Network Algorithms

Abstract

Nowadays, computers often function as nodes of a network. In such a network, two nodes can be connected to each other by a communications channel via which they can exchange messages. Such nodes are neighbors.

In a network, there exist some typical tasks: a node sends a message over the network to all other nodes, the nodes synchronize themselves (as far as possible) in cycles or they reach mutual agreements. In this chapter, we discuss solutions to such tasks. Other typical tasks relate to the organization of limited resources, the distribution of tasks or the reinitialization after a critical error.

Such tasks are not easy to solve, because each node generally only has a small number of neighbors. No node “knows” the entire network. Furthermore, a solution is supposed to work not only for a specific network, but for infinitely many, for instance, for all connected or for all acyclic networks.