Generalized Maximum Independent Sets for Trees in Subquadratic Time

  • B. K. Bhattacharya
  • M. E. Houle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1741)


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.


Leaf Node Binary Tree Optimal Placement Vertex Weight Segment Tree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • B. K. Bhattacharya
    • 1
  • M. E. Houle
    • 2
  1. 1.School of Computing ScienceSimon Fraser UniversityBurnabyCanada
  2. 2.Basser Department of Computer ScienceThe University of SydneySydneyAustralia

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