Layout Problems on Lattice Graphs

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 the value for the constant in the mentioned theorem. ∗This research was partially supported by ESPRIT LTR Project no. 20244 — ALCOM-IT, CICYT Project TIC97-1475-CE, and CIRIT project 1997SGR-00366. †Departament de Llenguatges i Sistemes Informàtics. Universitat Politècnica de Catalunya. Campus Nord C6. c/ Jordi Girona 1-3. 08034 Barcelona (Spain). {diaz,jpetit,mjserna}@lsi.upc.es ‡Department of Mathematical Sciences, University of Durham, South Road, Durham DH1 3LE, England. [email protected]