An Efficient Algorithm for Enumerating Chordless Cycles and Chordless Paths

A chordless cycle (induced cycle) $C$ of a graph is a cycle without any chord, meaning that there is no edge outside the cycle connecting two vertices of the cycle. A chordless path is defined similarly. In this paper, we consider the problems of enumerating chordless cycles/paths of a given graph $G=(V,E),$ and propose algorithms taking $O(|E|)$ time for each chordless cycle/path. In the existing studies, the problems had not been deeply studied in the theoretical computer science area, and no output polynomial time algorithm has been proposed. Our experiments showed that the computation time of our algorithms is constant per chordless cycle/path for non-dense random graphs and real-world graphs. They also show that the number of chordless cycles is much smaller than the number of cycles. We applied the algorithm to prediction of NMR (Nuclear Magnetic Resonance) spectra, and increased the accuracy of the prediction

Compactly generating all satisfying truth assignments of a Horn formula

As instance of an overarching principle of exclusion an algorithm is presented that compactly (thus not one by one) generates all models of a Horn formula. The principle of exclusion can be adapted to generate only the models of weight $k$. We compare and contrast it with constraint programming, $0,1$ integer programming, and binary decision diagrams.Comment: Considerably improves upon the readibility of the previous versio

On the use of generating functions for topics in clustered networks

In this thesis we relax the locally tree-like assumption of configuration model random networks to examine the properties of clustering, and the effects thereof, on bond percolation. We introduce an algorithmic enumeration method to evaluate the probability that a vertex remains unattached to the giant connected component during percolation. The properties of the non-giant, finite components of clustered networks are also examined, along with the degree correlations between subgraphs. In a second avenue of research, we investigate the role of clustering on 2-strain epidemic processes under various disease interaction schedules. We then examine an -generation epidemic by performing repeated percolation events

Generating all cycles, chordless cycles, and Hamiltonian cycles with the principle of exclusion

Please help us populate SUNScholar with the post print version of this article. It can be e-mailed to: [email protected]