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On the Value of Multiple Read/Write Streams for Approximating Frequency Moments
"... We consider the read/write streams model, an extension of the standard data stream model in which an algorithm can create and manipulate multiple read/write streams in addition to its input data stream. We show that any randomized read/write stream algorithm with a fixed number of streams and a subl ..."
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We consider the read/write streams model, an extension of the standard data stream model in which an algorithm can create and manipulate multiple read/write streams in addition to its input data stream. We show that any randomized read/write stream algorithm with a fixed number of streams and a sublogarithmic number of passes that produces a constant factor approximation of the kth frequency moment Fk of an input sequence of length of at most N from {1,..., N} requires space Ω(N 1−4/k−δ) for any δ> 0. For comparison, it is known that with a single readonly data stream there is a randomized constantfactor approximation for Fk using Õ(N 1−2/k) space and that there is a deterministic algorithm computing Fk exactly using 3 read/write streams, O(log N) passes, and O(log N) space. Therefore, although the ability to manipulate multiple read/write streams can add substantial power to the data stream model, with a sublogarithmic number of passes this does not significantly improve the ability to approximate higher frequency moments efficiently. Our lower bounds also apply to (1 + ɛ)approximations of Fk for ɛ ≥ 1/N.
Validating XML documents in the streaming model with external memory
 In ICDT
, 2012
"... We study the problem of validating XML documents of size N against general DTDs in the context of streaming algorithms. The starting point of this work is a wellknown space lower bound. There are XML documents and DTDs for which ppass streaming algorithms require Ω(N/p) space. We show that when al ..."
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We study the problem of validating XML documents of size N against general DTDs in the context of streaming algorithms. The starting point of this work is a wellknown space lower bound. There are XML documents and DTDs for which ppass streaming algorithms require Ω(N/p) space. We show that when allowing access to external memory, there is a deterministic streaming algorithm that solves this problem with memory space O(log 2 N), a constant number of auxiliary read/write streams, and O(log N) total number of passes on the XML document and auxiliary streams. An important intermediate step of this algorithm is the computation of the FirstChildNextSibling (FCNS) encoding of the initial XML document in a streaming fashion. We study this problem independently, and we also provide memory efficient streaming algorithms for decoding an XML document given in its FCNS encoding. Furthermore, validating XML documents encoding binary trees in the usual streaming model without external memory can be done with sublinear memory. There is a onepass algorithm using O ( √ N log N) space, and a bidirectional twopass algorithm using O(log 2 N) space performing this task.
GrammarBased Compression in a Streaming Model
 LATA 2010. LNCS
, 2010
"... We show that, given a string s of length n, with constant memory and logarithmic passes over a constant number of streams we can build a contextfree grammar that generates s and only s and whose size is within an O min g log g, n / log nfactor of the minimum g. This stands in contrast to our pre ..."
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Cited by 4 (2 self)
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We show that, given a string s of length n, with constant memory and logarithmic passes over a constant number of streams we can build a contextfree grammar that generates s and only s and whose size is within an O min g log g, n / log nfactor of the minimum g. This stands in contrast to our previous result that, with polylogarithmic memory and polylogarithmic passes over a single stream, we cannot build such a grammar whose size is within any polynomial of g.
Machine Models for Query Processing
"... The massive data sets that have to be processed in many application areas are often far too large to fit completely into a computer’s internal memory. When evaluating queries on such large data sets, the resulting communication ..."
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The massive data sets that have to be processed in many application areas are often far too large to fit completely into a computer’s internal memory. When evaluating queries on such large data sets, the resulting communication
Strategy Machines and their Complexity (with addendum)
"... Abstract. We introduce a machine model for the execution of strategies in (regular) infinite games that refines the standard model of Mealy automata. This model of controllers is formalized in the terminological framework of Turing machines. We show how polynomially sized controllers can be found fo ..."
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Abstract. We introduce a machine model for the execution of strategies in (regular) infinite games that refines the standard model of Mealy automata. This model of controllers is formalized in the terminological framework of Turing machines. We show how polynomially sized controllers can be found for Muller and Streett games. We are able to distinguish aspects of executing strategies (“size”, “latency”, “space consumption”) that are not visible in Mealy automata. Also, lower bound results are obtained. 1
Input/Output Streaming Complexity of Reversal and Sorting ∗
"... This work revisits the study of streaming algorithms where both input and output are data streams. While streaming algorithms with multiple streams have been studied before, such as in the context of sorting, most assumed very nonrestrictive models and thus had weak lower bounds. We consider data st ..."
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This work revisits the study of streaming algorithms where both input and output are data streams. While streaming algorithms with multiple streams have been studied before, such as in the context of sorting, most assumed very nonrestrictive models and thus had weak lower bounds. We consider data streams with restricted access, such as readonly and writeonly streams, as opposed to readwrite streams. We also require streams to be processed in one direction only when multiple passes are allowed. Last, we forbid the use of any other external streams. Reversing a stream has been demonstrated to allow exponential speedup for several decision problems. Therefore, it naturally arises as the bottleneck problem of our model. We give several tight bounds for reversing the input stream depending on the model. We also study the problem of sorting, and improve previously known algorithms in terms of space used on the two streams. Partially supported by the French ANR Blanc project ANR12BS02005 (RDAM)
Cryptography with Streaming Algorithms
"... Abstract. We put forth the question of whether cryptography is feasible using streaming devices. We give constructions and prove lower bounds. In streaming cryptography (not to be confused with streamciphers) everything—the keys, the messages, and the seeds—are huge compared to the internal memory ..."
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Abstract. We put forth the question of whether cryptography is feasible using streaming devices. We give constructions and prove lower bounds. In streaming cryptography (not to be confused with streamciphers) everything—the keys, the messages, and the seeds—are huge compared to the internal memory of the device. These streaming algorithms have small internal memory size and make a constant number of passes over big data maintained in a constant number of read/write external tapes. Typically, the internal memory size is O(log n) and we use 2 external tapes; whereas 1 tape is provably insufficient. In this setting we cannot compute instances of popular intractability assumptions. Nevertheless, we base cryptography on these assumptions by employing nonblackbox techniques, and study its limitations. We introduce new techniques to obtain unconditional lower bounds showing that no superlinear stretch pseudorandom generator exists, and no Public Key Encryption (PKE) exists with privatekeys of size sublinear in the plaintext length. For possibility results, assuming the existence of oneway functions computable in NC1—e.g. factoring, lattice assumptions—we obtain streaming algorithms computing oneway functions and pseudorandom generators. Given the Learning With Errors (LWE) assumption we construct PKE where both the encryption and decryption are streaming algorithms. The starting point of our work is the groundbreaking work of ApplebaumIshaiKushilevitz on Cryptography in NC0. In the end, our developments are technically orthogonal to their work; e.g. there is a PKE where the decryption is a streaming algorithm, whereas no PKE decryption can be in NC0.