A succinct encoding of planar graphs supports BFS in O(n) time with o(n) extra bits, keeps the BFS tree queryable, and yields sublinear-space planar separator and bipartiteness algorithms.
Space efficient linear time algorithms for BFS, DFS and applications.Theory Comput
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Breadth-First Search in Succinct Planar Graphs
A succinct encoding of planar graphs supports BFS in O(n) time with o(n) extra bits, keeps the BFS tree queryable, and yields sublinear-space planar separator and bipartiteness algorithms.