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Property Testing and its connection to Learning and Approximation
"... We study the question of determining whether an unknown function has a particular property or is fflfar from any function with that property. A property testing algorithm is given a sample of the value of the function on instances drawn according to some distribution, and possibly may query the fun ..."
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Cited by 475 (67 self)
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the function on instances of its choice. First, we establish some connections between property testing and problems in learning theory. Next, we focus on testing graph properties, and devise algorithms to test whether a graph has properties such as being kcolorable or having a aeclique (clique of density ae
A characterization of the (natural) graph properties testable with onesided error
 Proc. of FOCS 2005
, 2005
"... The problem of characterizing all the testable graph properties is considered by many to be the most important open problem in the area of propertytesting. Our main result in this paper is a solution of an important special case of this general problem; Call a property tester oblivious if its decis ..."
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Cited by 107 (18 self)
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] of the graphpartitioning problems that are testable with onesided error, the induced vertex colorability properties of [3], the induced edge colorability properties of [14], a transformation from twosided to onesided error testing [21], as well as a recent result about testing monotone graph properties [10
Every monotone graph property is testable
 Proc. of STOC 2005
, 2005
"... A graph property is called monotone if it is closed under removal of edges and vertices. Many monotone graph properties are some of the most wellstudied properties in graph theory, and the abstract family of all monotone graph properties was also extensively studied. Our main result in this paper i ..."
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Cited by 52 (9 self)
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is that any monotone graph property can be tested with onesided error, and with query complexity depending only on ɛ. This result unifies several previous results in the area of property testing, and also implies the testability of wellstudied graph properties that were previously not known to be testable
A combinatorial characterization of the testable graph properties: it’s all about regularity
 Proc. of STOC 2006
, 2006
"... A common thread in all the recent results concerning testing dense graphs is the use of Szemerédi’s regularity lemma. In this paper we show that in some sense this is not a coincidence. Our first result is that the property defined by having any given Szemerédipartition is testable with a constant ..."
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Cited by 83 (15 self)
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A common thread in all the recent results concerning testing dense graphs is the use of Szemerédi’s regularity lemma. In this paper we show that in some sense this is not a coincidence. Our first result is that the property defined by having any given Szemerédipartition is testable with a constant
Easily Testable Graph Properties
"... A graph on n vertices is ɛfar from a property P if one has to add or delete from it at least ɛn2 edges to get a graph satisfying P. A graph property P is strongly testable (in the dense model) if for every fixed ɛ> 0 it is possible to distinguish, with onesided error, between graphs satisfying ..."
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A graph on n vertices is ɛfar from a property P if one has to add or delete from it at least ɛn2 edges to get a graph satisfying P. A graph property P is strongly testable (in the dense model) if for every fixed ɛ> 0 it is possible to distinguish, with onesided error, between graphs satisfying
Symbolic model checking for sequential circuit verification
 IEEE TRANSACTIONS ON COMPUTERAIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS
, 1994
"... The temporal logic model checking algorithm of Clarke, Emerson, and Sistla [17] is modified to represent state graphs using binary decision diagrams (BDD’s) [7] and partitioned trunsirion relations [lo], 1111. Because this representation captures some of the regularity in the state space of circuit ..."
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Cited by 271 (12 self)
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The temporal logic model checking algorithm of Clarke, Emerson, and Sistla [17] is modified to represent state graphs using binary decision diagrams (BDD’s) [7] and partitioned trunsirion relations [lo], 1111. Because this representation captures some of the regularity in the state space
Efficient Testing of Large Graphs
 Combinatorica
"... Let P be a property of graphs. An test for P is a randomized algorithm which, given the ability to make queries whether a desired pair of vertices of an input graph G with n vertices are adjacent or not, distinguishes, with high probability, between the case of G satisfying P and the case that it h ..."
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Cited by 176 (47 self)
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that it has to be modified by adding and removing more than n 2 edges to make it satisfy P . The property P is called testable, if for every there exists an test for P whose total number of queries is independent of the size of the input graph. Goldreich, Goldwasser and Ron [8] showed that certain graph
Every Property of Hyperfinite Graphs is Testable
 PROCEEDINGS OF THE . 43RD ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING (STOC
, 2011
"... A kdisc around a vertex v of a graph G = (V, E) is the subgraph induced by all vertices of distance at most k from v. We show that the structure of a planar graph on n vertices, and with constant maximum degree d, is determined, up to the modification (insertion or deletion) of at most ɛdn edges, ..."
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Cited by 8 (2 self)
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the following new results in the area of property testing, which are essentially equivalent to the above statement. We prove that • graph isomorphism is testable for every class of hyperfinite graphs, • every graph property is testable for every class of hyperfinite graphs, • every hyperfinite graph property
Every minorclosed property of sparse graphs is testable
, 2007
"... Suppose G is a graph of bounded degree d, and one needs to remove ɛn of its edges in order to make it planar. We show that in this case the statistics of local neighborhoods around vertices of G is far from the statistics of local neighborhoods around vertices of any planar graph G ′. In fact, a sim ..."
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Cited by 33 (3 self)
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similar result is proved for any minorclosed property of bounded degree graphs. As an immediate corollary of the above result we infer that many well studied graph properties, like being planar, outerplanar, seriesparallel, bounded genus, bounded treewidth and several others, are testable with a
Local Graph Partitions for Approximation and Testing
"... We introduce a new tool for approximation and testing algorithms called partitioning oracles. We develop methods for constructing them for any class of boundeddegree graphs with an excluded minor, and in general, for any hyperfinite class of boundeddegree graphs. These oracles utilize only local ..."
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Cited by 14 (1 self)
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minor. • We show a simple proof that any minorclosed graph property is testable in constant time in the bounded degree model. • We prove that it is possible to approximate the distance to almost any hereditary property in any bounded degree hereditary families of graphs. Hereditary properties
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