Applications
The mathematical theory of interval graphs was developed with a view towards applications by researchers at the RAND Corporation's mathematics department, which included young researchers—such as Peter C. Fishburn and students like Alan C. Tucker and Joel E. Cohen—besides leaders—such as Delbert Fulkerson and (recurring visitor) Victor Klee. Cohen applied interval graphs to mathematical models of population biology, specifically food webs.
Other applications include genetics, bioinformatics, and computer science. Finding a set of intervals that represent an interval graph can also be used as a way of assembling contiguous subsequences in DNA mapping. Interval graphs are used to represent resource allocation problems in operations research and scheduling theory. Each interval represents a request for a resource for a specific period of time; the maximum weight independent set problem for the graph represents the problem of finding the best subset of requests that can be satisfied without conflicts. Interval graphs also play an important role in temporal reasoning.
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