Examples
Many natural problems are actually promise problems. For instance, consider the following problem: Given a directed acyclic graph, determine if the graph has a path of length 10. The yes instances are directed acyclic graphs with a path of length 10, whereas the no instances are directed acyclic graphs with no path of length 10. The promise is the set of directed acyclic graphs. In this example, the promise is easy to check. In particular, it is very easy to check if a given graph is cyclic. However, the promised property could be difficult to evaluate. For instance, consider the problem "Given a Hamiltonian graph, determine if the graph has a cycle of size 4." Now the promise is NP-hard to evaluate, yet the promise problem is easy to solve since checking for cycles of size 4 can be done in polynomial time.
Read more about this topic: Promise Problem
Famous quotes containing the word examples:
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—André Breton (1896–1966)
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