Typical Solution Time for a VertexCovering Algorithm on FiniteConnectivity Random Graphs
Abstract
We analytically describe the typical solution time needed by a backtracking algorithm to solve the vertexcover problem on finiteconnectivity random graphs. We find two different transitions: The first one is algorithm dependent and marks the dynamical transition from linear to exponential solution times. The second one gives the maximum computational complexity, and is found exactly at the threshold where the system undergoes an algorithmindependent phase transition in its solvability. Analytical results are corroborated by numerical simulations.
 Publication:

Physical Review Letters
 Pub Date:
 February 2001
 DOI:
 10.1103/PhysRevLett.86.1658
 arXiv:
 arXiv:condmat/0009417
 Bibcode:
 2001PhRvL..86.1658W
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics;
 Computer Science  Computational Complexity
 EPrint:
 4 pages, 2 figures, to appear in Phys. Rev. Lett