Oded Goldreich, Avi Wigderson

We consider the size of circuits which perfectly hash

an arbitrary subset $S\!\subset\!\bitset^n$ of cardinality $2^k$

into $\bitset^m$.

We observe that, in general, the size of such circuits is

exponential in $2k-m$,

and provide a matching upper bound.

Noga Alon, Shai Gutner

Color Coding is an algorithmic technique for deciding efficiently

if a given input graph contains a path of a given length (or

another small subgraph of constant tree-width). Applications of the

method in computational biology motivate the study of similar

algorithms for counting the number of copies of a ...
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Aditya Bhaskara, Devendra Desai, Srikanth Srinivasan

We consider the problem of constructing explicit Hitting sets for Combinatorial Shapes, a class of statistical tests first studied by Gopalan, Meka, Reingold, and Zuckerman (STOC 2011). These generalize many well-studied classes of tests, including symmetric functions and combinatorial rectangles. Generalizing results of Linial, Luby, Saks, and Zuckerman (Combinatorica 1997) ... more >>>