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Tight Bounds for Distributed Functional Monitoring
"... We resolve several fundamental questions in the area of distributed functional monitoring, initiated by Cormode, Muthukrishnan, and Yi (SODA, 2008), and receiving recent attention. In this model there are k sites each tracking their input streams and communicating with a central coordinator. The coo ..."
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Cited by 3 (2 self)
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We resolve several fundamental questions in the area of distributed functional monitoring, initiated by Cormode, Muthukrishnan, and Yi (SODA, 2008), and receiving recent attention. In this model there are k sites each tracking their input streams and communicating with a central coordinator. The coordinator’s task is to continuously maintain an approximate output to a function computed over the union of the k streams. The goal is to minimize the number of bits communicated. Let the pth frequency moment be defined as Fp f
Streaming Complexity of Checking Priority Queues ∗
"... This work is in the line of designing efficient checkers for testing the reliability of some massive data structures. Given a sequential access to the insert/extract operations on such a structure, one would like to decide, a posteriori only, if it corresponds to the evolution of a reliable structur ..."
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Cited by 1 (1 self)
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This work is in the line of designing efficient checkers for testing the reliability of some massive data structures. Given a sequential access to the insert/extract operations on such a structure, one would like to decide, a posteriori only, if it corresponds to the evolution of a reliable structure. In a context of massive data, one would like to minimize both the amount of reliable memory of the checker and the number of passes on the sequence of operations. Chu, Kannan and McGregor [9] initiated the study of checking priority queues in this setting. They showed that the use of timestamps allows to check a priority queue with a single pass and memory space Õ( √ N). Later, Chakrabarti, Cormode, Kondapally and McGregor [7] removed the use of timestamps, and proved that more passes do not help. We show that, even in the presence of timestamps, more passes do not help, solving an open problem of [9, 7]. On the other hand, we show that a second pass, but in reverse direction, shrinks the memory space to Õ((log N)2), extending a phenomenon the first time observed by Magniez, Mathieu and Nayak [15] for checking wellparenthesized expressions. 1
BERTINORO WORKSHOP PARTICIPANTS:
, 2011
"... ABSTRACT. This document contains a list of open problems and research directions that have been suggested ..."
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ABSTRACT. This document contains a list of open problems and research directions that have been suggested
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)