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The problem of monotonicity testing over the hypergrid and its special case, the hypercube, is a classic, well-studied, yet unsolved question in property testing.
Improved testing algorithms for monotonicity
Dodis, Y · 1999
Earlier work this paper cites.
Spot-checkers
Ergun, F · 2000
Earlier work this paper cites.
Testing monotonicity
Goldreich, O · 2000
Earlier work this paper cites.
On disjoint chains of subsets
Lehman, E · 2001
Earlier work this paper cites.
Monotonicity testing over general poset domains
Fischer, E · 2002
Earlier work this paper cites.
On the strength of comparisons in property testing
Fischer, E · 2004
Earlier work this paper cites.
Fast approximate P C P PCP s for multidimensional bin-packing problems
Batu, T · 2005
Earlier work this paper cites.
Information theory in property testing and monotonicity testing in higher dimension
Ailon, N · 2006
Cited alongside, same era.
Estimating the distance to a monotone function
Ailon, N · 2006
Cited alongside, same era.
Calibrating noise to sensitivity in private data analysis
Dwork, C · 2006
Cited alongside, same era.
Tolerant property testing and distance approximation
Parnas, M · 2006
Cited alongside, same era.
Testing monotonicity over graph products
Halevy, S · 2008
Cited alongside, same era.
Transitive-closure spanners
Bhattacharyya, A · 2009
Cited alongside, same era.
Lower bounds for local monotonicity reconstruction from transitive-closure spanners
Open problems in data streams, property testing, and related topics
2011 · 2011
Later among the works it cites.
Proving programs robust
Chaudhuri, S · 2011
Later among the works it cites.
Testing and reconstruction of Lipschitz functions with applications to data privacy
Jha, M · 2011
Later among the works it cites.
Testing Lipschitz functions on hypergrid domains
Awasthi, P · 2012
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Property testing lower bounds via communication complexity
Blais, E · 2012
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Monotonicity testing and shortest-path routing on the cube
Briët, J · 2012
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Lower bounds for testing properties of functions on hypergrid domains
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Bhattacharyya, A · 2010
Cited alongside, same era.
Optimal bounds for monotonicity and Lipschitz testing over hypercubes and hypergrids
Chakrabarty, D
Cited in the paper.
An optimal lower bound for monotonicity testing over hypergrids
Chakrabarty, D
Cited in the paper.
Blais, E · 2014
Closest in time.