Approximate Coloring of Uniform Hypergraphs (Extended Abstract)

@inproceedings{Krivelevich1998ApproximateCO,
  title={Approximate Coloring of Uniform Hypergraphs (Extended Abstract)},
  author={Michael Krivelevich and Benny Sudakov},
  booktitle={ESA},
  year={1998}
}
We consider an algorithmic problem of coloring r-uniform hypergraphs. The problem of finding the exact value of the chromatic number of a hypergraph is known to be NP-hard, so we discuss approximate solutions to it. Using a simple construction and known results on hardness of graph coloring, we show that for any r ≥ 3 it is impossible to approximate in polynomial time the chromatic number of r-uniform hypergraphs on n vertices within a factor n1-Ɛ for any Ɛ > 0, unless NP ⊆ ZPP. On the positive… 
View via Publisher
8 Citations
Background Citations
2

8 Citations

Approximate coloring of uniform hypergraphs
Coloring k-colorable graphs using relatively small palettes
Testing Hypergraph Coloring
TLDR
It is proved that the fundamental problem of l-colorability of k-uniform hypergraphs can be tested in time independent of the size of the hypergraph.
Strong Colorings of Hypergraphs
TLDR
An algebraic scheme using integer programming to color graphs of bounded composition-width is given, to give a unified treatment of general hypergraphs, both offline and online.
Testing hypergraph colorability
Hardness results for approximate hypergraph coloring
TLDR
This work builds on the idea of "covering complexity" of probabilistically checkable proof systems (PCPs) developed in [6] and introduces some new techniques as well.
Throughput and Delay Optimization of Linear Network Coding in Wireless Broadcast
TLDR
This thesis presents a comprehensive study on the joint optimization of throughput and average packet decoding delay (APDD) for LNC in wireless broadcast and reveals the fundamental performance limits of LNC.
Feedback-Assisted Random Linear Network Coding in Wireless Broadcast
TLDR
This paper focuses on the reliable delivery of a stream of packets from a sender to a set of receivers over a lossy broadcast channel with limited receiver feedback and presents the optimal sub-generation partitioning problem which limits the number of transmissions required to deliver all packets that belong to each sub- generation.

References

SHOWING 1-10 OF 29 REFERENCES
Coloring Bipartite Hypergraphs
It is NP-Hard to find a proper 2-coloring of a given 2-colorable (bipartite) hypergraph H. We consider algorithms that will color such a hypergraph using few colors in polynomial time. The results of…
Coloring 2-colorable hypergraphs with a sublinear number of colors
TLDR
This paper develops approximation algorithms for the problem of coloring 2-colorable hypergraphs and achieves a sublinear number of colors in polynomial time, and shows that the semidefinite programming approach fails for larger dimensions.
A Still Better Performance Guarantee for Approximate Graph Coloring
On the Hardness of Approximating the Chromatic Number
TLDR
It is NP-hard to find a 4-coloring of a 3-chromatic graph and as an immediate corollary it is obtained that it isNP- hard to color a k- chromatic graph with at most colors.
The Complexity of Generalized Graph Colorings
Approximate graph coloring by semidefinite programming
TLDR
A duality relationship established between the value of the optimum solution to the authors' semidefinite program and the Lovász &thgr;-function is established and lower bounds on the gap between the best known approximation ratio in terms of n are shown.
Approximate graph coloring by semidefinite programming
TLDR
A randomized polynomial time algorithm which colors a 3-colorable graph on n vertices with min {O(/spl Delta//sup 1/3/log/sup 4/3//spl Delta/), O(n/Sup 1/4/ log n)} colors is given, marking the first non-trivial approximation result as a function of the maximum degree /spl Delta/.
Approximate Hypergraph Coloring
TLDR
This work is interested in the problem of coloring 2-colorable hypergraphs, where no hyperedge is monochromatic and the result of Lovasz implies that the problem is NP-hard even if all hyperedges have size three.
Approximating Maximum Independent Sets by Excluding Subgraphs 1
An approximation algorithm for the maximum independent set problem is given, improving the best performance guarantee known to O(n=(logn) 2 ). We also obtain the same performance guarantee for graph…
On the algorithmic complexity of coloring simple hypergraphs and steiner triple systems
TLDR
It is established that decidingt-colorability for a simplek-graph whent≧3,k ≤3 is NP-complete and it is shown that if there is a polynomial time algorithm for finding the chromatic number of a Steiner Triple system then such an algorithm would imply that P=NP.
...
...