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- Timo Dewenter, Alexander K. Hartmann
- Physical review. E, Statistical, nonlinear, and…
- 2012

We study the vertex-cover problem, which is a nondeterministic polynomial-time hard optimization problem and a prototypical model exhibiting phase transitions on random graphs, such as Erdős-Rényi (ER) random graphs. These phase transitions coincide with changes of the solution space structure, e.g., for the ER ensemble at connectivity c=e≈2.7183 from… (More)

- Timo Dewenter, Gunnar Claussen, Alexander K. Hartmann, Satya N. Majumdar
- Physical review. E
- 2016

We study the polygons governing the convex hull of a point set created by the steps of n independent two-dimensional random walkers. Each such walk consists of T discrete time steps, where x and y increments are independent and identically distributed Gaussian. We analyze area A and perimeter L of the convex hulls. We obtain probability densities for these… (More)

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