A distributed algorithm is an algorithm that tries to solve a typical problem in distributed computing.
Here is a list of distributed algorithms by problem:
Leader Election
Consensus Algorithms try to solve the problem of a number of processes agreeing on a common decision. A typical algorithm for solving consensus is the paxos algorithm.
The atomic commit problem is a variant of the consensus Algorithms for solving the atomic commig protocol include the two-phase commit protocol and the three-phase commit protocol.
Reliable Broadcast
Causal Order/Total Order
Replication
ROWA, ROWAA, QA