
Lower Bounds for Approximating Graph Parameters via Communication Complexity
We present a new framework for proving query complexity lower bounds for...
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Streaming Hardness of Unique Games
We study the problem of approximating the value of a Unique Game instanc...
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Streaming Frequent Items with Timestamps and Detecting Large Neighborhoods in Graph Streams
Detecting frequent items is a fundamental problem in data streaming rese...
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An Optimal Space Lower Bound for Approximating MAXCUT
We consider the problem of estimating the value of MAXCUT in a graph in...
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The Sketching Complexity of Graph and Hypergraph Counting
Subgraph counting is a fundamental primitive in graph processing, with a...
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Advice Complexity of Priority Algorithms
The priority model of "greedylike" algorithms was introduced by Borodin...
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Approximation Schemes for Covering and Packing in the Streaming Model
The shifting strategy, introduced by Hochbaum and Maass, and independent...
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Polynomial Pass Lower Bounds for Graph Streaming Algorithms
We present new lower bounds that show that a polynomial number of passes are necessary for solving some fundamental graph problems in the streaming model of computation. For instance, we show that any streaming algorithm that finds a weighted minimum st cut in an nvertex undirected graph requires n^2o(1) space unless it makes n^Ω(1) passes over the stream. To prove our lower bounds, we introduce and analyze a new fourplayer communication problem that we refer to as the hiddenpointer chasing problem. This is a problem in spirit of the standard pointer chasing problem with the key difference that the pointers in this problem are hidden to players and finding each one of them requires solving another communication problem, namely the set intersection problem. Our lower bounds for graph problems are then obtained by reductions from the hiddenpointer chasing problem. Our hiddenpointer chasing problem appears flexible enough to find other applications and is therefore interesting in its own right. To showcase this, we further present an interesting application of this problem beyond streaming algorithms. Using a reduction from hiddenpointer chasing, we prove that any algorithm for submodular function minimization needs to make n^2o(1) value queries to the function unless it has a polynomial degree of adaptivity.
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