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  • $\begingroup$ Okay so with your algorithm we know that we want use more than k skips, but maybe we will use less right? So k isn't the minimum number of skips we are looking for. $\endgroup$ Commented Mar 1, 2023 at 19:54
  • $\begingroup$ So, in this case $k$ is an upper bound on the minimum number of skips (it's not impossible that it's not possible to do better), and therefore also an upper bound on the size of the graph you build $\endgroup$ Commented Mar 1, 2023 at 21:57