Most uniform path partitioning and its use in image processing
Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
A shifting algorithm for constrained min-max partition on trees
Discrete Applied Mathematics
The Profile Minimization Problem in Trees
SIAM Journal on Computing
The shifting algorithm technique for the partitioning of trees
Discrete Applied Mathematics - Special volume on partitioning and decomposition in combinatorial optimization
Journal of the ACM (JACM)
Maintaining hierarchical graph views
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Clustering Techniques for Minimizing External Path Length
VLDB '96 Proceedings of the 22th International Conference on Very Large Data Bases
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We present algorithms for computing hierarchical decompositions of trees satisfying different optimization criteria, including balanced cluster size, bounded number of clusters, and logarithmic depth of the decomposition. Furthermore, every high-level representation of the tree obtained from such decompositions is guaranteed to be a tree. These criteria are relevant in many application settings, but appear to be difficult to achieve simultaneously. Our algorithms work by vertex deletion and hinge upon the new concept of t-divider, that generalizes the well-known concepts of centroid and separator. The use of t-dividers, combined with a reduction to a classical scheduling problem, yields an algorithm that, given a n-vertex tree T, builds in O(n log n) worst-case time a hierarchical decomposition of T satisfying all the aforementioned requirements.