Tight bounds for k-party one-way MVC with linear communication

Establish tight approximation ratio bounds for Minimum Vertex Cover in the k-party one-way communication model under O(n) total communication by determining whether the upper bound (2 − 2^{-k+1} + ε) is optimal for k > 2 and by developing lower bounds that extend the two-party case to k parties.

Background

The paper proves an (2 − 2^{-k+1} + ε)-approximation protocol for Minimum Vertex Cover in the k-party one-way communication model using O(n) communication, and shows tightness for k = 2 via a lower bound. However, for k > 2, the optimal approximation ratio under linear communication is not settled, and extending lower bounds beyond two parties requires new techniques.

This problem seeks to close the gap by either improving the upper bound or proving stronger lower bounds that match it, thereby fully characterizing the approximation-communication trade-off in the multi-party one-way setting.