There are some issues in this paper.
Issue 1:
There is a mistake on referring.
In Section 5 (the experiments), all [19] should be changed to [17].
That is, CD which is the greedy method using the CD model, was proposed in [17], not [19].
All referred contents about CD actually come from [17].
Note that in Section 2 (the related works), we properly introduced [17] and [19].
Thus, there is no error in the reference section.
Issue 2:
I found that the definition of the local influencer is ambiguous.
Remember that a node is a local influencer of itself.
Issue 3:
Since Algorithm 4 is incorrectly described, we corrected it.
- Lines 18-19 (from the published version) are removed.
Issue 4:
Since Algorithm 5 is incorrectly described, we corrected it.
- In Line 3, leaves(s,t) is replaced with copied^{*}(s,t) which is the set of nodes, each of which is copied from new seed s as a local influencer of t in T_{t}.
Issue 5:
For Algorithm 7, we add some explanation for initializing \Delta\sigma^{S}_{T}(l,t) for any t in T and any l in \lambda(t).
Issue 6:
In Line 27 of Algorithm 7, \lambda(t) is changed to \lambda(t)\setminus S.
This is because we do not need to update the marginal gain of the seeds.
In addition, Line 20 is modified to clarify that we do not update any value for already selected seeds.
Issue 7:
In Algorithm 2, the condition of the if statement is changed to "i is a seed".
This is because a seed can be included in some influence path of another seed as an intermediate node.
Issue 8:
In Algorithm 7, Lines 11-13 are newly added.
If a node becomes a new seed in Algorithm 7 and this is included in an influence path of another seed, the new seed blocks the path.
Thus, we need to update the influence probability of the destination node of the path, because the path is now blocked.
Since this case is unhandled in Algorithm 7, we add Lines 11-13 in Algorithm 7.
Please note that Algorithm 4 and Algorithm 5 were correctly implemented in the experiments.
Algorithm 7 was also correctly implemented except Issue 8.
In other words, all the above issues except Issue 8 are just some mistakes in the paper, not the implementation.
If we apply Issue 8 to our implementation for Algorithm 7, then the accuracy and the query time of our algorithm may increase.
Fortunately, the asymptotic query time is still the same as before, because the cost for Lines 10-14 (including Lines 11-13) is dominated by the cost for Lines 24-30.
Based on this, we expect that the total query time of our method is almost the same as before.
There are some mistakes and an unhandled case (Issue 8) in this paper, but all these things do not affect the main contributions of this paper.
In the uploaded version, all the corrections and additional explanations are applied.
Sorry for the above corrections and issues.
We will publish soon the corrected program implemented with C++.