr 2015 14 Citations	Not addressed in the paper.
Open access•Posted Content•DOI Adding an Edge in a $P_4$-sparse Graph 31 Jan 2023	Not addressed in the paper.
Adding an Edge in a $P_4$-sparse Graph Anna Mpanti, Stavros D. Nikolopoulos, Leonidas Palios - Show less +2 more 31 Jan 2023	The time complexity of adding an edge to a $P_4$-sparse graph is polynomial due to a small number of possible optimal solutions, enabling a polynomial-time algorithm.
Open access•Journal Article•DOI The complexity of list edge-partitions for simple graphs Payam Valadkhan 01 Mar 2017-The Journal of Combinatorics	Not addressed in the paper.
Book Chapter•DOI Edge-Connectivity augmentation and network matrices Michele Conforti, Anna Galluccio, Guido Proietti - Show less +2 more 21 Jun 2004 10 Citations	Not addressed in the paper.

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