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We present an O(n) time algorithm for simultaneous embedding of pairs of planar graphs on the O(n 2 )×O(n 2 ) grid, with at most three bends per edge, where n is the number of vertices. For the case when the input graphs are are both trees, only one bend per edge is required. We also describe an O(n) time algorithm for simultaneous embedding with fixed-edges for tree-path pairs on the O(n) × O(n 2 ) grid with at most one bend per tree-edge and no bends along path edges.doi:10.7155/jgaa.00113 fatcat:jnloyknqozbxzkf4a6wlmxeadq