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We introduce a novel framework of graph modifications specific to intervalgraphs. We study interdiction problems with respect to these graphmodifications. Given a list of original intervals, each interval has areplacement interval such that either the replacement contains the original, orthe original contains the replacement. The interdictor is allowed to replace upto $k$ original intervals with their replacements. Using this framework we alsostudy the contrary of interdiction problems which we call assistance problems.We study these problems for the independence number, the clique number,shortest paths, and the scattering number. We obtain polynomial time algorithmsfor most of the studied problems. Via easy reductions, it follows that oninterval graphs, the most vital nodes problem with respect to shortest path,independence number and Hamiltonicity can be solved in polynomial time.

Assistance and Interdiction Problems on Interval Graphs