Foremost Walks and Paths in Interval Temporal Graphs^†

Round 1

Reviewer 1 Report

The paper is very interesting. It is also well written, clear, concise and well explained. It presents significant contributions to graph theory and practice.

There are just some minor formatting issues: in some lines (i.e. line 225) the equations overlap, and the text surpasses the margins. Please check.

In my opinion, algorithm are better explained when they have inputs and outputs, to help the reader. I suggest to add those two rows in your algorithms' description.

Author Response

1. Problems with line 225 where text was surpassing the margins and the equations were overlapping has been fixed.
2. INPUT and OUTPUT has been added to both the mwf and mhf algorithms as suggested. Please check these changes on starting line# 304 for mhf algorithm and starting line#498 for mwf algorithm

Reviewer 2 Report

The authors propose an algorithm for solving some graphs problems. They prove that the problems are NP-hard. They prove the correctness of the proposed algorithm. The proposed algorithm is describe with pseudo-code.

Paper is well written and understandable. The only weakness is comparison. The problem is NP-hard, thus for it is very appropriate to apply some metaheuristic approach. Can you compare the performance of your algorithm with some metaheuristics?

Author Response

Our pseudopolynomial time algorithm finds the optimal solution and its runtime is quite acceptable on our test data. Hence we see no value in developing a meta-heuristic for the kind of datasets we have.

Further, the fine tuning of a meta heuristic to obtain good performance is sufficiently detailed to warrant a separate publication.