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CORR
2010
Springer

Is submodularity testable?

13 years 9 months ago
Is submodularity testable?
: We initiate the study of property testing of submodularity on the boolean hypercube. Submodular functions come up in a variety of applications in combinatorial optimization. For a vast range of algorithms, the existence of an oracle to a submodular function is assumed. But how does one check if this oracle indeed represents a submodular function? Consider a function f : {0, 1}n → R. The distance to submodularity is the minimum fraction of values of f that need to be modified to make f submodular. If this distance is more than > 0, then we say that f is -far from being submodular. The aim is to have an efficient procedure that, given input f that is -far from being submodular, certifies that f is not submodular. We analyze a very natural tester for this problem, and prove that it runs in subexponential time. This gives the first non-trivial tester for submodularity. On the other hand, we prove an interesting lower bound (that is, unfortunately, quite far from the upper bound) ...
C. Seshadhri, Jan Vondrák
Added 24 Jan 2011
Updated 24 Jan 2011
Type Journal
Year 2010
Where CORR
Authors C. Seshadhri, Jan Vondrák
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