Approximation algorithm for maximum total transitivity

Develop an approximation algorithm for the Maximum Total Transitivity Problem.

Background

The Maximum Total Transitivity Problem asks for a total transitive partition of a graph with the maximum possible number of parts. The paper proves that its decision version is NP-complete for bipartite graphs, while giving a polynomial-time algorithm for trees. The authors explicitly identify the design of an approximation algorithm as an unresolved computational problem for this optimization problem.

References

Designing an approximation algorithm for this problem would be another challenging open problem.

— On total transitivity of graphs  (2501.13760 - Santra, 23 Jan 2025) in Section 6, Conclusion and future works