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- W2963923487 abstract "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 2k, 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 of Gramm et al. is essentially optimal: we present a polynomial time algorithm that reduces an arbitrary 3-CNF-SAT formula with n variables and m clauses to an equivalent ECC instance (G, k) with k = O(log n) and |V(G)| = O(n + m). Consequently, there is no 22o(k) poly(n) time algorithm for the ECC problem, unless the Exponential Time Hypothesis fails. To the best of our knowledge, these are the first results for a natural, fixed-parameter tractable problem, and proving that a doubly-exponential dependency on the parameter is essentially necessary." @default.
- W2963923487 created "2019-07-30" @default.
- W2963923487 creator A5000479623 @default.
- W2963923487 creator A5037989463 @default.
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- W2963923487 date "2013-01-06" @default.
- W2963923487 modified "2023-09-26" @default.
- W2963923487 title "Known algorithms for edge clique cover are probably optimal" @default.
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- W2963923487 doi "https://doi.org/10.5555/2627817.2627892" @default.
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