Assigning Coordinates to Events: Solving Combinatorial problems using Discrete Event Simulation

This paper is inspired by the “event list” mechanism in discrete event simulations. We argue that descriptions of many combinatorial algorithms can be simplified by casting the solution in terms of processing events according to some order. We propose generalizations of the event list mechanism, and show their applications in problems from graph theory and computational geometry. Discrete event simulation is used to mimic the real time behavior of a physical system. Typically, the physical system generates “events” at specific times, and the execution of an event may cause other events to happen in the future. Many combinatorial problems have the same structure as discrete event simulation in that they generate events, the events have to be processed in some order, and the processing of events may generate yet more events (to be processed later). Explicit real-time does not play a role in combinatorial problems, but processing of events imposes an order akin to the real-time order. Such problems can be solved by specifying (1) the order in which the events have to be processed, and (2) the steps needed for processing each event, where the steps may also generate new events. The management of the data structure for events, the event list, may be delegated to a standard run-time routine called the “event list manager”. Structuring the solution in such a manner often simplifies the algorithm description by eliminating book keeping, as we show with several examples in this paper.