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Testing stconnectivity
 11th International Workshop on Randomization and Computation (RANDOM 2007
, 2007
"... We continue the study, started in [9], of property testing of graphs in the orientation model. A major question which was left open in [9] is whether the property of stconnectivity can be tested with a constant number of queries. Here we answer this question on the affirmative. To this end we const ..."
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Cited by 6 (5 self)
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We continue the study, started in [9], of property testing of graphs in the orientation model. A major question which was left open in [9] is whether the property of stconnectivity can be tested with a constant number of queries. Here we answer this question on the affirmative. To this end we construct a nontrivial reduction of the stconnectivity problem to the problem of testing languages that are decidable by branching programs, which was solved in [11]. The reduction combines combinatorial arguments with a concentration type lemma that is proven for this purpose. Unlike many other property testing results, here the resulting testing algorithm is highly nontrivial itself, and not only its analysis.
On the query complexity of testing orientations for being Eulerian
 In Proceedings of the Twelveth International Workshop on Randomization and Computation (RANDOM
, 2008
"... Abstract. We consider testing directed graphs for being Eulerian in the orientation model introduced in [15]. Despite the local nature of the property of being Eulerian, it turns out to be significantly harder for testing than other properties studied in the orientation model. We show a nonconstant ..."
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Cited by 5 (0 self)
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Abstract. We consider testing directed graphs for being Eulerian in the orientation model introduced in [15]. Despite the local nature of the property of being Eulerian, it turns out to be significantly harder for testing than other properties studied in the orientation model. We show a nonconstant lower bound on the query complexity of 2sided tests and a linear lower bound on the query complexity of 1sided tests for this property. On the positive side, we give several 1sided and 2sided tests, including a sublinear query complexity 2sided test for general graphs. For special classes of graphs, including boundeddegree graphs and expander graphs, we provide improved results. In particular, we give a 2sided test with constant query complexity for dense graphs, as well as for expander graphs with a constant expansion parameter. 1
Testing convexity properties of tree colorings
 Proc. of the 24th International Symposium on Theoretical Aspects of Computer Science (STACS 2007), LNCS 4393, SpringerVerlag 2007
"... ..."
On the Query Complexity of Testing for Eulerian Orientations
"... We consider testing directed graphs for being Eulerian in the orientation model introduced in [15]. Despite the local nature of the property of being Eulerian, it turns out to be significantly harder for testing than other properties studied in the orientation model. We show a superconstant lower bo ..."
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Cited by 2 (1 self)
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We consider testing directed graphs for being Eulerian in the orientation model introduced in [15]. Despite the local nature of the property of being Eulerian, it turns out to be significantly harder for testing than other properties studied in the orientation model. We show a superconstant lower bound on the query complexity of 2sided tests and a linear lower bound on the query complexity of 1sided tests for this property. On the positive side, we give several 1sided and 2sided tests, including a sublinear 2sided test for general graphs. For special classes of graphs, including boundeddegree graphs and expander graphs, we provide improved results. In particular, for dense graphs we give a 2sided test with constant query complexity. 1
MODELS OF QUERY COMPLEXITY FOR BOOLEAN FUNCTIONS
, 2008
"... In this thesis we study various models of query complexity. A query algorithm computes a function under the restriction that the input can be accessed only by making probes to the the bits of the input. The query complexity of a function f is the minimum number of probes made by any query algorithm ..."
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In this thesis we study various models of query complexity. A query algorithm computes a function under the restriction that the input can be accessed only by making probes to the the bits of the input. The query complexity of a function f is the minimum number of probes made by any query algorithm that computes f. In this thesis, we consider three different models of query complexity, (1) deterministic decision tree complexity (query complexity when the underlying algorithm is deterministic), (2) approximate decision tree complexity aka. property testing (query complexity when the underlying algorithm is probabilistic and only expected to ”approximately ” compute f) and quantum query complexity (query complexity when the underlying algorithm is allowed to make quantum queries). The main results in this thesis are: • We study the relation between deterministic decision tree complexity and other combinatorial measures of complexity measures like sensitivity and block sensitivity. We prove that for mintermtransitive functions the sensitivity is quadratically related to block sensitivity which is polynomially
Property Testing of Massively Parametrized problems A survey ∗
"... We survey here property testing results for the so called ’massively parametrized ’ model (or problems). This paper is based on a survey talk gave at the workshop on property testing, Beijing, ..."
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We survey here property testing results for the so called ’massively parametrized ’ model (or problems). This paper is based on a survey talk gave at the workshop on property testing, Beijing,