# Known Algorithms for Edge Clique Cover are Probably Optimal

@article{Cygan2016KnownAF,
title={Known Algorithms for Edge Clique Cover are Probably Optimal},
author={Marek Cygan and Marcin Pilipczuk and Michal Pilipczuk},
journal={SIAM J. Comput.},
year={2016},
volume={45},
pages={67-83}
}
• Published 8 March 2012
• Mathematics, Computer Science
• SIAM J. Comput.
In the EDGE CLIQUE COVER (ECC) problem, given a graph G and an integer k, we ask whether the edges of G can be covered with k complete subgraphs of G or, equivalently, whether G admits an intersection model on k-element universe. Gramm et al. [JEA 2008] have shown a set of simple rules that reduce the number of vertices of G to 2^k, and no algorithm is known with significantly better running time bound than a brute-force search on this reduced instance. In this paper we show that the approach…

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