Fixed-Parameter Tractability of the Weighted Edge Clique Partition Problem

Authors Andreas Emil Feldmann , Davis Issac , Ashutosh Rai

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Author Details

Andreas Emil Feldmann
  • Department of Applied Mathematics, Charles University, Prague, Czech Republic
Davis Issac
  • Hasso Plattner Institute, Potsdam, Germany
Ashutosh Rai
  • Department of Applied Mathematics, Charles University, Prague, Czech Republic

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Andreas Emil Feldmann, Davis Issac, and Ashutosh Rai. Fixed-Parameter Tractability of the Weighted Edge Clique Partition Problem. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We develop an FPT algorithm and a compression for the Weighted Edge Clique Partition (WECP) problem, where a graph with n vertices and integer edge weights is given together with an integer k, and the aim is to find k cliques, such that every edge appears in exactly as many cliques as its weight. The problem has been previously only studied in the unweighted version called Edge Clique Partition (ECP), where the edges need to be partitioned into k cliques. It was shown that ECP admits a kernel with k² vertices [Mujuni and Rosamond, 2008], but this kernel does not extend to WECP. The previously fastest algorithm known for ECP has a runtime of 2^𝒪(k²)n^O(1) [Issac, 2019]. For WECP we develop a compression (to a slightly more general problem) with 4^k vertices, and an algorithm with runtime 2^𝒪(k^(3/2)w^(1/2)log(k/w))n^O(1), where w is the maximum edge weight. The latter in particular improves the runtime for ECP to 2^𝒪(k^(3/2)log k)n^O(1).

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
  • Edge Clique Partition
  • fixed-parameter tractability
  • kernelization


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