Cartesian graph factorization at logarithmic cost per edge Authors F. Aurenhammer Institute for Theoretical Computer Science Technische Universitaet Graz J. Hagauer Institute for Theoretical Computer Science Technische Universitaet Graz W. Imrich Dept. of Mathematics and Applied Geometry Montanuniversitaet Leoben Article

DOI :
10.1007/BF01200428

Cite this article as: Aurenhammer, F., Hagauer, J. & Imrich, W. Comput Complexity (1992) 2: 331. doi:10.1007/BF01200428
Abstract LetG be a connected graph withn vertices andm edges. We develop an algorithm that finds the (unique) prime factors ofG with respect to the Cartesian product inO (m logn ) time andO (m ) space. This shows that factoringG is at most as costly as sorting its edges. The algorithm gains its efficiency and practicality from using only basic properties of product graphs and simple data structures.

Key words Cartesian product graphs Factorization Algorithms

Subject classifications 68Q05C

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