Abstract
In this paper we consider a special case of the Maximum Weighted Independent Set problem for graphs: given a vertex- and edge- weighted tree T = (V,E) where |V| = n, and a real number b, determine the largest weighted subset P of V such that the distance between the two closest elements of P is at least b. We present an O(n log3 n) algorithm for this problem when the vertices have unequal weights. The space requirement is O(n log n). This is the first known subquadratic algorithm for the problem. This solution leads to an O(n log4 n) algorithm to the previously-studied Weighted Max-Min Dispersion Problem.
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© 1999 Springer-Verlag Berlin Heidelberg
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Bhattacharya, B.K., Houle, M.E. (1999). Generalized Maximum Independent Sets for Trees in Subquadratic Time. In: Algorithms and Computation. ISAAC 1999. Lecture Notes in Computer Science, vol 1741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46632-0_44
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DOI: https://doi.org/10.1007/3-540-46632-0_44
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