论文信息 - The complexity of the bootstraping percolation and other problems

The complexity of the bootstraping percolation and other problems

We study the problem of predicting the state of a vertex in automata networks, where the state at each site is given by the majority function over its neighborhood. We show that for networks with maximum degree greater than 5 the problem is P-Complete, simulating a monotone Boolean circuit. Then, we show that the problem for networks with no vertex with degree greater than 4 is in NC, giving a fast parallel algorithm. Finally, we apply the result to the study of related problems.

[1] Indranil Gupta,et al. ContagAlert: Using Contagion Theory for Adaptive, Distributed Alert Propagation , 2006, Fifth IEEE International Symposium on Network Computing and Applications (NCA'06).

[2] Martín Matamala,et al. Small Alliances in Graphs , 2007, MFCS.

[3] Joseph JáJá,et al. An Introduction to Parallel Algorithms , 1992 .

[4] H. James Hoover,et al. Limits to Parallel Computation: P-Completeness Theory , 1995 .

[5] Robert A. Meyers. Encyclopedia of Complexity and Systems Science - v. 1-10 , 2009 .

[6] Cristopher Moore. Majority-Vote Cellular Automata, Ising Dynamics, and P-Completeness , 1997 .

[7] J. Balogh,et al. Random disease on the square grid , 1998 .

[8] Cristopher Moore,et al. Life Without Death is P-complete , 1997, Complex Syst..

[9] S. S. Manna. Abelian cascade dynamics in bootstrap percolation , 1998 .

[10] S. Rao Kosaraju,et al. An NC Algorithm for Evaluating Monotone Planar Circuits , 1995, SIAM J. Comput..

[11] Ivan Rapaport,et al. On Dissemination Thresholds in Regular and Irregular Graph Classes , 2009, Algorithmica.

[12] P. Leath,et al. Bootstrap percolation on a Bethe lattice , 1979 .