Computing a Minimum-Weight k-Link Path in Graphs with the Concave Monge Property
نویسنده
چکیده
Let G be a weighted, complete, directed acyclic graph whose edge weights obey the concave Monge condition. We give an efficient algorithm for finding the minimum weight k-link path between a given pair of vertices for any given k. The log k log log n ' O Ž . Ž . algorithm runs in n2 time, for k s V log n . Our algorithm can be applied to get efficient solutions for the following problems, improving on previous Ž . Ž . results: 1 computing length-limited Huffman codes, 2 computing optimal disŽ . Ž . crete quantization, 3 computing maximum k-cliques of an interval graph, 4 Ž . finding the largest k-gon contained in a given convex polygon, 5 finding the smallest k-gon that is the intersection of k half-planes out of n half-planes defining a convex n-gon. Q 1998 Academic Press
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