Combinatorial Approximations for Cluster Deletion: Simpler, Faster, and Better
arxiv(2024)
摘要
Cluster deletion is an NP-hard graph clustering objective with applications
in computational biology and social network analysis, where the goal is to
delete a minimum number of edges to partition a graph into cliques. We first
provide a tighter analysis of two previous approximation algorithms, improving
their approximation guarantees from 4 to 3. Moreover, we show that both
algorithms can be derandomized in a surprisingly simple way, by greedily taking
a vertex of maximum degree in an auxiliary graph and forming a cluster around
it. One of these algorithms relies on solving a linear program. Our final
contribution is to design a new and purely combinatorial approach for doing so
that is far more scalable in theory and practice.
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