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Creators/Authors contains: "Hershberger, J."

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  1. ; ; (, Algorithmica)
    We study the problem of finding shortest paths in the plane among h convex obstacles, where the path is allowed to pass through (violate) up to k obstacles, for 𝑘≤ℎ. Equivalently, the problem is to find shortest paths that become obstacle-free if k obstacles are removed from the input. Given a fixed source point s, we show how to construct a map, called a shortest k-path map, so that all destinations in the same region of the map have the same combinatorial shortest path passing through at most k obstacles. We prove a tight bound of 𝛩(𝑘𝑛) on the size of this map, and show that it can be computed in 𝑂(𝑘2𝑛log𝑛) time, where n is the total number of obstacle vertices. 
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  2. (, Kansas State University 4th Biennial Plant Breeding and Genetics Symposium)
    Accepted Manuscript Full Text Available