no code implementations • 1 Feb 2023 • Roman Erhardt, Kathrin Hanauer, Nils Kriege, Christian Schulz, Darren Strash
We propose improved exact and heuristic algorithms for solving the maximum weight clique problem, a well-known problem in graph theory with many applications.
1 code implementation • 16 Dec 2016 • Pierre-Louis Giscard, Nils Kriege, Richard C. Wilson
These comparisons show that the algorithm described here is the best general purpose algorithm for the class of graphs where $(\ell^{\omega-1}\Delta^{-1}+1) |S_\ell|\leq |\text{Cycle}_\ell|$, with $|\text{Cycle}_\ell|$ the total number of simple cycles of length at most $\ell$, including backtracks and self-loops.
Data Structures and Algorithms Discrete Mathematics Combinatorics 68Q25, 68W40, 05C30, 05C38, 05C22
no code implementations • 27 Jun 2012 • Nils Kriege, Petra Mutzel
To compute the kernel we propose a graph-theoretical algorithm inspired by a classical relation between common subgraphs of two graphs and cliques in their product graph observed by Levi (1973).