Dieter van Melkebeek, Holger Dell

Consider the following two-player communication process to decide a language $L$: The first player holds the entire input $x$ but is polynomially bounded; the second player is computationally unbounded but does not know any part of $x$; their goal is to cooperatively decide whether $x$ belongs to $L$ at small ... more >>>

Rahul Santhanam, Srikanth Srinivasan

Impagliazzo, Paturi and Zane (JCSS 2001) proved a sparsification lemma for $k$-CNFs:

every k-CNF is a sub-exponential size disjunction of $k$-CNFs with a linear

number of clauses. This lemma has subsequently played a key role in the study

of the exact complexity of the satisfiability problem. A natural question is

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Dean Doron, Jack Murtagh, Salil Vadhan, David Zuckerman

We give a deterministic, nearly logarithmic-space algorithm for mild spectral sparsification of undirected graphs. Given a weighted, undirected graph $G$ on $n$ vertices described by a binary string of length $N$, an integer $k\leq \log n$ and an error parameter $\varepsilon > 0$, our algorithm runs in space $\tilde{O}(k\log (N\cdot ... more >>>