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We describe a data structure for submatrix maximum queries in Monge matrices or Monge partial matrices, where a query specifies a contiguous submatrix of the given matrix, and its output is the maximum element of that submatrix. Our data structure for an n ×

We give two new algorithms for recognizing proper circulararc graphs and unit circular-arc graphs. The algorithms either provide a model for the input graph, or a certificate that proves that such a model does not exist and can be authenticated in O(n) time.

We give an O(n log 3 n) algorithm that, given an n-node directed planar graph with arc capacities, a set of source nodes, and a set of sink nodes, finds a maximum flow from the sources to the sinks. Previously, the fastest algorithms known for this problem were those for general graphs.