Combinatorial Approximations for Cluster Deletion: Simpler, Faster, and Better
This work provides incremental improvements for graph clustering applications in computational biology and social network analysis.
The paper tackles the NP-hard cluster deletion problem by improving the approximation guarantees of two existing algorithms from 4 to 3 and introducing a new combinatorial method that enhances scalability.
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.