Dima Grigoriev, Marek Karpinski, A. C. Yao

We prove an exponential lower bound on the size of any

fixed-degree algebraic decision tree for solving MAX, the

problem of finding the maximum of $n$ real numbers. This

complements the $n-1$ lower bound of Rabin \cite{R72} on

the depth of ...
more >>>

Marek Karpinski

We survey some of the recent results on the complexity of recognizing

n-dimensional linear arrangements and convex polyhedra by randomized

algebraic decision trees. We give also a number of concrete applications

of these results. In particular, we derive first nontrivial, in fact

quadratic, ...
more >>>

Piotr Berman, Marek Karpinski

We prove that the problems of minimum bisection on k-uniform

hypergraphs are almost exactly as hard to approximate,

up to the factor k/3, as the problem of minimum bisection

on graphs. On a positive side, our argument gives also the

first approximation ...
more >>>

Venkatesan Guruswami, Ali Kemal Sinop

We prove almost tight hardness results for finding independent sets in bounded degree graphs and hypergraphs that admit a good

coloring. Our specific results include the following (where $\Delta$, assumed to be a constant, is a bound on the degree, and

$n$ is the number of vertices):

Guy Moshkovitz

In this paper we present a combinatorial approach for proving complexity lower bounds. We mainly focus on the following instantiation of it. Consider a pair of properties of $m$-edge regular hypergraphs. Suppose they are ``indistinguishable'' with respect to hypergraphs with $m-t$ edges, in the sense that every such hypergraph has ... more >>>

Andrzej Dudek , Marek Karpinski, Andrzej Rucinski, Edyta Szymanska

We design a fully polynomial time approximation scheme (FPTAS) for counting the number of matchings (packings) in arbitrary 3-uniform hypergraphs of maximum degree three, referred to as $(3,3)$-hypergraphs. It is the first polynomial time approximation scheme for that problem, which includes also, as a special case, the 3D Matching counting ... more >>>

Guy Blanc, Dean Doron

We construct a family of binary codes of relative distance $\frac{1}{2}-\varepsilon$ and rate $\varepsilon^{2} \cdot 2^{-\log^{\alpha}(1/\varepsilon)}$ for $\alpha \approx \frac{1}{2}$ that are decodable, probabilistically, in near linear time. This improves upon the rate of the state-of-the-art near-linear time decoding near the GV bound due to Jeronimo, Srivastava, and Tulsiani, who ... more >>>