
Several Separations Based on a Partial Boolean Function
We show a partial Boolean function f together with an input x∈ f^1(*) s...
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Distributed Maximization of Submodular and Approximately Submodular Functions
We study the problem of maximizing a submodular function, subject to a c...
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Complexity of nearoptimal robust versions of multilevel optimization problems
Nearoptimality robustness extends multilevel optimization with a limite...
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Optimal pointwise sampling for L^2 approximation
Given a function u∈ L^2=L^2(D,μ), where D⊂ℝ^d and μ is a measure on D, a...
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Revisiting Graph Width Measures for CNFEncodings
We consider bounded width CNFformulas where the width is measured by po...
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Solving quantum linear system problem with nearoptimal complexity
We present a simple algorithm to solve the quantum linear system problem...
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Sample Efficient GraphBased Optimization with Noisy Observations
We study sample complexity of optimizing "hillclimbing friendly" functi...
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Unambiguous DNFs and AlonSaksSeymour
We exhibit an unambiguous kDNF formula that requires CNF width Ω̃(k^2), which is optimal up to logarithmic factors. As a consequence, we get a nearoptimal solution to the Alon–Saks–Seymour problem in graph theory (posed in 1991), which asks: How large a gap can there be between the chromatic number of a graph and its biclique partition number? Our result is also known to imply several other improved separations in query and communication complexity.
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