Abstract
LetGbe a weighted, complete, directed acyclic graph whose edge weights obey the concave Monge condition. We give an efficient algorithm for finding the minimum weightk-link path between a given pair of vertices for any givenk. The algorithm runs in time, fork=?(logn). Our algorithm can be applied to get efficient solutions for the following problems, improving on previous results: (1) computing length-limited Huffman codes, (2) computing optimal discrete quantization, (3) computing maximumk-cliques of an interval graph, (4) finding the largestk-gon contained in a given convex polygon, (5) finding the smallestk-gon that is the intersection ofkhalf-planes out ofnhalf-planes defining a convexn-gon.
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