We present an algorithm for computing k-link rectilinear shortest paths among rectilinear obstacles in the plane. We extend the "continuous Dijkstra" paradigm to store the link distance information associated with each propagating "wavefront". Our algorithm runs in time O(kn log 2 n) and space O(kn), where n is the number of vertices of the obstacles. Previous algorithms for the problem had worst-case time complexity O(kn 2 ). Our algorithm builds a j-link shortest path map, rooted at a given

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... urce s, for each j ≤ k. A shortest path query from s to a query point t can then be answered in time O(log n + j).