What problem is this? Largest sum produced by selecting one number at each index from n lists, with restrictions
I believe this can be solved in $O(nm)$ time using dynamic programming:
$$\begin{align*}
B[i,k] &amp;= A[i,k] + \dots + A[i,k+r-1] + C[i,r]\\
C[i,k] &amp;= \max(A[i,k] + C[i,k+1], \max_{i'} B[i',k])
\end{align*}$$
Note that you can compute $A[i,k] + \dots + A[i,k+r-1]$ in $O(1)$ time as the difference of two prefix sums (assuming you have done a one-time precomputation to compute all prefix-sums).
The answer is then $\max_i B[i,1]$.  Computing it takes $O(nm)$ time, as there are $O(nm)$ entries to fill in, and each one takes $O(1)$ time to fill in, using the equations above.
Interpretation:

$B[i,k]$ is the maximum possible value of $\sum_{j=k}^m A[i_j,j]$ such that $i_k=i$ and $i_k,\dots,i_m$ satisfy the repetition rule

$C[i,k]$ is the maximum possible value of $\sum_{j=k}^m A[i_j,j]$ such that $i_k,\dots,i_m$ satisfy the repetition rule except that if $i_k=i$, the run starting at $i_k$ can be of any length (but all subsequent runs must be at least $r$ long).  In other words,
$$C[i,k] = \max_\ell A[i,k] + \dots + A[i,k+\ell-1] + \max_{i'} B[i',k+\ell]$$


Generally, this is not the kind of thing I would expect to find papers about.  I would expect to see a one-sentence &quot;can be solved by dynamic programming&quot;, possibly with an explanation of the max-trick above to reduce the running time from $O(nmr)$ to $O(nm)$, but not an entire paper about it.  So I would not bet on such a paper existing.  But I could be wrong.  It's certainly possible there could be such a paper.  I would not know how to go about looking for it.