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Many other algorithms were suggested for different kinds of network graphs, such as undirected rings, unidirectional rings, complete graphs, grids, directed Euler graphs, and others. A general method that decouples the issue of the graph family from the design of the coordinator election algorithm was suggested by Korach, Kutten, and Moran.

In order to perform coordination, distributed systems employ the concept of coordinators. The coordinator election problem is to choose a process from among a group of processes on different processors in a distributed system to act as the central coordinator. Several central coordinator election algorithms exist.

So far the focus has been on designing a distributed system that solves a given problem. A complementary research problem is studying the properties of a given distributed system.

The halting problem is an analogous example from the field of centralised computation: we are given a computer program and the task is to decide whether it halts or runs forever. The halting problem is undecidable in the general case, and naturally understanding the behaviour of a computer network is at least as hard as understanding the behaviour of one computer.

However, there are many interesting special cases that are decidable. In particular, it is possible to reason about the behaviour of a network of finite-state machines. One example is telling whether a given network of interacting finite-state machines can reach a deadlock. This problem is PSPACE-complete, i.e., it is decidable, but not likely that there is an efficient algorithm that solves the problem in the case of large networks.

According to Rob Pike, concurrency is the composition of independently executing computations, and concurrency is not parallelism: concurrency is about dealing with lots of things at once but parallelism is about doing lots of things at once. Concurrency is about structure, parallelism is about execution, concurrency provides a way to structure a solution to solve a problem that may be parallelizable.

A number of mathematical models have been developed for general concurrent computation including Petri nets, process calculi, the parallel random-access machine model, the actor model and the Reo Coordination Language.

As Leslie Lamport notes, "While concurrent program execution had been considered for years, the computer science of concurrency began with Edsger Dijkstra's seminal 1965 paper that introduced the mutual exclusion problem. ... The ensuing decades have seen a huge growth of interest in concurrency—particularly in distributed systems. Looking back at the origins of the field, what stands out is the fundamental role played by Edsger Dijkstra".

Because computations in a concurrent system can interact with each other while being executed, the number of possible execution paths in the system can be extremely large, and the resulting outcome can be indeterminate. Concurrent use of shared resources can be a source of indeterminacy leading to issues such as deadlocks, and resource starvation.