Lower Bounds for Testing Computability by Small Width OBDDs

Brody, Joshua; Matulef, Kevin; Wu, Chenggang

doi:10.1007/978-3-642-20877-5_32

Cited by 10 publications

(7 citation statements)

References 31 publications

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“…Again with the kind permission of Oded Goldreich, we present his proof of Theorem 1.4. We again remark that this result was obtained independently by Brody et al (2011), who gave a similar proof.…”

Section: Testing K-linearity and Related Propertiesmentioning

confidence: 53%

Property Testing Lower Bounds via Communication Complexity

2012

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We develop a new technique for proving lower bounds in property testing, by showing a strong connection between testing and communication complexity. We give a simple scheme for reducing communication problems to testing problems, thus allowing us to use known lower bounds in communication complexity to prove lower bounds in testing. This scheme is general and implies a number of new testing bounds, as well as simpler proofs of several known bounds.For the problem of testing whether a boolean function is k-linear (a parity function on k variables), we achieve a lower bound of Ω(k) queries, even for adaptive algorithms with two-sided error, thus confirming a conjecture of Goldreich [25]. The same argument behind this lower bound also implies a new proof of known lower bounds for testing related classes such as k-juntas. For some classes, such as the class of monotone functions and the class of s-sparse GF(2) polynomials, we significantly strengthen the best known bounds.

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Section: Testing K-linearity and Related Propertiesmentioning

confidence: 53%

Property Testing Lower Bounds via Communication Complexity

2012

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“…Another benefit of the non-adaptive variant is that it gives a one-pass streaming algorithm for correlation clustering that uses only ( ) space and processes edges in arbitrary order. Another interesting consequence of this result (coupled with our lower bound, Theorem 4.1), is that adaptivity does not help for correlation clustering (beyond possibly a constant factor), in stark contrast to other problems where an exponential separation is known between the query complexity of adaptive and non-adaptive algorithms (e.g., [10,14]).…”

Section: A Non-adaptive Algorithmmentioning

confidence: 78%

Query-Efficient Correlation Clustering

García-Soriano

Kutzkov

Bonchi³

et al. 2020

Proceedings of the Web Conference 2020

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Correlation clustering is arguably the most natural formulation of clustering. Given objects and a pairwise similarity measure, the goal is to cluster the objects so that, to the best possible extent, similar objects are put in the same cluster and dissimilar objects are put in different clusters. A main drawback of correlation clustering is that it requires as input the Θ(2) pairwise similarities. This is often infeasible to compute or even just to store. In this paper we study queryefficient algorithms for correlation clustering. Specifically, we devise a correlation clustering algorithm that, given a budget of queries, attains a solution whose expected number of disagreements is at most 3•OPT + (3), where OPT is the optimal cost for the instance. Its running time is (), and can be easily made non-adaptive (meaning it can specify all its queries at the outset and make them in parallel) with the same guarantees. Up to constant factors, our algorithm yields a provably optimal trade-off between the number of queries and the worst-case error attained, even for adaptive algorithms. Finally, we perform an experimental study of our proposed method on both synthetic and real data, showing the scalability and the accuracy of our algorithm.

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“…Remark Note that throughout the paper the width of an OBDD is defined via the complete or leveled model as is often the case in the literature (see, e.g., [7,11,14,15,18]). One might argue that in applications often reduced OBDDs are used and therefore another definition of the width like the maximal number of nodes labeled by the same variable or the maximal number of nodes with the same distance from the source would be more appropriate.…”

Section: Corollary 2 There Exists a Sandwich Variable Ordering That Imentioning

confidence: 99%

“…Moreover, also in complexity theory the width of OBDDs has been investigated, e.g., in property testing. Lower and upper bounds have been shown for testing functions for the property of being computable by an ordered binary decision diagram of small width, i.e., given oracle access to a Boolean function f testing whether f can be represented by an OBDD of small width or is in a certain sense far from any such function [7,14,18]. Newman has presented a property testing algorithm for any property decidable by an ordered binary decision diagram of constant width [15].…”

Section: Introductionmentioning

confidence: 98%

On the Minimization of (Complete) Ordered Binary Decision Diagrams

Bollig

2015

Theory Comput Syst

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Ordered binary decision diagrams (OBDDs) are a popular data structure for Boolean functions. Some applications work with a restricted variant called complete OBDDs which is strongly related to nonuniform deterministic finite automata. One of its complexity measures is the width which has been investigated in several areas in computer science like machine learning, property testing, and the design and analysis of implicit graph algorithms. For a given function the size and the width of a (complete) OBDD is very sensitive to the choice of the variable ordering but the computation of an optimal variable ordering for the OBDD size is known to be NP-hard. Since optimal variable orderings with respect to the OBDD size are not necessarily optimal for the complete model or the OBDD width and hardly anything about the relation between optimal variable orderings with respect to the size and the width is known, this relationship is investigated. Here, using a new reduction idea it is shown that the size minimization problem for complete OBDDs and the width minimization problem are NP-hard.Preliminary versions of parts of this paper have been appeared in [2,3] The author is supported by DFG project BO 2755/1-2.Beate Bollig

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Lower Bounds for Testing Computability by Small Width OBDDs

Cited by 10 publications

References 31 publications

Property Testing Lower Bounds via Communication Complexity

Property Testing Lower Bounds via Communication Complexity

Query-Efficient Correlation Clustering

On the Minimization of (Complete) Ordered Binary Decision Diagrams

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