Layout Problems on Lattice Graphs [chapter]

Josep Díaz, Mathew D. Penrose, Jordi Petit, María Serna
1999 Lecture Notes in Computer Science  
This work deals with bounds on the cost of layout problems for lattice graphs and random lattice graphs. Our main result in this paper is a convergence theorem for the optimal cost of the Minimum Linear Arrangement problem and the Minimum Sum Cut problem, for the case where the underlying graph is obtained through a subcritical site percolation process. This result can be viewed as an analogue of the Beardwood, Halton and Hammersley theorem for the Euclidian TSP. Finally we estimate empirically
more » ... the value for the constant in the mentioned theorem. *
doi:10.1007/3-540-48686-0_10 fatcat:dlte6pxzp5ebhip6nfqu3she74