Fast Graph Search Algorithms For When the Graph is Dense

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I've been researching graph search algorithms that are practically fast on dense weighted graphs. Was just wondering if anyone has any papers to link to or suggestions on practically performant algorithms that achieve this. Furthermore, the graph algorithm does not have to provide an optimal solution, but a satisficing solution is sufficient.

Some of the options I've already explored includes the common ones such as $A^*$ and Dijkstra's.