A (4/3+ε)-Approximation Algorithm for Arboricity From Pseudoforest Partitions
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The arboricity of a graph is the minimum number of forests it can be partitioned into. Previous approximation schemes only approximated this value without computing a corresponding forest partition, as they operate on the related pseudoforest partitions or the dual problem. We propose a linear-time algorithm for converting a partition of k pseudoforests into a partition of 4k/3 forests. For every fixed ϵ > 0, this implies an O(m n)-time algorithm that constructively approximates the arboricity within a factor of (4/3+ϵ) plus a small additive constant. We also make several remarks on approximation algorithms for the pseudoarboricity and the equivalent graph orientations with smallest maximum indegree, and correct some mistakes made in the literature.
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