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Electronic Colloquium on Computational Complexity

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Reports tagged with Hypergraphs:
TR95-057 | 24th November 1995
Dima Grigoriev, Marek Karpinski, A. C. Yao

An Exponential Lower Bound on the Size of Algebraic Decision Trees for MAX

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 >>>

TR99-020 | 9th June 1999
Marek Karpinski

Randomized Complexity of Linear Arrangements and Polyhedra

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 >>>

TR03-056 | 29th July 2003
Piotr Berman, Marek Karpinski

Approximability of Hypergraph Minimum Bisection

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 >>>

TR10-111 | 14th July 2010
Venkatesan Guruswami, Ali Kemal Sinop

The complexity of finding independent sets in bounded degree (hyper)graphs of low chromatic number

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):

... more >>>

TR11-138 | 24th October 2011
Guy Moshkovitz

Complexity Lower Bounds through Balanced Graph Properties

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 >>>

TR14-065 | 2nd May 2014
Andrzej Dudek , Marek Karpinski, Andrzej Rucinski, Edyta Szymanska

Approximate Counting of Matchings in $(3,3)$-Hypergraphs

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 >>>

TR22-027 | 22nd February 2022
Guy Blanc, Dean Doron

New Near-Linear Time Decodable Codes Closer to the GV Bound

Revisions: 1

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 >>>

ISSN 1433-8092 | Imprint