A Failure Detector for k-Set Agreement in Dynamic Systems

The k-set agreement problem is a generalization of the consensus problem where processes can decide up to k different values. Very few papers have tackled this problem in dynamic networks, and to the best of our knowledge, every algorithm proposed so far for k-set agreement in dynamic networks assumed synchronous communications or made strong failure pattern assumptions. Exploiting the formalism of the Time-Varying Graph model, this paper proposes a new quorum-based failure detector for solving k-set agreement in dynamic networks with asynchronous communications. We present two algorithms that implement this new failure detector using graph connectivity and message pattern assumptions. We also provide an algorithm for solving k-set agreement using our new failure detector.