The submodularity ratio of the effective graph resistance under link addition can be made arbitrarily close to zero, so generalized submodularity provides no greedy guarantee for k-GRIP.
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On the non-submodularity of the problem of adding links to minimize the effective graph resistance
The submodularity ratio of the effective graph resistance under link addition can be made arbitrarily close to zero, so generalized submodularity provides no greedy guarantee for k-GRIP.